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1
Pethiyagoda, Ravindra, Scott W. McCue, and Timothy J. Moroney. "What is the apparent angle of a Kelvin ship wave pattern?" Journal of Fluid Mechanics 758 (October 9, 2014): 468–85. http://dx.doi.org/10.1017/jfm.2014.530.
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AbstractWhile the half-angle which encloses a Kelvin ship wave pattern is commonly accepted to be 19.47°, recent observations and calculations for sufficiently fast-moving ships suggest that the apparent wake angle decreases with ship speed. One explanation for this decrease in angle relies on the assumption that a ship cannot generate wavelengths much greater than its hull length. An alternative interpretation is that the wave pattern that is observed in practice is defined by the location of the highest peaks; for wakes created by sufficiently fast-moving objects, these highest peaks no longer lie on the outermost divergent waves, resulting in a smaller apparent angle. In this paper, we focus on the problems of free-surface flow past a single submerged point source and past a submerged source doublet. In the linear version of these problems, we measure the apparent wake angle formed by the highest peaks, and observe the following three regimes: a small Froude number pattern, in which the divergent waves are not visible; standard wave patterns for which the maximum peaks occur on the outermost divergent waves; and a third regime in which the highest peaks form a V-shape with an angle much less than the Kelvin angle. For nonlinear flows, we demonstrate that nonlinearity has the effect of increasing the apparent wake angle so that some highly nonlinear solutions have apparent wake angles that are greater than Kelvin’s angle. For large Froude numbers, the effect on apparent wake angle can be more dramatic, with the possibility of strong nonlinearity shifting the wave pattern from the third regime to the second. We expect that our nonlinear results will translate to other more complicated flow configurations, such as flow due to a steadily moving closed body such as a submarine.
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Liang, Hui, and Xiaobo Chen. "Viscous effects on the fundamental solution to ship waves." Journal of Fluid Mechanics 879 (October 1, 2019): 744–74. http://dx.doi.org/10.1017/jfm.2019.698.
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The fundamental solution to steady ship waves accounting for viscous effects (the viscous-ship-wave Green function) is investigated within the framework of the weakly damped free-surface flow theory. An explicit expression of the viscous-ship-wave Green function is firstly derived, and an accurate and efficient technique is described to evaluate the Green function via decomposing the free-surface term into the local-flow component and wave component. To delve into the physical features of the viscous-ship-wave Green function, the asymptotic approximations in the far field due to Kelvin, Havelock and Peters are presented for the flow-field point located inside, at and outside the Kelvin wedge. In addition, uniform approximations to the wave component based on the Chester–Friedman–Ursell (CFU) approximation and the Kelvin–Havelock–Peters (KHP) approximation are carried out. Both numerical evaluation and asymptotic approximations show that the singular behaviour is eliminated and the divergent waves associated with large wavenumbers leading to rapid oscillations are severely damped when viscous effects are accounted for. In addition, viscous effects also alter the apparent wake angle associated with the wave pattern created by a high-speed translating source, and the apparent wake angle is dependent on both $\mathscr{U}^{-1}$ and $\mathscr{U}^{-2}$, where $\mathscr{U}$ is the translating speed of the source.
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Fang, M. C., R. Y. Yang, and I. V. Shugan. "Kelvin Ship Wake in the Wind Waves Field and on the Finite Sea Depth." Journal of Mechanics 27, no. 1 (March 2011): 71–77. http://dx.doi.org/10.1017/jmech.2011.9.
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ABSTRACTA kinematics model of the ship wake in the presence of surface waves, generated by wind is presented. It was found that the stationary wave structure behind the ship covered a wedge region with the 16.9° half an angle at the top of the wake and only divergent waves are present in a ship wake for co propagating wind waves. Wind waves field directed at some nonzero angle to the ship motion can cause essential asymmetry of the wake and compressing of its windward half. The extension of Whitham-Lighthill kinematics theory of ship wake for the intermediate sea depth is also presented. The ship wake structure essentially depends from the Froude (Fr) number based on the value of the sea depth and ship velocity. For Froude number less than unit both longitudinal and cross waves are presented in the wake region and Kelvin wake angle increased with Fr. For Fr > 1 wake angle decreased with Froude number and finally only divergent waves are presented in the very narrow ship wake.
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ZHU, QIANG, YUMING LIU, and DICK K. P. YUE. "Resonant interactions between Kelvin ship waves and ambient waves." Journal of Fluid Mechanics 597 (February 1, 2008): 171–97. http://dx.doi.org/10.1017/s002211200700969x.
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We consider the nonlinear interactions between the steady Kelvin waves behind an advancing ship and an (unsteady) ambient wave. It is shown that, for moderately steep ship waves and/or ambient waves, third-order (quartet) resonant interaction among the two wave systems could occur, leading to the generation of a new propagating wave along a specific ray in the Kelvin wake. The wave vector of the generated wave as well as the angle of the resonance ray are determined by the resonance condition and are functions of the ship forward speed and the wave vector of the ambient wave. To understand the resonance mechanism and the characteristics of the generated wave, we perform theoretical analyses of this problem using two related approaches. To obtain a relatively simple model in the form of a nonlinear Schrödinger (NLS) equation for the evolution of the resonant wave, we first consider a multiple-scale approach assuming locally discrete Kelvin wave components, with constant wave vectors but varying amplitudes along the resonance ray. This NLS model captures the key resonance mechanism but does not account for the detuning effect associated with the wave vector variation of Kevin waves in the neighbourhood of the resonance ray. To obtain the full quantitative features and evolution characteristics, we also consider a more complete model based on Zakharov's integral equation applied in the context of a continuous wave vector spectrum. The resulting evolution equation can be reduced to an NLS form with, however, cross-ray variable coefficients, on imposing a narrow-band assumption valid in the neighbourhood of the resonance ray. As expected, the two models compare well when wave vector detuning is small, in the near wake close to the ray. To verify the analyses, direct high-resolution simulations of the nonlinear wave interaction problem are obtained using a high-order spectral method. The simulations capture the salient features of the resonance in the near wake of the ship, with good agreements with theory for the location of the resonance and the growth rate of the generated wave.
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THIEBAUT, S., and R. VENNELL. "Resonance of long waves generated by storms obliquely crossing shelf topography in a rotating ocean." Journal of Fluid Mechanics 682 (July 7, 2011): 261–88. http://dx.doi.org/10.1017/jfm.2011.221.
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The oceanic forced wave beneath a moving atmospheric disturbance is amplified by Proudman resonance. When modified by the Earth's rotation this classical resonance only occurs if the disturbance time scale is smaller than the inertial period. With or without Coriolis effects, free transients generated by storm forced waves obliquely crossing step changes in water depth at particular angles are shown to resonate by exciting a range of long barotropic free waves. Rotationally influenced slow atmospherically forced waves crossing a vertical coast at a critical angle lead to a form of subcritical resonance, which occurs only when the component of the disturbances' phase velocities along the coast matches that of a free Kelvin wave (KW). In a rotating ocean, transients generated by disturbances crossing a step at a particular angle are shown to excite a free double Kelvin wave (DKW). This new type of resonance only occurs for sufficiently large steps and disturbances with time scale greater than the inertial period. A storm crossing a step shelf can result in the excitation of an infinite set of edge waves, a single KW, a unique DKW and a first-mode continental shelf wave, depending on the topography and the disturbance time scale, translation speed and incident angle. The study of resonances and wave mode excitations generated by storms crossing a coast or a continental shelf may contribute to understanding how a particular combination of the storm characteristics can result in destructive coastal events with time scales encompassing the typical meteotsunami period band (tens of minutes) and storm surges with periods of several hours or days.
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Gnevyshev, Vladimir, and Sergei Badulin. "Wave Patterns of Gravity–Capillary Waves from Moving Localized Sources." Fluids 5, no. 4 (November 24, 2020): 219. http://dx.doi.org/10.3390/fluids5040219.
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We study wave patterns of gravity–capillary waves from moving localized sources within the classic setup of the problem of ship wakes. The focus is on the co-existence of two wave systems with opposite signatures of group velocity relative to the localized source. It leads to the problem of choice of signs for phase functions of the gravity (“slow”) and capillary (“fast”) branches of the dispersion relation: the question generally ignored when constructing phase patterns of the solutions. We detail characteristic angles of the wake patterns: (i) angle of demarcation of gravity and capillary waves—“the phase Mach” cone, (ii) angle of the minimal group velocity of gravity–capillary waves—“the group Mach” cone, (iii, iv) angles of cusps of isophases that appear after a threshold current speed. The outer cusp cone is naturally associated with the classic cone of Kelvin for pure gravity waves. The inner one results from the effect of capillarity and tends to the “group Mach” pattern at high speeds of current. Amplitudes of the wave patterns are estimated within the recently proposed approach of reference functions for the problem of propagation of packets of linear dispersive waves. The effect of shape is discussed for elliptic reference sources.
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Tings, Björn. "Non-Linear Modeling of Detectability of Ship Wake Components in Dependency to Influencing Parameters Using Spaceborne X-Band SAR." Remote Sensing 13, no. 2 (January 6, 2021): 165. http://dx.doi.org/10.3390/rs13020165.
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The detection of the wakes of moving ships in Synthetic Aperture Radar (SAR) imagery requires the presence of wake signatures, which are sufficiently distinctive from the ocean background. Various wake components exist, which constitute the SAR signatures of ship wakes. For successful wake detection, the contrast between the detectable wake components and the background is crucial. The detectability of those wake components is affected by a number of parameters, which represent the image acquisition settings, environmental conditions or ship properties including voyage information. In this study the dependency of the detectability of individual wake components to these parameters is characterized. For each wake component a detectability model is built, which takes the influence of incidence angle, polarization, wind speed, wind direction, sea state (significant wave height, wavelength, wave direction), vessel’s velocity, vessel’s course over ground and vessel’s length into account. The presented detectability models are based on regression or classification using Support Vector Machines and a dataset of manually labelled TerraSAR‑X wake samples. The considered wake components are: near‑hull turbulences, turbulent wakes, Kelvin wake arms, Kelvin wake’s transverse waves, Kelvin wake’s divergent waves, V‑narrow wakes and ship‑generated internal waves. The statements derived about wake component detectability are mainly in good agreement with statements from previous research, but also some new assumptions are provided. The most expressive influencing parameter is the movement velocity of the vessels, as all wake components are more detectable the faster vessels move.
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Zilman, Gregory, and Touvia Miloh. "Kelvin and V-like Ship Wakes Affected by Surfactants." Journal of Ship Research 45, no. 02 (June 1, 2001): 150–63. http://dx.doi.org/10.5957/jsr.2001.45.2.150.
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Synthetic aperture radar (SAR) ship wake images in light wind and calm sea conditions frequently appear in the form of a bright V with a half-angle of 2 to 3 deg. Sophisticated and conflicting explanations of this phenomenon, based on the Bragg scattering mechanism, have been proposed. There is a belief that the narrow V-wake is not a part of the Kelvin wake. An alternative approach, which is not generally accepted, suggests that short divergent Kelvin waves may contribute to the V-wake imaging although these waves are mixed with unsteady surface waves generated by the ship-induced turbulence. Ship-generated divergent waves contaminated by surfactants and their radar backscattering cross section are studied. The hull of the ship is represented by a single layer of hydrodynamic singularities. The Green function of a point source moving below a free surface covered by surfactants is derived. A closed-form asymptotic solution for the far ship wave wake is obtained. It is used to calculate analytically the corresponding radar backscattering cross section. The radiative, viscous, and surfactant-induced decay of the V-wake brightness along the V-arms is discussed. The theoretical results are compared against available experimental data.
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Бимбереков, Павел, and Pavel Bimberekov. "GRAPHICAL ANALYSIS OF FREE-SURFACE WAVE FIELDS FROM MOVING SHIPS AND A PAIR OF CONSECUTIVE POSTS." Vestnik of Astrakhan State Technical University. Series: Marine engineering and technologies 2019, no. 4 (November 15, 2019): 7–22. http://dx.doi.org/10.24143/2073-1574-2019-4-7-22.
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The paper presents a comparison of the photographic material of the wave patterns resulted from the movement of a ship in situ and a model ship, as well as from two consecutive posts, their regularities being found through graphical processing. The possibility to find the fore imaginary source of Kelvin wave pattern forming the ship's wave system is given at a distance
of one wavelength before the top of the bow retaining wave. The equality of the length of trans-verse waves and divergent waves along the outer boundaries of the latter zone is fixed. It has been assumed that the intermediate waves generated between the main waves in the model ship and the posts are regular, imposition of wave patterns in a pair of consistently moving racks depending on the hit of the rear rack in the wave field of the first rack has been stated. Regularly occurring flows around moving posts are discussed. The bow and stern system of Kelvin waves in a ship wave sys-tem has been illustrated (the angle of the midpoint of diverging wave crests with the ship’s diamet-rical plane and the angle of diverging wave crests with the ship’s diametrical plane). The photo-graphs presented were taken in the experimental tank of Siberian State University of Water Transport (Novosibirsk State Academy of Water Transport) in 2006. A thin film naturally generat-ed on the water surface of the experimental tank and given a structure directed along the tank due to previous runs helped to visualize the distortion of the free water surface in better quality and to obtain clearly outlined contours in lighting.
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ROOS, P. C., and H. M. SCHUTTELAARS. "Horizontally viscous effects in a tidal basin: extending Taylor's problem." Journal of Fluid Mechanics 640 (October 27, 2009): 421–39. http://dx.doi.org/10.1017/s0022112009991327.
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The classical problem of Taylor (Proc. Lond. Math. Soc., vol. 20, 1921, pp. 148–181) of Kelvin wave reflection in a semi-enclosed rectangular basin of uniform depth is extended to account for horizontally viscous effects. To this end, we add horizontally viscous terms to the hydrodynamic model (linearized depth-averaged shallow-water equations on a rotating plane, including bottom friction) and introduce a no-slip condition at the closed boundaries.In a straight channel of infinite length, we obtain three types of wave solutions (normal modes). The first two wave types are viscous Kelvin and Poincaré modes. Compared to their inviscid counterparts, they display longitudinal boundary layers and a slight decrease in the characteristic length scales (wavelength or along-channel decay distance). For each viscous Poincaré mode, we additionally find a new mode with a nearly similar lateral structure. This third type, entirely due to viscous effects, represents evanescent waves with an along-channel decay distance bounded by the boundary-layer thickness.The solution to the viscous Taylor problem is then written as a superposition of these normal modes: an incoming Kelvin wave and a truncated sum of reflected modes. To satisfy no slip at the lateral boundary, we apply a Galerkin method. The solution displays boundary layers, the lateral one at the basin's closed end being created by the (new) modes of the third type. Amphidromic points, in the inviscid and frictionless case located on the centreline of the basin, are now found on a line making a small angle to the longitudinal direction. Using parameter values representative for the Southern Bight of the North Sea, we finally compare the modelled and observed tide propagation in this basin.
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Dorofeev, V. L. "Diffraction of a long Kelvin wave at the apex angle formed by intersecting shores." Physical Oceanography 7, no. 2 (March 1996): 79–89. http://dx.doi.org/10.1007/bf02509812.
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Masunaga, Eiji, Oliver B. Fringer, Yujiro Kitade, Hidekatsu Yamazaki, and Scott M. Gallager. "Dynamics and Energetics of Trapped Diurnal Internal Kelvin Waves around a Midlatitude Island." Journal of Physical Oceanography 47, no. 10 (October 2017): 2479–98. http://dx.doi.org/10.1175/jpo-d-16-0167.1.
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AbstractThe generation of trapped and radiating internal tides around Izu‐Oshima Island located off Sagami Bay, Japan, is investigated using the three-dimensional Stanford Unstructured Nonhydrostatic Terrain-following Adaptive Navier–Stokes Simulator (SUNTANS) that is validated with observations of isotherm displacements in shallow water. The model is forced by barotropic tides, which generate strong baroclinic internal tides in the study region. Model results showed that when diurnal K1 barotropic tides dominate, resonance of a trapped internal Kelvin wave leads to large-amplitude internal tides in shallow waters on the coast. This resonance produces diurnal motions that are much stronger than the semidiurnal motions. The weaker, freely propagating, semidiurnal internal tides are generated on the western side of the island, where the M2 internal tide beam angle matches the topographic slope. The internal wave energy flux due to the diurnal internal tides is much higher than that of the semidiurnal tides in the study region. Although the diurnal internal tide energy is trapped, this study shows that steepening of the Kelvin waves produces high-frequency internal tides that radiate from the island, thus acting as a mechanism to extract energy from the diurnal motions.
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Bimberekov, Pavel. "Graphical analysis of free-surface wave fields from moving two consecutive posts connected by thin plate." Vestnik of Astrakhan State Technical University. Series: Marine engineering and technologies 2020, no. 1 (February 17, 2020): 45–53. http://dx.doi.org/10.24143/2073-1574-2020-1-45-53.
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The article presents photographic materials of wave pictures from two consecutive posts of teardrop cross-section and the same posts with a thin plate installed between them, which introduces into consideration not only separate sequentially moving sources, but also reunites them into a single object, interacting along its entire length with the system of waves from the first source. The regularities of the wave field of consecutive posts with a plate in-stalled between them by means of graphic processing are considered. The possibility of finding the front imaginary source of the Kelvin wave pattern forming the ship's wave system at the position of both one and two wave-lengths in front of the top of the bow retaining wave is estimated. A method is proposed for determining the position of the fictitious location of the aft Kelvin wave system of the ship's wave system based on the results of the analysis of the wave field at the characteristic speeds
of movement, leading to the most successfully fixed inter-location of the wave pattern from the bow and aft extremities. There are shown the pictures of moving forward a pair of posts with
a blunt end of a horizontal section at the same speed and photo fixation from a close angle, pictures of moving forward the posts with a plate between them with a blunt end of a teardrop-shaped cross section at a low speed, moving forward posts with a plate at the side with a sharp end of a teardrop-shaped cross section, etc. All presented photographs were taken in the experimental pool of the Siberian state University of water transport (Novosibirsk state Academy of water transport) in 2006.
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Alshoufi, Hajar. "KdV Equation Model in Open Cylindrical Channel under Precession." Journal of Nonlinear Mathematical Physics 28, no. 4 (September 20, 2021): 466–91. http://dx.doi.org/10.1007/s44198-021-00007-8.
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AbstractA new model for Korteweg and de-Vries equation (KdV) is derived. The system under study is an open channel consisting of two concentric cylinders, rotating about their vertical axis, which is tilted by slope $$\tau$$ τ from the inertial vertical $$z$$ z , in uniform rate $${\Omega }_{1}=\tau \Omega$$ Ω 1 = τ Ω , and the whole tank is elevated over other table rotating at rate $$\Omega$$ Ω . Under these conditions, a set of Kelvin waves is formed on the free surface depending on the angle of tilt, characterized by the slope $$\tau$$ τ , volume of water, and rotation rate. The resonant mode in the system appears in the form of a single Kelvin solitary wave, whose amplitude satisfies the Korteweg-de Vries equation with forced term. The equation was derived following classical perturbation methods, the additional term made the equation a non-integrable one, that cannot be solved without the help of numerical methods. Invoking the simple finite difference scheme method, it was found that the numerical results are in a good agreement with the experiment.
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Renouard, Dominique P. "Experimental study of the reflection of an internal solitary Kelvin wave in a right-angle corner." Continental Shelf Research 15, no. 7 (June 1995): 871–82. http://dx.doi.org/10.1016/0278-4343(94)e0033-i.
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Sulistyawati, W., _. Yanuar, and A. S. Pamitran. "Michell Investigation of the Significant Influence on the Hydrodynamic of a Warp-Chine Pentamaran." Journal of Ship Production and Design 36, no. 03 (August 17, 2020): 202–12. http://dx.doi.org/10.5957/jspd.02190011.
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This study attempted to investigate the hydrodynamic performance of various pentamaran configurations with a focus on the interference flow around the component hulls. A computer simulation was conducted based on Michell’s thin ship theory alongside a commercial CFD computation as a comparison. Experiments in the towing tank were performed to validate the numerical calculations, resulting in some hydrodynamic characteristics on the far-field wave pattern, wave interference, wave resistance, and total resistance. Analyses on both transversal and divergent waves were performed to assess the magnitude of wave resistance occurring due to the placement of the side hull to the main hull. Analyses on both waves were also conducted to assess the magnitude of wave resistance due to the placement of outriggers. Looking at the results, numerical calculations based on Michell’s theory were in parallel with experimental data, particularly at Fn greater than .4. Michell’s theory was observed as doing a little preferable agreement with the results of experiments than CFD. Besides, flow patterns obtained numerically from Michell’s and CFD analyses appeared as identical to photographs observed in a towing tank. This investigation identified that a configuration with aligning placement of the main to side hull on the formation of arrow tri-hull, near the Kelvin angle, would cancel the wave formed by the leading hull and can be used as a practical setting to reduce the total wave resistance.
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Terziev, Momchil, Guangwei Zhao, Tahsin Tezdogan, Zhiming Yuan, and Atilla Incecik. "Virtual Replica of a Towing Tank Experiment to Determine the Kelvin Half-Angle of a Ship in Restricted Water." Journal of Marine Science and Engineering 8, no. 4 (April 6, 2020): 258. http://dx.doi.org/10.3390/jmse8040258.
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The numerical simulation of ship flows has evolved into a highly practical approach in naval architecture. In typical virtual towing tanks, the principle of Galilean relativity is invoked to maintain the ship as fixed, while the surrounding water is prescribed to flow past it. This assumption may be identified, at least partly, as being responsible for the wide-scale adoption of computational solutions within practitioners’ toolkits. However, it carries several assumptions, such as the levels of inlet turbulence and their effect on flow properties. This study presents an alternative virtual towing tank, where the ship is simulated to advance over a stationary fluid. To supplement the present work, the free surface disturbance is processed into Fourier space to determine the Kelvin half-angle for an example case. The results suggest that it is possible to construct a fully unsteady virtual towing tank using the overset method, without relying on Galilean relativity. Differences between theoretical and numerical predictions for the Kelvin half-angle are predominantly attributed to the assumptions used by the theoretical method. The methods presented in this work can potentially be used to validate free-surface flows, even when one does not have access to experimental wave elevation data.
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Wang, Huiqun, and Gonzalo González Abad. "Cloud Masks Derived from the Mars Daily Global Maps and an Application to the Tropical Cloud Belt on Mars." Geosciences 11, no. 8 (July 31, 2021): 324. http://dx.doi.org/10.3390/geosciences11080324.
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An image processing technique is used to derive cloud masks from the color Mars Daily Global Maps (MDGMs) that are composed from the Mars Reconnaissance Orbiter (MRO) Mars Color Imager (MARCI) wide-angle image swaths. The blue channel of each MDGM is used to select cloud candidates and the blue-to-red ratio map is compared with a reference ratio map to filter out false positives. Quality control is performed manually. The derived cloud masks cover 1 Mars year from the summer of Mars year (MY) 28 to the summer of MY 29. The product has a 0.1° longitude by 0.1° latitude resolution and is available each day. This makes it possible to characterize the evolution of the tropical cloud belt from several new perspectives. The tropical cloud belt steadily builds up during northern spring and early summer, peaks near the early- to mid-summer transitional period, and rapidly declines afterward. From the perspective of cloud occurrence frequency and time mean, the cloud belt appears meandrous and zonally discontinuous, with minima in the Amazonis Planitia and Arabia Terra longitudinal sectors. A pronounced cloud branch diverges from the main cloud belt and extends from the Valles Marineris towards the Noachis and Hellas region. The cloud belt exhibits noticeable oscillatory behavior whereby cloud brightening alternates between the western and eastern hemispheres near the equator with a periodicity between 20 and 30 sols. The cloud belt oscillation occurred each Mars year around Ls = 140°, except for the Mars years when intense dust storms made disruptions. The phenomenon appears to be associated with an eastward propagating equatorial Kelvin wave with zonal wavenumber 1. This wave has a much longer wave period than the diurnal and semidiurnal Kelvin waves discussed in most of the previous studies and may be an important factor for the intra-seasonal variability of the tropical cloud belt. The convolution of clouds’ local time variation with MRO’s orbit shift pattern results in a seemingly highly regular 5-day traveling wave in Hovmöller diagrams of cloud masks.
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He, W., R. S. Gioria, J. M. Pérez, and V. Theofilis. "Linear instability of low Reynolds number massively separated flow around three NACA airfoils." Journal of Fluid Mechanics 811 (December 15, 2016): 701–41. http://dx.doi.org/10.1017/jfm.2016.778.
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Two- and three-dimensional modal and non-modal instability mechanisms of steady spanwise-homogeneous laminar separated flow over airfoil profiles, placed at large angles of attack against the oncoming flow, have been investigated using global linear stability theory. Three NACA profiles of distinct thickness and camber were considered in order to assess geometry effects on the laminar–turbulent transition paths discussed. At the conditions investigated, large-scale steady separation occurs, such that Tollmien–Schlichting and cross-flow mechanisms have not been considered. It has been found that the leading modal instability on all three airfoils is that associated with the Kelvin–Helmholtz mechanism, taking the form of the eigenmodes known from analysis of generic bluff bodies. The three-dimensional stationary eigenmode of the two-dimensional laminar separation bubble, associated in earlier analyses with the formation on the airfoil surface of large-scale separation patterns akin to stall cells, is shown to be more strongly damped than the Kelvin–Helmholtz mode at all conditions examined. Non-modal instability analysis reveals the potential of the flows considered to sustain transient growth which becomes stronger with increasing angle of attack and Reynolds number. Optimal initial conditions have been computed and found to be analogous to those on a cascade of low pressure turbine blades. By changing the time horizon of the analysis, these linear optimal initial conditions have been found to evolve into the Kelvin–Helmholtz mode. The time-periodic base flows ensuing linear amplification of the Kelvin–Helmholtz mode have been analysed via temporal Floquet theory. Two amplified modes have been discovered, having characteristic spanwise wavelengths of approximately 0.6 and 2 chord lengths, respectively. Unlike secondary instabilities on the circular cylinder, three-dimensional short-wavelength perturbations are the first to become linearly unstable on all airfoils. Long-wavelength perturbations are quasi-periodic, standing or travelling-wave perturbations that also become unstable as the Reynolds number is further increased. The dominant short-wavelength instability gives rise to spanwise periodic wall-shear patterns, akin to the separation cells encountered on airfoils at low angles of attack and the stall cells found in flight at conditions close to stall. Thickness and camber have quantitative but not qualitative effect on the secondary instability analysis results obtained.
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Teixeira, Miguel A. C., Alexandre Paci, and Anne Belleudy. "Drag Produced by Waves Trapped at a Density Interface in Nonhydrostatic Flow over an Axisymmetric Hill." Journal of the Atmospheric Sciences 74, no. 6 (May 17, 2017): 1839–57. http://dx.doi.org/10.1175/jas-d-16-0199.1.
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Abstract Linear nonhydrostatic theory is used to evaluate the drag produced by 3D trapped lee waves forced by an axisymmetric hill at a density interface. These waves occur at atmospheric temperature inversions, for example, at the top of the boundary layer, and contribute to low-level drag possibly misrepresented as turbulent form drag in large-scale numerical models. Unlike in 2D waves, the drag has contributions from a continuous range of wavenumbers forced by the topography, because the waves can vary their angle of incidence to match the resonance condition. This leads to nonzero drag for Froude numbers (Fr) both <1 and >1 and a drag maximum typically for Fr slightly below 1, with lower magnitude than in hydrostatic conditions owing to wave dispersion. These features are in good agreement with laboratory experiments using two axisymmetric obstacles, particularly for the lower obstacle, if the effects of a rigid lid above the upper layer and friction are taken into account. Quantitative agreement is less satisfactory for the higher obstacle, as flow nonlinearity increases. However, even in that case the model still largely outperforms both 3D hydrostatic and 2D nonhydrostatic theories, emphasizing the importance of both 3D and nonhydrostatic effects. The associated wave signatures are dominated by transverse waves for Fr lower than at the drag maximum, a dispersive “Kelvin ship-wave” pattern near the maximum, and divergent waves for Fr beyond the maximum. The minimum elevation at the density-interface depression existing immediately downstream of the obstacle is significantly correlated with the drag magnitude.
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PHAM, HIEU T., SUTANU SARKAR, and KYLE A. BRUCKER. "Dynamics of a stratified shear layer above a region of uniform stratification." Journal of Fluid Mechanics 630 (July 10, 2009): 191–223. http://dx.doi.org/10.1017/s0022112009006478.
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Direct numerical simulations (DNS) are performed to investigate the behaviour of a weakly stratified shear layer in the presence of a strongly stratified region beneath it. Both, coherent Kelvin–Helmholtz (KH) rollers and small-scale turbulence, are observed during the evolution of the shear layer. The deep stratification measured by the Richardson number Jd is varied to study its effect on the dynamics. In all cases, a pycnocline is found to develop at the edges of the shear layer. The region of maximum shear shifts downward with increasing time. Internal waves are excited, initially by KH rollers, and later by small-scale turbulence. The wave field generated by the KH rollers is narrowband and of stronger amplitude than the broadband wave field generated by turbulence. Linear theory based on Doppler-shifted frequency of the KH mode is able to predict the angle of the internal wave phase lines during the direct generation of internal waves by KH rollers. Waves generated by turbulence are relatively weaker with a broader range of excitation angles which, in the deep region, tend towards a narrower band. The linear theory that works for the internal waves excited by KH rollers does not work for the turbulence generated waves. The momentum transported by the internal waves into the interior can be large, about 10% of the initial momentum in the shear layer, when Jd ≃ 0.25. Integration of the turbulent kinetic energy budget in time and over the shear layer thickness shows that the energy flux can be up to 17% of the turbulent production, 33% of the turbulent dissipation rate and 75% of the buoyancy flux. These numbers quantify the dynamical importance of internal waves. In contrast to linear theory where the effect of deep stratification on the shear layer instabilities has been found to be weak, the present nonlinear simulations show that the evolution of the shear layer is significantly altered because of the significant momentum and energy carried away by the internal waves.
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Sembian, S., M. Liverts, and N. Apazidis. "Plane blast wave interaction with an elongated straight and inclined heat-generated inhomogeneity." Journal of Fluid Mechanics 851 (July 19, 2018): 245–67. http://dx.doi.org/10.1017/jfm.2018.495.
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The unstable evolution of an elongated elliptically shaped inhomogeneity that is embedded in ambient air and aligned both normal and at an angle to an incident plane blast wave of impact Mach number 2.15 is investigated both experimentally and numerically. The elliptic inhomogeneities and the blast waves are generated using gas heating and exploding wire technique and their interaction is captured optically using shadowgraph method. While two symmetric counter-rotating vortices due to Richtmyer–Meshkov instability are observed for the straight interaction, the formation of a train of vortices similar to Kelvin–Helmholtz instability, introducing asymmetry into the flow field, are observed for an inclined interaction. During the early phase of the interaction process in the straight case, the growth of the counter-rotating vortices (based on the sequence of images obtained from the high-speed camera) and circulation (calculated with the aid of numerical data) are found to be linear in both space and time. Moreover, the normalized circulation is independent of the inhomogeneity density and the ellipse thickness, enabling the formulation of a unique linear fit equation. Conversely, the circulation for an inclined case follows a quadratic function, with each vortex in the train estimated to move with a different velocity directly related to its size at that instant. Two factors influencing the quadratic nature are identified: the reduction in strength of the transmitted shock thereby generating vortices with reduced vorticity, along with the gradual loss of vorticity of the earlier-generated vortices.
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Hannawald, Patrick, Carsten Schmidt, Sabine Wüst, and Michael Bittner. "A fast SWIR imager for observations of transient features in OH airglow." Atmospheric Measurement Techniques 9, no. 4 (April 4, 2016): 1461–72. http://dx.doi.org/10.5194/amt-9-1461-2016.
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Abstract. Since December 2013 the new imaging system FAIM (Fast Airglow IMager) for the study of smaller-scale features (both in space and time) is in routine operation at the NDMC (Network for the Detection of Mesospheric Change) station at DLR (German Aerospace Center) in Oberpfaffenhofen (48.1° N, 11.3° E).Covering the brightest OH vibrational bands between 1 and 1.7 µm, this imaging system can acquire two frames per second. The field of view is approximately 55 km times 60 km at the mesopause heights. A mean spatial resolution of 200 m at a zenith angle of 45° and up to 120 m for zenith conditions are achieved. The observations show a large variety of atmospheric waves.This paper introduces the instrument and compares the FAIM data with spectrally resolved GRIPS (GRound-based Infrared P-branch Spectrometer) data. In addition, a case study of a breaking gravity wave event, which we assume to be associated with Kelvin–Helmholtz instabilities, is discussed.
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Marques, Francisco, and Juan M. Lopez. "Precession of a rapidly rotating cylinder flow: traverse through resonance." Journal of Fluid Mechanics 782 (October 6, 2015): 63–98. http://dx.doi.org/10.1017/jfm.2015.524.
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Recent experiments using a rapidly rotating and precessing cylinder have shown that for specific values of the precession rate, aspect ratio and tilt angle, sudden catastrophic transitions to turbulence occur. Even if the precessional forcing is not too strong, there can be intermittent recurrences between a laminar state and small-scale chaotic flow. The inviscid linearized Navier–Stokes equations have inertial-wave solutions called Kelvin eigenmodes. The precession forces the flow to have azimuthal wavenumber $m=1$ (spin-over mode). Depending on the cylinder aspect ratio and on the ratio of the rotating and precessing frequencies, additional Kelvin modes can be in resonance with the spin-over mode. This resonant flow would grow unbounded if not for the presence of viscous and nonlinear effects. In practice, one observes a rapid transition to turbulence, and the precise nature of the transition is not entirely clear. When both the precessional forcing and viscous effects are small, weakly nonlinear models and experimental observations suggest that triadic resonance is at play. Here, we used direct numerical simulations of the full Navier–Stokes equations in a narrow region of parameter space where triadic resonance has been previously predicted from a weakly nonlinear model and observed experimentally. The detailed parametric studies enabled by the numerics reveal the complex dynamics associated with weak precessional forcing, involving symmetry-breaking, hysteresis and heteroclinic cycles between states that are quasiperiodic, with two or three independent frequencies. The detailed analysis of these states leads to associations of physical mechanisms with the various time scales involved.
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Zauner, Markus, and Neil D. Sandham. "Modal Analysis of a Laminar-Flow Airfoil under Buffet Conditions at Re = 500,000." Flow, Turbulence and Combustion 104, no. 2-3 (December 3, 2019): 509–32. http://dx.doi.org/10.1007/s10494-019-00087-z.
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AbstractAn airfoil undergoing transonic buffet exhibits a complex combination of unsteady shock-wave and boundary-layer phenomena, for which prediction models are deficient. Recent approaches applying computational fluid mechanics methods using turbulence models seem promising, but are still unable to answer some fundamental questions on the detailed buffet mechanism. The present contribution is based on direct numerical simulations of a laminar flow airfoil undergoing transonic buffet at Mach number M = 0.7 and a moderate Reynolds number Re = 500, 000. At an angle of attack α = 4∘, a significant change of the boundary layer stability depending on the aerodynamic load of the airfoil is observed. Besides Kelvin Helmholtz instabilities, a global mode, showing the coupled acoustic and flow-separation dynamics, can be identified, in agreement with literature. These modes are also present in a dynamic mode decomposition (DMD) of the unsteady direct numerical solution. Furthermore, DMD picks up the buffet mode at a Strouhal number of St = 0.12 that agrees with experiments. The reconstruction of the flow fluctuations was found to be more complete and robust with the DMD analysis, compared to the global stability analysis of the mean flow. Raising the angle of attack from α = 3∘ to α = 4∘ leads to an increase in strength of DMD modes corresponding to type C shock motion. An important observation is that, in the present example, transonic buffet is not directly coupled with the shock motion.
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NICHOLS, JOSEPH W., and SANJIVA K. LELE. "Global modes and transient response of a cold supersonic jet." Journal of Fluid Mechanics 669 (January 31, 2011): 225–41. http://dx.doi.org/10.1017/s0022112010005380.
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Global-mode analysis is applied to a cold, M = 2.5 laminar jet. Global modes of the non-parallel jet capture directly both near-field dynamics and far-field acoustics which, in this case, are coupled by Mach wave radiation. In addition to type (a) modes corresponding to Kelvin–Helmholtz instability, it is found that the jet also supports upstream-propagating type (b) modes which could not be resolved by previous analyses of the parabolized stability equations. The locally neutrally propagating part of a type (a) mode consists of the growth and decay of an aerodynamic wavepacket attached to the jet, coupled with a beam of acoustic radiation at a low angle to the jet downstream axis. Type (b) modes are shown to be related to the subsonic family of modes predicted by Tam & Hu (1989). Finally, significant transient growth is recovered by superposing damped, but non-normal, global modes, leading to a novel interpretation of jet noise production. The mechanism of optimal transient growth is identified with a propagating aerodynamic wavepacket which emits an acoustic wavepacket to the far field at an axial location consistent with the peaks of the locally neutrally propagating parts of type (a) modes.
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Mamatsashvili, G. R., V. S. Avsarkisov, G. D. Chagelishvili, R. G. Chanishvili, and M. V. Kalashnik. "Transient Dynamics of Nonsymmetric Perturbations versus Symmetric Instability in Baroclinic Zonal Shear Flows." Journal of the Atmospheric Sciences 67, no. 9 (September 1, 2010): 2972–89. http://dx.doi.org/10.1175/2010jas3313.1.
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Abstract The linear dynamics of symmetric and nonsymmetric perturbations in unbounded zonal inviscid flows with a constant vertical shear of velocity, when a fluid is incompressible and density is stably stratified along the vertical and meridional directions, is investigated. A small–Richardson number Ri ≲ 1 and large–Rossby number Ro ≳ 1 regime is considered, which satisfies the condition for symmetric instability. Specific features of this dynamics are closely related to the nonnormality of linear operators in shear flows and are well interpreted in the framework of the nonmodal approach by tracing the linear dynamics of spatial Fourier harmonics (Kelvin modes) of perturbations in time. The roles of stable stratification, the Coriolis parameter, and vertical shear in the dynamics of perturbations are analyzed. Classification of perturbations into two types or modes—vortex (i.e., quasigeostrophic balanced motions) and inertia–gravity wave—is made according to the value of potential vorticity. The emerging picture of the (linear) transient dynamics for these two modes at Ri ≲ 1 and Ro ≳ 1 indicates that vortex mode perturbations are able to gain basic flow energy and undergo exponential transient amplification and in this process generate inertia–gravity waves. Transient growth of the vortex mode and, consequently, the effectiveness of the wave generation both increase with decreasing Ri and increasing Ro. This linear coupling of perturbation modes is, in general, specific to shear flows but is not fully appreciated yet. A parallel analysis of the transient dynamics of nonsymmetric perturbations versus symmetric instability is also presented. It is shown that the nonnormality-induced transient growth of nonsymmetric perturbations can prevail over the symmetric instability for a wide range of Ri and Ro. The current analysis suggests that the dynamical activity of fronts and jet streaks at Ri ≲ 1 and Ro ≳ 1 should be determined by nonsymmetric perturbations rather than by symmetric ones, as was accepted in earlier papers. It is noteworthy that the transient growth of perturbations is asymmetric in the wavenumber space—the constant phase plane of maximally amplified perturbations is inclined in a direction northeast to the zonal one and the inclination angle is different for different Ri and Ro.
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Meyer, Colin R., and P. F. Linden. "Stratified shear flow: experiments in an inclined duct." Journal of Fluid Mechanics 753 (July 22, 2014): 242–53. http://dx.doi.org/10.1017/jfm.2014.358.
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AbstractWe present results of experiments on stratified shear flow in an inclined duct. The duct connects two reservoirs of fluid with different densities, and contains a counterflow with a dense layer flowing beneath a less dense layer moving in the opposite direction. We identify four flow states in this experiment, depending on the fractional density differences, characterised by the dimensionless Atwood number, and the angle of inclination $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\theta $, which is defined to be positive (negative) when the along-duct component of gravity reinforces (opposes) the buoyancy-induced pressure differences across the ends of the duct. For sufficiently negative angles and small fractional density differences, the flow is observed to be laminar ($\mathsf{L}$ state), with an undisturbed density interface separating the two layers. For positive angles and/or high fractional density differences, three other states are observed. For small angles of inclination, the flow is wave-dominated and exhibits Holmboe modes ($\mathsf{H}$ state) on the interface, with characteristic cusp-like wave breaking. At the highest positive angles and density differences, there is a turbulent ($\mathsf{T}$ state) high-dissipation interfacial region typically containing Kelvin–Helmholtz (KH)-like structures sheared in the direction of the mean shear and connecting both layers. For intermediate angles and density differences, an intermittent state ($\mathsf{I}$ state) is found, which exhibits a rich range of spatio-temporal behaviour and an interfacial region that contains features of KH-like structures and of the other two lower-dissipation states: thin interfaces and Holmboe-like structures. We map the state diagram of these flows in the Atwood number–$\theta $ plane and examine the force balances that determine each of these states. We find that the $\mathsf{L}$ and $\mathsf{H}$ states are hydraulically controlled at the ends of the duct and the flow is determined by the pressure difference associated with the density difference between the reservoirs. As the inclination increases, the along-slope component of the buoyancy force becomes more significant and the $\mathsf{I}$ and $\mathsf{T}$ states are associated with increasing dissipation within the duct. We replot the state space in the Grashof number–$\theta $ phase plane and find the transition to the $\mathsf{T}$ state is governed by a critical Grashof number. We find that the corresponding buoyancy Reynolds number of the transition to the $\mathsf{T}$ state is of the order of 100, and that this state is also found to be hydraulically controlled at the ends of the duct. In this state the dissipation balances the force associated with the along-slope component of buoyancy and the counterflow has a critical composite Froude number.
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Shugan, Igor, and Yang-Yih Chen. "Kinematics of the Ship’s Wake in the Presence of a Shear Flow." Journal of Marine Science and Engineering 9, no. 1 (December 23, 2020): 7. http://dx.doi.org/10.3390/jmse9010007.
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We present the kinematic model of the ship wake in the presence of horizontal subsurface current linearly varying with the depth of water. An extension of the Whitham–Lighthill theory for calm water is developed. It has been established that the structure of ship waves under the action of a shear flow can radically differ from the classical Kelvin ship wake model. Co propagating ship and shear current lead to increasing the total wedge angle up to full one 180° and decreases for the counter shear current. At relatively large unidirectional values of the shear current, cusp waves in the vicinity of the wedge boundary are represented by transverse waves and, conversely, by diverging waves directed almost perpendicular to the ship track for the opposite shear current. The presence of a shear flow crossing the direction of the ship’s movement gives a strong asymmetry of the wake. An increase in the perpendicular shear flow leads to an increase in the difference between the angles of the wake arms. The limiting value of the shear current corresponds to one or both arms angles equal to 90°. Transverse and divergent edge waves for this limiting case coincide.
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Dias, F. "Ship waves and Kelvin." Journal of Fluid Mechanics 746 (April 1, 2014): 1–4. http://dx.doi.org/10.1017/jfm.2014.69.
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AbstractShip wakes are fascinating. They can be observed by the human eye and appear to have a V shape when the ship is advancing at constant speed along a straight trajectory. Under idealized conditions, Kelvin found that the angle between the two branches of the V is ${\sim }39^\circ $. However, in a number of cases, this angle appears to be smaller. This phenomenon has been studied by various authors, and several explanations have been suggested. The most elegant one, which is based on the amplitude of the ship waves rather than their phase, has recently been revisited by Darmon, Benzaquen & Raphaël (J. Fluid Mech., vol. 738, 2014, R3).
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Abdilghanie, Ammar M., and Peter J. Diamessis. "The internal gravity wave field emitted by a stably stratified turbulent wake." Journal of Fluid Mechanics 720 (February 27, 2013): 104–39. http://dx.doi.org/10.1017/jfm.2012.640.
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AbstractThe internal gravity wave (IGW) field emitted by a stably stratified, initially turbulent, wake of a towed sphere in a linearly stratified fluid is studied using fully nonlinear numerical simulations. A wide range of Reynolds numbers, $\mathit{Re}= UD/ \nu \in [5\times 1{0}^{3} , 1{0}^{5} ] $ and internal Froude numbers, $\mathit{Fr}= 2U/ (ND)\in [4, 16, 64] $ ($U$, $D$ are characteristic body velocity and length scales, and $N$ is the buoyancy frequency) is examined. At the higher $\mathit{Re}$ examined, secondary Kelvin–Helmholtz instabilities and the resulting turbulent events, directly linked to a prolonged non-equilibrium (NEQ) regime in wake evolution, are responsible for IGW emission that persists up to $Nt\approx 100$. In contrast, IGW emission at the lower $\mathit{Re}$ investigated does not continue beyond $Nt\approx 50$ for the three $\mathit{Fr}$ values considered. The horizontal wavelengths of the most energetic IGWs, obtained by continuous wavelet transforms, increase with $\mathit{Fr}$ and appear to be smaller at the higher $\mathit{Re}$, especially at late times. The initial value of these wavelengths is set by the wake height at the beginning of the NEQ regime. At the lower $\mathit{Re}$, consistent with a recently proposed model, the waves propagate over a narrow range of angles that minimize viscous decay along their path. At the higher $\mathit{Re}$, wave motion is much less affected by viscosity, at least initially, and early-time wave propagation angles extend over a broader range of values which are linked to increased efficiency in momentum extraction from the turbulent wake source.
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Yang, Qiu, and Andrew J. Majda. "Upscale Impact of Mesoscale Disturbances of Tropical Convection on Convectively Coupled Kelvin Waves." Journal of the Atmospheric Sciences 75, no. 1 (January 2018): 85–111. http://dx.doi.org/10.1175/jas-d-17-0178.1.
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Tropical convection associated with convectively coupled Kelvin waves (CCKWs) is typically organized by an eastward-moving synoptic-scale convective envelope with numerous embedded westward-moving mesoscale disturbances. Such a multiscale structure of tropical convection is a challenge for present-day cloud-resolving simulations and its representation in global climate models. It is of central importance to assess the upscale impact of mesoscale disturbances on CCKWs as mesoscale disturbances propagate at various tilt angles and speeds. Besides, it is still poorly understood whether the front-to-rear-tilted vertical structure of CCKWs can be induced by the upscale impact of mesoscale disturbances in the presence of upright mean heating. Here, a simple multiscale model is used to capture this multiscale structure, where mesoscale fluctuations are directly driven by mesoscale heating and synoptic-scale circulation is forced by mean heating and eddy transfer of momentum and temperature. The results show that the upscale impact of mesoscale disturbances that propagate at tilt angles of 110°–250° induces negative lower-tropospheric potential temperature anomalies in the leading edge, providing favorable conditions for shallow convection in a moist environment, while the remaining tilt-angle cases have opposite effects. Even in the presence of upright mean heating, the front-to-rear-tilted synoptic-scale circulation can still be induced by eddy terms at tilt angles of 120°–240°. In the case with fast-propagating mesoscale heating, positive potential temperature anomalies are induced in the lower troposphere, suppressing convection in a moist environment. This simple model also reproduces convective momentum transport and CCKWs in agreement with results from a recent cloud-resolving simulation.
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Yang, Qiu, and Andrew J. Majda. "Upscale Impact of Mesoscale Disturbances of Tropical Convection on 2-Day Waves." Journal of the Atmospheric Sciences 76, no. 1 (January 1, 2019): 171–94. http://dx.doi.org/10.1175/jas-d-18-0049.1.
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Abstract Westward-propagating 2-day waves with embedded mesoscale disturbances contribute a large portion of synoptic variability of tropical convection over the western Pacific. It is of crucial importance to assess the upscale impact on 2-day waves of these mesoscale disturbances that propagate at various tilt angles. Also, it will be informative to consider the upscale impact on both symmetric and asymmetric 2-day waves in terms of convection, morphology of circulation, and tropical cyclogenesis. A simple multiscale asymptotic model is used to simulate the two-scale structure of 2-day waves. The synoptic-scale circulation response is driven by westward-propagating mean heating and eddy transfer of momentum and temperature. The latter is interpreted as the upscale impact of mesoscale fluctuations. The upscale impact of mesoscale disturbances that propagate at a tilt angle between 315° and 45° induces low-level negative potential temperature anomalies and westerly inflow. Shallow congestus convection triggered in a moist environment at the leading edge of the 2-day waves supports the westward propagation. For asymmetric 2-day waves in the Northern Hemisphere, the upscale impact of mesoscale disturbances propagating at a tilt angle between 315° and 0° induces lower-tropospheric cyclonic flows and negative pressure perturbation. This provides a new mechanism to precondition tropical cyclogenesis. A comparison of the upscale impact on symmetric westward-propagating 2-day waves and eastward-propagating convectively coupled Kelvin waves shows that their tilt angle ranges with favorable conditions for convection and enhanced inflow are simply opposite.
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Haro, Marco Polo Espinoza, Jong-Chun Park, Dong-Hyun Kim, and Sung-Bum Lee. "CFD Simulation on Workability of a Seaweed Harvesting Boat Due to Wake-Wash." Journal of Marine Science and Engineering 8, no. 8 (July 22, 2020): 544. http://dx.doi.org/10.3390/jmse8080544.
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In the present study, a 2-ton class seaweed harvesting boat was optimized by employing a W-shape hull form to reduce roll motion due to wake-wash from passing boats. A series of numerical simulations were conducted using Star-CCM+, a commercial CFD (computational fluid dynamics) software, to improve workability by optimizing the hull form from the conventional design (original hull form). The 2-dimensional roll decay motion of various hull forms with W-shape midsection were simulated and the hull form with the best performance in free roll decay test was selected. To evaluate stability of each hull in wake-wash, the original or optimized hull was alternately located at the middle of a computational domain as a target ship while an advancing ship (original hull) moved forward generating Kelvin waves which impact the original or optimized boat. Two kinds of working conditions, i.e., ballast and full loading conditions, of the target ship were considered with and without initial roll angle. It was observed through the comparison of motion between the original and optimized hulls a decrement of roll motion for the optimized ship demonstrating the effectiveness of the W-shape hull. Decrement of roll motion was observed for both working conditions. Additionally, the optimized W-shape hull showed an extraordinary performance under the ballast condition without initial roll angle.
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KOKUBO, Kazuki, Keisuke NAKAYAMA, Tetsuya SHINTANI, Jyunichi OTSUKA, Yasunori WATANABE, Taro KAKINUMA, Katsuaki KOMAI, and Kenji SHIMIZU. "CURRENT INDUCED BY BREAKING OF INTERNAL KELVIN WAVES ON SLOPES WITH DIFFERENT ANGLES." Journal of Japan Society of Civil Engineers, Ser. B3 (Ocean Engineering) 70, no. 2 (2014): I_193—I_198. http://dx.doi.org/10.2208/jscejoe.70.i_193.
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Choudhury, S. Roy. "Kelvin-Helmholtz instabilities of supersonic, magnetized shear layers." Journal of Plasma Physics 35, no. 3 (June 1986): 375–92. http://dx.doi.org/10.1017/s0022377800011417.
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The linear stability of finite-thickness, compressible, ideal magnetohydrodynamic sheared flows along the z direction, with a magnetic field in the (y, z) plane is studied. This paper extends earlier work with the magnetic field parallel to the flow. The present formulation also includes the effects of density and pressure gradients in the equilibrium shear layer. Analytical solutions are obtained for strongly and weakly magnetized shear layers having a vortex sheet profile (where the velocity is a step function). For an equilibrium layer having a linear velocity profile, and uniform pressure and density, contour plots of the real and imaginary parts of the perturbation frequency (corresponding to unstable waves) are numerically generated in (wavenumber, Mach number) plane using a shooting technique. The structure of two distinct regimes of instability (unstable standing modes and unstable travelling modes) is mapped out for various values of the inverse plasma beta, and various angles of propagation of the mode to the flow and the magnetic field.
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Bosco, M., and P. Meunier. "Three-dimensional instabilities of a stratified cylinder wake." Journal of Fluid Mechanics 759 (October 20, 2014): 149–80. http://dx.doi.org/10.1017/jfm.2014.517.
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AbstractThis paper describes experimentally, numerically and theoretically how the three-dimensional instabilities of a cylinder wake are modified by the presence of a linear density stratification. The first part is focused on the case of a cylinder with a small tilt angle between the cylinder’s axis and the vertical. The classical mode A well-known for a homogeneous fluid is still present. It is more unstable for moderate stratifications but it is stabilized by a strong stratification. The second part treats the case of a moderate tilt angle. For moderate stratifications, a new unstable mode appears, mode S, characterized by undulated layers of strong density gradients and axial flow. These structures correspond to Kelvin–Helmholtz billows created by the strong shear present in the critical layer of each tilted von Kármán vortex. The last two parts deal with the case of a strongly tilted cylinder. For a weak stratification, an instability (mode RT) appears far from the cylinder, due to the overturning of the isopycnals by the von Kármán vortices. For a strong stratification, a short wavelength unstable mode (mode L) appears, even in the absence of von Kármán vortices. It is probably due to the strong shear created by the lee waves upstream of a secondary recirculation bubble. A map of the four different unstable modes is established in terms of the three parameters of the study: the Reynolds number, the Froude number (characterizing the stratification) and the tilt angle.
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Sedlak, René, Patrick Hannawald, Carsten Schmidt, Sabine Wüst, and Michael Bittner. "High-resolution observations of small-scale gravity waves and turbulence features in the OH airglow layer." Atmospheric Measurement Techniques 9, no. 12 (December 12, 2016): 5955–63. http://dx.doi.org/10.5194/amt-9-5955-2016.
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Abstract. A new version of the Fast Airglow Imager (FAIM) for the detection of atmospheric waves in the OH airglow layer has been set up at the German Remote Sensing Data Center (DFD) of the German Aerospace Center (DLR) at Oberpfaffenhofen (48.09° N, 11.28° E), Germany. The spatial resolution of the instrument is 17 m pixel−1 in zenith direction with a field of view (FOV) of 11.1 km × 9.0 km at the OH layer height of ca. 87 km. Since November 2015, the system has been in operation in two different setups (zenith angles 46 and 0°) with a temporal resolution of 2.5 to 2.8 s. In a first case study we present observations of two small wave-like features that might be attributed to gravity wave instabilities. In order to spectrally analyse harmonic structures even on small spatial scales down to 550 m horizontal wavelength, we made use of the maximum entropy method (MEM) since this method exhibits an excellent wavelength resolution. MEM further allows analysing relatively short data series, which considerably helps to reduce problems such as stationarity of the underlying data series from a statistical point of view. We present an observation of the subsequent decay of well-organized wave fronts into eddies, which we tentatively interpret in terms of an indication for the onset of turbulence. Another remarkable event which demonstrates the technical capabilities of the instrument was observed during the night of 4–5 April 2016. It reveals the disintegration of a rather homogenous brightness variation into several filaments moving in different directions and with different speeds. It resembles the formation of a vortex with a horizontal axis of rotation likely related to a vertical wind shear. This case shows a notable similarity to what is expected from theoretical modelling of Kelvin–Helmholtz instabilities (KHIs). The comparatively high spatial resolution of the presented new version of the FAIM provides new insights into the structure of atmospheric wave instability and turbulent processes. Infrared imaging of wave dynamics on the sub-kilometre scale in the airglow layer supports the findings of theoretical simulations and modellings.
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Tam, Christopher K. W., and Hongbin Ju. "Aerofoil tones at moderate Reynolds number." Journal of Fluid Mechanics 690 (December 1, 2011): 536–70. http://dx.doi.org/10.1017/jfm.2011.465.
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AbstractIt is known experimentally that an aerofoil immersed in a uniform stream at a moderate Reynolds number emits tones. However, there have been major differences in the experimental observations in the past. Some experiments reported the observation of multiple tones, with strong evidence that these tones are most probably generated by a feedback loop. There is also an experiment reporting the observation of a single tone with no tonal jump or other features associated with feedback. In spite of the obvious differences in the experimental observations published in the literature, it is noted that all the dominant tone frequencies measured in all the investigations are in agreement with an empirically derived Paterson formula. The objective of the present study is to perform a direct numerical simulation (DNS) of the flow and acoustic phenomenon to investigate the tone generation mechanism. When comparing with experimental studies, numerical simulations appear to have two important advantages. The first is that there is no background wind tunnel noise in numerical simulation. This avoids the signal-to-noise ratio problem inherent in wind tunnel experiments. In other words, it is possible to study tones emitted by a truly isolated aerofoil computationally. The second advantage is that DNS produces a full set of space–time data, which can be very useful in determining the tone generation processes. The present effort concentrates on the tones emitted by three NACA0012 aerofoils with a slightly rounded trailing edge but with different trailing edge thickness at zero degree angle of attack. At zero degree angle of attack, in the Reynolds number range of$2\ensuremath{\times} 1{0}^{5} $to$5\ensuremath{\times} 1{0}^{5} $, the boundary layer flow is attached nearly all the way to the trailing edge of the aerofoil. Unlike an aerofoil at an angle of attack, there is no separation bubble, no open flow separation. All the flow separation features tend to increase the complexity of the tone generation processes. The present goal is limited to finding the basic tone generation mechanism in the simplest flow configuration. Our DNS results show that, for the flow configuration under study, the aerofoil emits only a single tone. This is true for all three aerofoils over the entire Reynolds number range of the present study. In the literature, it is known that Kelvin–Helmholtz instabilities of free shear layers generally have a much higher spatial growth rate than that of the Tollmien–Schlichting boundary layer instabilities. A near-wake non-parallel flow instability analysis is performed. It is found that the tone frequencies are the same as the most amplified Kelvin–Helmholtz instability at the location where the wake has a minimum half-width. This suggests that near-wake instability is the energy source of aerofoil tones. However, flow instabilities at low subsonic Mach numbers generally do not cause strong tones. An investigation of how near-wake instability generates tones is carried out using the space–time data provided by numerical simulations. Our observations indicate that the dominant tone generation process is the interaction of the oscillatory motion of the near wake, driven by flow instability, with the trailing edge of the aerofoil. Secondary mechanisms involving unsteady near-wake motion and the formation of discrete vortices in regions further downstream are also observed.
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Gaiser, James E., Terrance J. Fulp, Steve G. Petermann, and Gary M. Karner. "Vertical seismic profile sonde coupling." GEOPHYSICS 53, no. 2 (February 1988): 206–14. http://dx.doi.org/10.1190/1.1442456.
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P-wave and S-wave displacements occur at high angles of incidence in vertical seismic profiles (VSPs). Therefore, the coupling of a geophone sonde to the borehole wall must be rigid in all directions. A sonde that is well coupled should have no resonant frequency within the seismic band and should provide geophone outputs that accurately represent the earth’s ground motion. An in‐situ coupling response experiment conducted under normal VSP field conditions provides a measure of the sonde‐to‐borehole wall coupling. The sonde is locked in the borehole and a surface source is excited at different offsets and azimuths. An analysis of the P-wave direct arrivals enhances damped oscillations that represent an estimate of the coupling impulse response. This response is characterized by the viscoelastic behavior of a Kelvin model related to the complex compliance [Formula: see text], where κ is the elastic spring constant, η is the damping constant, and ω is the angular frequency. The complex modulus κ−iωη is proportional to the contact width of the sonde with the borehole wall. Increasing the width by a factor of 4.5 causes a similar increase in κ−iωη where the resonant frequency and initial amplitude of the coupling impulse response increase by a factor of two. Also, the initial amplitude of the coupling impulse response appears to be inversely proportional to the locking force of the sonde. For a constant contact width, increasing the locking force by a factor of 1.37 decreases the amplitude of the response by 3.5 dB.
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Hamed, A. M., A. Pagan-Vazquez, D. Khovalyg, Z. Zhang, and L. P. Chamorro. "Vortical structures in the near wake of tabs with various geometries." Journal of Fluid Mechanics 825 (July 20, 2017): 167–88. http://dx.doi.org/10.1017/jfm.2017.384.
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The vortical structures and turbulence statistics in the near wake of rectangular, trapezoidal, triangular and ellipsoidal tabs were experimentally studied in a refractive-index-matching channel. The tabs share the same bulk dimensions, including a 17 mm height, a 28 mm base width and a $24.5^{\circ }$ inclination angle. Measurements were performed at two Reynolds numbers based on the tab height, $Re_{h}\simeq 2000$ (laminar incoming flow) and 13 000 (turbulent incoming flow). Three-dimensional, three-component particle image velocimetry (PIV) was used to study the mean flow distribution and dominant large-scale vortices, while complementary high-spatial-resolution planar PIV measurements were used to quantify high-order statistics. Instantaneous three-dimensional fields revealed the coexistence of a coherent counter-rotating vortex pair (CVP) and hairpin structures. The CVP and hairpin vortices (the primary structures) exhibit distinctive characteristics and strength across $Re_{h}$ and tab geometries. The CVP is coherently present in the mean flow field and grows in strength over a significantly longer distance at the low $Re_{h}$ due to the lower turbulence levels and the delayed shedding of the hairpin vortices. These features at the low $Re_{h}$ are associated with the presence of Kelvin–Helmholtz instability that develops over three tab heights downstream of the trailing edge. Moreover, a secondary CVP with an opposite sense of rotation resides below the primary one for the four tabs at the low $Re_{h}$. The interaction between the hairpin structures and the primary CVP is experimentally measured in three dimensions and shows complex coexistence. Although the CVP undergoes deformation and splitting at times, it maintains its presence and leads to significant mean spanwise and wall-normal flows.
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Hasheminejad, Seyyed M., Masoud Cheraghi, and Ali Jamalpoor. "Active damping of sound transmission through an electrorheological fluid-actuated sandwich cylindrical shell." Journal of Sandwich Structures & Materials 22, no. 3 (May 21, 2018): 833–65. http://dx.doi.org/10.1177/1099636218777966.
Full textAbstract:
An exact model is proposed for sound transmission through a sandwich cylindrical shell of infinite extent that includes a tunable electrorheological fluid core, and is obliquely insonified by a plane progressive acoustic wave. The basic formulation utilizes Hamilton’s variational principle, the classical and first order shear deformation shell theories, the Kelvin–Voigt viscoelastic damping model (for the electrorheological fluid-core layer), and the wave equations for internal/external acoustic domains coupled by the proper fluid/structure compatibility relations. The Fourier–Bessel series expansions are used to arrange the governing (coupled) system equations in state-space form. The classical Sliding Mode Control law is then applied to semi-actively reduce sound transmission through the composite cylinder by smart variation of stiffness and damping characteristics of the electrorheological fluid-core actuator layer according to the control command. Numerical results present both the uncontrolled and controlled sound transmission loss spectra of the sandwich cylindrical shell at three angles of incidence for three distinct sets of material input parameters that represent the electric-field dependency of the complex shear modulus of the electrorheological fluid-core layer. The superior soundproof performance of electrorheological fluid-based sliding mode control system in avoiding the highly detrimental sound transmission loss dips occurring throughout the critical resonance and coincidence regions is demonstrated. Likewise, remarkable enhancements in the sound insulation characteristics of the electrorheological fluid-actuated structure utilizing the first or second electrorheological fluid material model are achieved within the stiffness-controlled region, especially at lower frequencies in near-grazing incidence situation. A number of limiting cases are introduced and validity of the formulation is confirmed by comparison with the available data.
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Nguyen, Lap, Vladimir Golubev, Reda Mankbadi, Gyuzel Yakhina, and Michel Roger. "Numerical Investigation of Tonal Trailing-Edge Noise Radiated by Low Reynolds Number Airfoils." Applied Sciences 11, no. 5 (March 4, 2021): 2257. http://dx.doi.org/10.3390/app11052257.
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A high-fidelity computational analysis carefully validated against concurrently obtained experimental results is employed to examine self-noise radiation of airfoils at transitional flow regimes, with a focus on elucidating the connection between the unsteady behavior of the laminar separation bubble (LSB) and the acoustic feedback-loop (AFL) resonant interactions observed in the airfoil boundary layers. The employed parametric study examines AFL sensitivity to the changes in the upstream flow conditions and the airfoil loading. Implicit Large-Eddy Simulations are performed for a NACA-0012 airfoil in selected transitional-flow regimes for which experimental measurements recorded characteristic multiple-tone acoustic spectra with a dual ladder-type frequency structure. The switch between the tone-producing and no-tone-producing regimes is traced to the LSB size and position as a function of the flow Reynolds number and the airfoil angle of attack, and further substantiated by the linear stability analysis. The results indicate a strong multi-tonal airfoil noise radiation associated with the AFL and attributed to the switch from the slowly-growing Tollmien–Schlichting to the fast-growing Kelvin–Helmholtz instabilities occurring in thin LSB regions when those are localized near the trailing-edge (TE) on either side of the airfoil. Such a process eventually results in the nonlinearly saturated flapping vortical modes (“rollers”) that scatter into acoustic waves at the TE.
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Sun, Weijie, Ryan M. Dewey, Sae Aizawa, Jia Huang, James A. Slavin, Suiyan Fu, Yong Wei, and Charles F. Bowers. "Review of Mercury’s dynamic magnetosphere: Post-MESSENGER era and comparative magnetospheres." Science China Earth Sciences 65, no. 1 (November 30, 2021): 25–74. http://dx.doi.org/10.1007/s11430-021-9828-0.
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AbstractThis review paper summarizes the research of Mercury’s magnetosphere in the Post-MESSENGER era and compares its dynamics to those in other planetary magnetospheres, especially to those in Earth’s magnetosphere. This review starts by introducing the planet Mercury, including its interplanetary environment, magnetosphere, exosphere, and conducting core. The frequent and intense magnetic reconnection on the dayside magnetopause, which is represented by the flux transfer event “shower”, is reviewed on how they depend on magnetosheath plasma β and magnetic shear angle across the magnetopause, following by how it contributes to the flux circulation and magnetosphere-surface-exosphere coupling. In the next, Mercury’s magnetosphere under extreme solar events, including the core induction and the reconnection erosion on the dayside magnetosphere, the responses of the nightside magnetosphere, are reviewed. Then, the dawn-dusk properties of the plasma sheet, including the features of the ions, the structure of the current sheet, and the dynamics of magnetic reconnection, are summarized. The last topic is devoted to the particle energization in Mercury’s magnetosphere, which includes the energization of the Kelvin-Helmholtz waves on the magnetopause boundaries, reconnection-generated magnetic structures, and the cross-tail electric field. In each chapter, the last section discusses the open questions related to each topic, which can be considered by the simulations and the future spacecraft mission. We end this paper by summarizing the future BepiColombo opportunities, which is a joint mission of ESA and JAXA and is en route to Mercury.
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Ianiro, Andrea, Kyle P. Lynch, Daniele Violato, Gennaro Cardone, and Fulvio Scarano. "Three-dimensional organization and dynamics of vortices in multichannel swirling jets." Journal of Fluid Mechanics 843 (March 21, 2018): 180–210. http://dx.doi.org/10.1017/jfm.2018.140.
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The unsteady three-dimensional flow organization of jets issued from a duct with swirl vanes at Reynolds number equal to 1000 and swirl number $S$ ranging between 0 and 0.8 is investigated. Time-resolved tomographic particle image velocimetry returns the instantaneous flow structure and its evolution by visualization of velocity and vortical features. The most relevant coherent motions are identified and characterized with the aid of dynamic mode decomposition. The time-averaged flow topology indicates that the vanes used to impart the swirling motion have a significant impact on the azimuthal modulation of momentum, with the jet exhibiting four sectors separated by a thin cross-like wake resulting from the boundary layer developed along the vane walls. The flow field is thus characterized by inner and outer shear regions. An increase in swirl, up to moderate levels ($S=0.4$), causes larger jet spreading angles. Further increase of the swirl number is accompanied by the appearance of a central recirculation zone due to vortex breakdown at $S=0.6$ which increases in size and is triggered upstream for increasing $S$. Although no shear layer instability development is observed at $S=0$, already at $S=0.2$ the swirling motion promotes the growth of helical vortices appearing as Kelvin–Helmholtz waves that deform the outer axial shear layer. The downstream evolution features successive pairing, which is observed for all the considered swirl numbers. The initial development of the instability is independent for each vane, whereas a mutual interaction between the vanes occurs after the vortex pairing. The reconnection from the four sectors vortices induces a significant increase of azimuthal vorticity, which affects the dynamical behaviour of the precessing vortex core. The latter is visualized by a low-order spatio-temporal reconstruction based on few dynamical modes. At a higher swirl number ($S\geqslant 0.6$), the axial vorticity component dominates the flow field; it interacts with the azimuthal vorticity, which penetrates inward through the meanders of the vane wakes and forces the vortex core precession and breakdown.
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Feng, Li-Hao, Kwing-So Choi, and Jin-Jun Wang. "Flow control over an airfoil using virtual Gurney flaps." Journal of Fluid Mechanics 767 (February 20, 2015): 595–626. http://dx.doi.org/10.1017/jfm.2015.22.
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AbstractFlow control over a NACA 0012 airfoil is carried out using a dielectric barrier discharge (DBD) plasma actuator at the Reynolds number of 20 000. Here, the plasma actuator is placed over the pressure (lower) side of the airfoil near the trailing edge, which produces a wall jet against the free stream. This reverse flow creates a quasi-steady recirculation region, reducing the velocity over the pressure side of the airfoil. On the other hand, the air over the suction (upper) side of the airfoil is drawn by the recirculation, increasing its velocity. Measured phase-averaged vorticity and velocity fields also indicate that the recirculation region created by the plasma actuator over the pressure surface modifies the near-wake dynamics. These flow modifications around the airfoil lead to an increase in the lift coefficient, which is similar to the effect of a mechanical Gurney flap. This configuration of DBD plasma actuators, which is investigated for the first time in this study, is therefore called a virtual Gurney flap. The purpose of this investigation is to understand the mechanism of lift enhancement by virtual Gurney flaps by carefully studying the global flow behaviour over the airfoil. First, the recirculation region draws the air from the suction surface around the trailing edge. The upper shear layer then interacts with the opposite-signed shear layer from the pressure surface, creating a stronger vortex shedding from the airfoil. Secondly, the recirculation region created by a DBD plasma actuator over the pressure surface displaces the positive shear layer away from the airfoil, thereby shifting the near-wake region downwards. The virtual Gurney flap also changes the dynamics of laminar separation bubbles and associated vortical structures by accelerating laminar-to-turbulent transition through the Kelvin–Helmholtz instability mechanism. In particular, the separation point and the start of transition are advanced. The reattachment point also moves upstream with plasma control, although it is slightly delayed at a large angle of attack.
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Inoue, Ryuichiro, and William D. Smyth. "Efficiency of Mixing Forced by Unsteady Shear Flow." Journal of Physical Oceanography 39, no. 5 (May 1, 2009): 1150–66. http://dx.doi.org/10.1175/2008jpo3927.1.
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Abstract The dependence of mixing efficiency on time-varying forcing is studied by direct numerical simulation (DNS) of Kelvin–Helmholtz (KH) instability. Time-dependent forcing fields are designed to reproduce a wavelike oscillation by solving the equations of motion in a tilted coordinate frame and allowing the tilt angle to vary in time. Mixing efficiency Γc is defined as the ratio of potential energy gain to dissipation, both averaged over one forcing cycle and first examined via parameters characterizing waves: the minimum Richardson number Rimin and the normalized frequency of the forcing ω/N. The effect of Reynolds number Re0 and the initial random disturbance amplitude b are also examined. In the experiments presented, Γc varies between 0.21 and 0.36 and is controlled by the timing of two events: the emergence of KH billows and the arrival of the deceleration of the mean shear by the wavelike forcing. Here, Γc is higher than a canonical value of 0.2 when the deceleration phase of the forcing suppresses the less efficient turbulence after breakdown of KH billows. However, when Rimin and ω/N are small, KH billows start to develop before Rimin is achieved. Therefore, the forcing accelerates the mean shear and thereby sustains turbulence after the breakdown of KH billows. The canonical value is then reproduced in the DNS. Although larger values of Re0 and b intensify the development of KH billows and modify Γc, this effect is less significant when forcing fields act to sustain turbulence. The time-averaged Thorpe scale and Ozmidov scale are also used to see how mixing is modified by forcing fields and compared with past microstructure measurements. It is found that DNS also corresponds to past observations if the forcing accelerates the mean shear to sustain turbulence.
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Melnikov, Valery M., and Richard J. Doviak. "Turbulence and Wind Shear in Layers of Large Doppler Spectrum Width in Stratiform Precipitation." Journal of Atmospheric and Oceanic Technology 26, no. 3 (March 1, 2009): 430–43. http://dx.doi.org/10.1175/2008jtecha1108.1.
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Abstract Weather radar observations of stratiform precipitation often reveal regions having very large measured Doppler spectrum widths, exceeding 7, and sometimes 10, m s−1. These widths are larger than those typically found in thunderstorms; widths larger than 4 m s−1 are associated with moderate or severe turbulence in thunderstorms. In this work, stratiform precipitation has been found to have layers of widths larger than 4 m s−1 in more than 80% of cases studied, wherein the shear of the wind on scales that are large compared to the dimensions of the radar resolution volume is the dominant contributor to spectrum width. Analyzed data show that if width ≤7 m s−1, and if the layers are not wavy or patchy, these layers have weak turbulence. On the other hand, regions having widths >4 m s−1 in patches or in wavelike structures are likely to have moderate to severe turbulence with the potential to be a hazard to safe flight. To separate the contributions to spectrum width from wind shear and turbulence and to evaluate the errors in turbulence estimates, data have been collected with elevation increments much less than a beamwidth. Despite beamwidth limitations, the small elevation increments reveal impressive structures in the fields. For example, the “cat’s eye” structure associated with Kelvin–Helmholtz waves is clearly exhibited in the fields of spectrum width observed at low-elevation angles, but not in the reflectivity or velocity fields. Reflectivity fields in stratiform precipitation are featureless compared to spectrum width fields.
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KITLV, Redactie. "Book Reviews." New West Indian Guide / Nieuwe West-Indische Gids 78, no. 1-2 (January 1, 2004): 123–91. http://dx.doi.org/10.1163/13822373-90002521.
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-Chuck Meide, Kathleen Deagan ,Columbus's outpost among the Taínos: Spain and America at La Isabela, 1493-1498. New Haven CT: Yale University Press, 2002. x + 294 pp., José María Cruxent (eds)-Lee D. Baker, George M. Fredrickson, Racism: A short history. Princeton NJ: Princeton University Press, 2002. x + 207 pp.-Evelyn Powell Jennings, Sherry Johnson, The social transformation of eighteenth-century Cuba. Gainesville: University Press of Florida, 2001. x + 267 pp.-Michael Zeuske, J.S. Thrasher, The island of Cuba: A political essay by Alexander von Humboldt. Translated from Spanish with notes and a preliminary essay by J.S. Thrasher. Princeton NJ: Markus Wiener; Kingston: Ian Randle, 2001. vii + 280 pp.-Matt D. Childs, Virginia M. Bouvier, Whose America? The war of 1898 and the battles to define the nation. Westport CT: Praeger, 2001. xi + 241 pp.-Carmelo Mesa-Lago, Antonio Santamaría García, Sin azúcar no hay país: La industria azucarera y la economía cubana (1919-1939). Seville: Consejo Superior de Investigaciones Científicas, Universidad de Sevilla y Diputación de Sevilla, 2001. 624 pp.-Charles Rutheiser, Joseph L. Scarpaci ,Havana: Two faces of the Antillean Metropolis. Chapel Hill: University of North Carolina Press, 2002. x + 437 pp., Roberto Segre, Mario Coyula (eds)-Thomas Neuner, Ottmar Ette ,Kuba Heute: Politik, Wirtschaft, Kultur. Frankfurt am Main, Germany: Vervuert, 2001. 863 pp., Martin Franzbach (eds)-Mark B. Padilla, Emilio Bejel, Gay Cuban nation. Chicago: University of Chicago Press, 2001. xxiv + 257 pp.-Mark B. Padilla, Kamala Kempadoo, Sun, sex, and gold: Tourism and sex work in the Caribbean. New York: Rowman & Littlefield, 1999. viii + 356 pp.-Jane Desmond, Susanna Sloat, Caribbean dance from Abakuá to Zouk: How movement shapes identity. Gainesville: University Press of Florida, 2002. xx + 408 pp.-Karen Fog Olwig, Nina Glick Schiller ,Georges woke up laughing: Long-distance nationalism and the search for home. Durham NC: Duke University Press, 2001. x + 324 pp., Georges Eugene Fouron (eds)-Karen Fog Olwig, Nancy Foner, From Ellis Island to JFK: New York's two great waves of immigration. Chelsea MI: Russell Sage Foundation, 2000. xvi + 334 pp.-Aviva Chomsky, Lara Putnam, The company they kept: Migrants and the politics of gender in Caribbean Costa Rica, 1870-1960. Chapel Hill: University of North Carolina Press, 2002. xi + 303 pp.-Rebecca B. Bateman, Rosalyn Howard, Black Seminoles in the Bahamas. Gainesville: University Press of Florida, 2002. xvii + 150 pp.-Virginia Kerns, Carel Roessingh, The Belizean Garífuna: Organization of identity in an ethnic community in Central America. Amsterdam: Rozenberg. 2001. 264 pp.-Nicole Roberts, Susanna Regazzoni, Cuba: una literatura sin fronteras / Cuba: A literature beyond boundaries. Madrid: Iberoamericana/Frankfurt am Main, Germany: Vervuert, 2001. 148 pp.-Nicole Roberts, Lisa Sánchez González, Boricua literature: A literary history of the Puerto Rican Diaspora. New York: New York University Press, 2001. viii + 216 pp.-Kathleen Gyssels, Ange-Séverin Malanda, Passages II: Histoire et pouvoir dans la littérature antillo-guyanaise. Paris: Editions du Ciref, 2002. 245 pp.-Sue N. Greene, Simone A. James Alexander, Mother imagery in the novels of Afro-Caribbean women. Columbia MO: University of Missouri Press, 2001. x + 215 pp.-Gert Oostindie, Aarón Gamaliel Ramos ,Islands at the crossroads: Politics in the non-independent Caribbean., Angel Israel Rivera (eds)-Katherine E. Browne, David A.B. Murray, Opacity: Gender, sexuality, race, and the 'problem' of identity in Martinique. New York: Peter Lang, 2002. xi + 188 pp.-James Houk, Kean Gibson, Comfa religion and Creole language in a Caribbean community. Albany: State University of New York Press, 2001. xvii + 243 pp.-Kelvin Singh, Frank J. Korom, Hosay Trinidad: Muharram performances in an Indo-Caribbean Diaspora.Philadelphia: University of Pennsylvania Press, 2003. viii + 305 pages.-Lise Winer, Kim Johnson, Renegades: The history of the renegades steel orchestra of Trinidad and Tobago. With photos by Jeffrey Chock. Oxford UK: Macmillan Caribbean Publishers, 2002. 170 pp.-Jerome Teelucksingh, Glenford Deroy Howe, Race, war and nationalism: A social history of West Indians in the first world war. Kingston: Ian Randle/Oxford UK: James Currey, 2002. vi + 270 pp.-Geneviève Escure, Glenn Gilbert, Pidgin and Creole linguistics in the twenty-first century. New York: Peter Lang Publishing, 2002. 379 pp.-George L. Huttar, Eithne B. Carlin ,Atlas of the languages of Suriname. Leiden, The Netherlands: KITLV Press/Kingston: Ian Randle, 2002. vii + 345 pp., Jacques Arends (eds)
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Ellingsen, Simen Å. "Ship waves in the presence of uniform vorticity." Journal of Fluid Mechanics 742 (February 21, 2014). http://dx.doi.org/10.1017/jfm.2014.28.
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AbstractLord Kelvin’s result that waves behind a ship lie within a half-angle $\phi _{\mathit{K}}\approx 19^{\circ }28'$ is perhaps the most famous and striking result in the field of surface waves. We solve the linear ship wave problem in the presence of a shear current of constant vorticity $S$, and show that the Kelvin angles (one each side of wake) as well as other aspects of the wake depend closely on the ‘shear Froude number’ $\mathit{Fr}_{\mathit{s}}=VS/g$ (based on length $g/S^2$ and the ship’s speed $V$), and on the angle between current and the ship’s line of motion. In all directions except exactly along the shear flow there exists a critical value of $\mathit{Fr}_{\mathit{s}}$ beyond which no transverse waves are produced, and where the full wake angle reaches $180^\circ $. Such critical behaviour is previously known from waves at finite depth. For side-on shear, one Kelvin angle can exceed $90^\circ $. On the other hand, the angle of maximum wave amplitude scales as $\mathit{Fr}^{-1}$ ($\mathit{Fr}$ based on size of ship) when $\mathit{Fr}\gg 1$, a scaling virtually unaffected by the shear flow.