Articoli di riviste: "Kirchhoff vortex"

1

Wan, Yieh-Hei. "Bifurcation At Kirchhoff Elliptic vortex with eccentricity." Dynamics and Stability of Systems 13, no. 3 (1998): 281–97. http://dx.doi.org/10.1080/02681119808806265.

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2

STRAWN, ROGER C., RUPAK BISWAS, and ANASTASIOS S. LYRINTZIS. "HELICOPTER NOISE PREDICTIONS USING KIRCHHOFF METHODS." Journal of Computational Acoustics 04, no. 03 (1996): 321–39. http://dx.doi.org/10.1142/s0218396x96000106.

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This paper presents two methods for predicting the noise from helicopter rotors in forward flight. Aerodynamic and acoustic solutions in the near field are computed with a finite-difference solver for the Euler equations. Two different Kirchhoff acoustics methods are then used to propagate the acoustic signals to the far field in a computationally-efficient manner. One of the methods uses a Kirchhoff surface that rotates with the rotor blades. The other uses a nonrotating Kirchhoff surface. Results from both methods are compared to experimental data for both high-speed impulsive noise and blade-vortex interaction noise. Agreement between experimental data and computational results is excellent for both cases. The rotating and nonrotating Kirchhoff methods are also compared for accuracy and efficiency. Both offer high accuracy with reasonable computer resource requirements. The Kirchhoff integrations efficiently extend the near-field finite-difference results to predict the far field helicopter noise.

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3

OVCHINNIKOV, Y. N., and I. M. SIGAL. "The energy of Ginzburg–Landau vortices." European Journal of Applied Mathematics 13, no. 2 (2002): 153–78. http://dx.doi.org/10.1017/s0956792501004752.

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We consider the Ginzburg–Landau equation in dimension two. We introduce a key notion of the vortex (interaction) energy. It is defined by minimizing the renormalized Ginzburg–Landau (free) energy functional over functions with a given set of zeros of given local indices. We find the asymptotic behaviour of the vortex energy as the inter-vortex distances grow. The leading term of the asymptotic expansion is the vortex self-energy while the next term is the classical Kirchhoff–Onsager Hamiltonian. To derive this expansion we use several novel techniques.

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4

Vladimirov, V. A., and K. I. Il'in. "Three-dimensional instability of an elliptic Kirchhoff vortex." Fluid Dynamics 23, no. 3 (1988): 356–60. http://dx.doi.org/10.1007/bf01054740.

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5

Crowdy, Darren, and Jonathan Marshall. "Analytical formulae for the Kirchhoff–Routh path function in multiply connected domains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2060 (2005): 2477–501. http://dx.doi.org/10.1098/rspa.2005.1492.

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Explicit formulae for the Kirchhoff–Routh path functions (or Hamiltonians) governing the motion of N -point vortices in multiply connected domains are derived when all circulations around the holes in the domain are zero. The method uses the Schottky–Klein prime function to find representations of the hydrodynamic Green's function in multiply connected circular domains. The Green's function is then used to construct the associated Kirchhoff–Routh path function. The path function in more general multiply connected domains then follows from a transformation property of the path function under conformal mapping of the canonical circular domains. Illustrative examples are presented for the case of single vortex motion in multiply connected domains.

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6

Liang, Bin, Roger M. Waxler, and Paul Markowski. "A theory for the emission of infrasound from Tornadoes." Journal of the Acoustical Society of America 155, no. 3_Supplement (2024): A202. http://dx.doi.org/10.1121/10.0027306.

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Tornadoes have been shown to radiate infrasound to great distances, however convincing fundamental sound mechanisms are still absent. After using vortex sound theory to study sound generated by two numerical tornadoes, we found that there is a significant low-frequency signal between 0.1 Hz and 1 Hz. The sound is closely related to rotation of the non-axisymmetric vorticity field and its frequency depends on the rotational frequency. The non-axisymmetric vorticity field is represented by a Kirchhoff vortex-like flow in baseline tornado model and by multiple-vortex flow in eddy injection tornado model. Interestingly, there also exist high-frequency components in the later model which are hypothesized to originate from vortex merging process. Field detection data of tornado infrasound provides some support for the low-frequency sound.

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7

Hong, Shuli, Jun Chi, Xin Xiang, and Weiyu Lu. "Theoretical Model and Numerical Analysis of the Tip Leakage Vortex Variations of a Centrifugal Compressor." Aerospace 9, no. 12 (2022): 830. http://dx.doi.org/10.3390/aerospace9120830.

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A centrifugal compressor of a micro turbine generator system is investigated by the theoretical model and numerical analysis to explore the characteristics of the tip leakage vortex as the centrifugal compressor approaches stall. The numerical simulation results show the cross-sectional shape of the tip leakage vortex is elliptical, and its long and short axes are gradually stretched as the compressor approaches stall. Moreover, the vortex trajectory is inclined to the pressure side of the adjacent blade. In addition, the Kirchhoff elliptical vortex model is introduced to analyze the flow passage constriction effect, the passage vortex squeezing effect, and the leakage flow translation effect. Results show that there is no upper limit for the flow passage constriction effect on the tip leakage vortex. Furthermore, relative to the original vortex, the minimum constriction effect depends on the axis ratio of the elliptical tip leakage vortex. The passage vortex has an expansion effect on the tip leakage vortex rather than a squeezing effect, which is limited and also depends on the axis ratio of the ellipse. However, the effect magnitude of the leakage flow depends on the scales both of the long and short axes, which also have no upper limit.

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8

Nagem, Raymond, Guido Sandri, David Uminsky, and C. Eugene Wayne. "Generalized Helmholtz–Kirchhoff Model for Two-Dimensional Distributed Vortex Motion." SIAM Journal on Applied Dynamical Systems 8, no. 1 (2009): 160–79. http://dx.doi.org/10.1137/080715056.

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9

Zhang, Xiaoxiao, Xiang Su, Zhensen Wu, and Shanzhe Wang. "Analyzing Vortex Light Beam Scattering Characteristics from a Random Rough Surface." Photonics 10, no. 9 (2023): 955. http://dx.doi.org/10.3390/photonics10090955.

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The propagation and scattering of vortex light beams in complex media have significant implications in the fields of laser imaging, optical manipulation, and communication. This paper investigates the scattering characteristics of vortex light beams from a random rough surface. Firstly, a two-dimensional Gaussian rough surface is generated using the Monte Carlo method combined with the linear filtering method. Subsequently, the vortex beams are decomposed into the superposition of infinite plane waves, and the scattering of each plane wave from the rough surface is calculated using the Kirchhoff Approximation method. Numerical results of the angle distribution and spatial distribution of OAM scattering Laser Radar Cross Section (LRCS) are presented, varying with different surface roughness parameters for a rough aluminum surface and the beam’s parameters. The results demonstrate that the scattering of vortex beams is influenced by the beam’s parameters, such as Orbital Angular Momentum (OAM) mode number and elevation angle, which may bring new insights into vortex wave-matter interactions and their applications in high resolution imaging.

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10

Fukumoto, Yasuhide. "Analogy between a vortex-jet filament and the Kirchhoff elastic rod." Fluid Dynamics Research 39, no. 7 (2007): 511–20. http://dx.doi.org/10.1016/j.fluiddyn.2006.12.004.

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11

Pérez-Chavela, Ernesto, and Sławomir Rybicki. "Topological bifurcation of relative equilibria for the Kirchhoff 8-vortex problem." Journal of Mathematical Analysis and Applications 427, no. 1 (2015): 1–16. http://dx.doi.org/10.1016/j.jmaa.2015.02.022.

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12

Müller, Bernhard, and H. C. Yee. "High order numerical simulation of sound generated by the Kirchhoff vortex." Computing and Visualization in Science 4, no. 3 (2002): 197–204. http://dx.doi.org/10.1007/s007910100072.

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13

Soifer, Viktor, Sergey Kharitonov, Svetlana Khonina, Yurii Strelkov, and Alexey Porfirev. "Spiral Caustics of Vortex Beams." Photonics 8, no. 1 (2021): 24. http://dx.doi.org/10.3390/photonics8010024.

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We discuss the nonparaxial focusing of laser light into a three-dimensional (3D) spiral distribution. For calculating the tangential and normal components of the electromagnetic field on a preset curved surface we propose an asymptotic method, using which we derive equations for calculating stationary points and asymptotic relations for the electromagnetic field components in the form of one-dimensional (1D) integrals over a radial component. The results obtained through the asymptotic approach and the direct calculation of the Kirchhoff integral are identical. For a particular case of focusing into a ring, an analytical relation for stationary points is derived. Based on the electromagnetic theory, we design and numerically model the performance of diffractive optical elements (DOEs) to generate field distributions shaped as two-dimensional (2D) and 3D light spirals with the variable angular momentum. We reveal that under certain conditions, there is an effect of splitting the longitudinal electromagnetic field component. Experimental results obtained with the use of a spatial light modulator are in good agreement with the modeling results.

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14

CROWDY, DARREN G. "Exact solutions for rotating vortex arrays with finite-area cores." Journal of Fluid Mechanics 469 (October 15, 2002): 209–35. http://dx.doi.org/10.1017/s0022112002001817.

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A class of explicit solutions of the two-dimensional Euler equations consisting of a finite-area patch of uniform vorticity surrounded by a finite distribution of co- rotating satellite line vortices is constructed. The results generalize the classic study of co-rotating vortex arrays by J. J. Thomson. For N satellite line vortices (N [ges ] 3) a continuous one-parameter family of rotating vortical equilibria is derived in which different values of the continuous parameter correspond to different shapes and areas of the central patch. In an appropriate limit, vortex patch equilibria with cusped boundaries are found. A study of the linear stability is performed and a wide range of the solutions found to be linearly stable. Contour dynamics methods are used to calculate the typical nonlinear evolution of the configurations. The results are believed to provide the only known exact solutions involving rotating vortex patches besides the classical Kirchhoff ellipse.

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15

Liang, Bin, Roger M. Waxler, and Paul Markowski. "A lower frequency signal emitted from tornadoes based on a new mechanism." Journal of the Acoustical Society of America 153, no. 3_supplement (2023): A283. http://dx.doi.org/10.1121/10.0018854.

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Tornadoes have been shown to radiate infrasound to great distances. After using Lighthill's acoustical analogy to study sound generated by a numerical tornado, we found that there is a significant low-frequency signal between 0.1 Hz and 0.5 Hz. We hypothesized that there is a Kirchhoff vortex-like source at the center of the numerical tornado. Based on vortex sound theory, characteristic frequencies only depend on the strength of the vertical vorticity which can change at different heights of the tornado. Compared to real data analysis, there is a possibility that when a tornado occurs, infrasonic sensors can detect a significant increase in low-frequency signals. This hypothesis is being tested against data collected in the field during the passage of tornado-producing storms.

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16

dos Santos, Carlos R., and Flávio D. Marques. "Lift Prediction Including Stall, Using Vortex Lattice Method with Kirchhoff-Based Correction." Journal of Aircraft 55, no. 2 (2018): 887–91. http://dx.doi.org/10.2514/1.c034451.

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17

Xue, Yu, and A. S. Lyrintzis. "Rotating Kirchhoff method for three-dimensional transonic blade-vortex interaction hover noise." AIAA Journal 32, no. 7 (1994): 1350–59. http://dx.doi.org/10.2514/3.12202.

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18

Peterson, Sean D., and Maurizio Porfiri. "Interaction of a vortex pair with a flexible plate in an ideal quiescent fluid." Journal of Intelligent Material Systems and Structures 23, no. 13 (2012): 1485–504. http://dx.doi.org/10.1177/1045389x11435995.

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The coupled interaction of a cantilevered Kirchhoff–Love plate with two vortex filaments of equal and opposite circulation in an infinite incompressible, inviscid, and irrotational fluid domain is investigated. The vortices initially advect toward the cantilevered plate, which is oriented perpendicular to the direction of propagation of the vortex pair and undergoes cylindrical bending. As the pair approaches the plate, the pressure field induced by the vortices deflects the plate and initiates vibration of the structure. The vibration of the structure, in turn, alters the path of the two vortices. The level of interaction depends on the vortex circulation and on the ratio of the plate inertia to the fluid inertia, termed the mass ratio. In general, the vortices tend to pass around the plate and eventually advect away from the plate, albeit with a modified trajectory, which depends on the strength of the fluid and structure coupling. The energy imparted to the plate increases with increasing vortex circulation and decreasing mass ratio. The findings of this study provide an initial framework for assessing the energy that can be imparted to a plate for energy harvesting purposes by coherent fluid structures in the absence of viscous effects.

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19

Konovalyuk, T. P., T. S. Krasnopolskaya, and E. D. Pechuk. "Influence of the internal dynamics of the interacting coherent vortex structures to the generated sound field." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 3 (2021): 51–54. http://dx.doi.org/10.17721/1812-5409.2021/3.7.

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The article is dedicated to the glowing memory of the talented Ukrainian scientist-mechanic, professor, doctor of physical and mathematical sciences Vyacheslav Vladimirovich Meleshko. The sound fields of several coherent vortex structures interacting with each other were calculated using the moment model (MZS-model) of the first and second orders. In the first-order MZS-model, vortices are described by point vortices, in the second-order MZS-model--by Kirchhoff vortices. Sound fields as a result of vortex interaction are calculated using the Lighthill's acoustic analogy under Powell's formulation. The spectrum of the sound field in the description of coherent vortices by point vortices is characterized by a single frequency band, which reflects the motion of the vortex centers of vortices (large-scale vortex movements). Taking into account the inner vortex dynamics leads to the expansion of spectrum and level increasing of calculated sound: the lower band describes the motion of the vorticity centers of spots, the higher band describes the internal dynamics of the vorticity. It is shown that large-scale vortex movements can be modeled by point vortices, when the sound spectrum of distributed vortices is clearly divided into bands and the width of the lower frequency band is close to the width of the sound spectrum from point vortices. The presence of an upper frequency band in the sound field of interacting vortex spots does not allow us to describe the distributed vortices as point vortices when constructing a sound source, since such a simplification leads to a significant underestimation of the level of the calculated sound field.

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MITCHELL, BRIAN E., SANJIVA K. LELE, and PARVIZ MOIN. "Direct computation of the sound generated by vortex pairing in an axisymmetric jet." Journal of Fluid Mechanics 383 (March 25, 1999): 113–42. http://dx.doi.org/10.1017/s0022112099003869.

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The sound generated by vortex pairing in axisymmetric jets is determined by direct solution of the compressible Navier–Stokes equations on a computational grid that includes both the near field and a portion of the acoustic far field. At low Mach number, the far-field sound has distinct angles of extinction in the range of 60°–70° from the jet's downstream axis which can be understood by analogy to axisymmetric, compact quadrupoles. As the Mach number is increased, the far-field sound takes on a superdirective character with the dominant sound directed at shallow angles to the jet's downstream axis. The directly computed sound is compared to predictions obtained from Lighthill's equation and the Kirchhoff surface method. These predictions are in good agreement with the directly computed data. The Lighthill source terms have a large spatial distribution in the axial direction necessitating the introduction of a model to describe the source terms in the region downstream of the last vortex pairing. The axial non-compactness of the quadrupole sources must be adequately treated in the prediction method.

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21

Ewert, R., J. W. Delfs, and M. Lummer. "The Simulation of Airframe Noise Applying Euler-Perturbation and Acoustic Analogy Approaches." International Journal of Aeroacoustics 4, no. 1-2 (2005): 69–91. http://dx.doi.org/10.1260/1475472053729996.

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The capability of three different perturbation approaches to tackle airframe noise problems is studied. The three approaches represent different levels of complexity and are applied to trailing edge noise problems. In the Euler-perturbation approach the linearized Euler equations without sources are used as governing acoustic equations. The sound generation and propagation is studied for several trailing edge shapes (blunt, sharp, and round trailing edges) by injecting upstream of the trailing edge test vortices into the mean-flow field. The efficiency to generate noise is determined for the trailing edge shapes by comparing the different generated sound intensities due to an initial standard vortex. Mach number scaling laws are determined varying the mean-flow Mach number. In the second simulation approach an extended acoustic analogy based on acoustic perturbation equations (APEs) is applied to simulate trailing edge noise of a flat plate. The acoustic source terms are computed from a synthetic turbulent velocity model. Furthermore, the far field is computed via additional Kirchhoff extrapolation. In the third approach the sources of the extended acoustic analogy are computed from a Large Eddy Simulation (LES) of the compressible flow problem. The directivities due to a modeled and a LES based source, respectively, compare qualitatively well in the near field. In the far field the asymptotic directivities from the Kirchhoff extrapolation agree very well with the analytical solution of Howe. Furthermore, the sound pressure spectra can be shown to have similar shape and magnitude for the last two approaches.

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SI, HAI-QING, and TONG-GUANG WANG. "CALCULATION OF THE UNSTEADY AIRLOADS ON WIND TURBINE BLADES UNDER YAWED FLOW." Modern Physics Letters B 23, no. 03 (2009): 493–96. http://dx.doi.org/10.1142/s0217984909018734.

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A dynamic stall model is coupled with the blade element momentum theory to calculate the cyclic variation of the aerodynamic characteristics of the wind turbine in yawed flow. In the dynamic stall model, unsteady effects under attached flow conditions are simulated by the superposition of indicial aerodynamic responses. The movement of the unsteady flow separation point is related to the static separation based on the Kirchhoff flow model via a deficiency function, in which the unsteady boundary layer response and the leading edge pressure response are taken into consideration. The induced vortex force and the associated pitching moment are represented empirically in a time-dependent manner during dynamic stall. The required input of the inflow velocity and incidence to the dynamic stall model is calculated using the improved blade element momentum theory. The calculated results are compared well with the NREL UAE Phase VI experimental data. For completeness, possible factors causing the difference between calculated and experimental results are analyzed and discussed in detail in this paper.

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23

Gai, S. L. "Some features of steady separated flow from low speed to hypersonic." Aeronautical Journal 112, no. 1128 (2008): 109–13. http://dx.doi.org/10.1017/s0001924000002049.

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Steady non-vortex shedding base flow behind a bluff body is considered. Such a flow is characterised by the flow separation at the trailing edge of the body with an emerging shear layer which reattaches on the axis with strong recompression and recirculating flow bounded by the base, the shear layer, and the axis. Steady wake flows behind a bluff body at low speeds have been studied for more than a century (for example, Kirchhoff; Riabouchinsky). Recently, research on steady bluff body wake flow at low speeds has been reviewed and reinterpreted by Roshko. Roshko has also commented on some basic aspects of steady supersonic base flow following on from Chapman and Korst analyses. In the present paper, we examine the steady base flow features both at low speeds and supersonic speeds in the light of Roshko’s model and expand on some further aspects of base flows at supersonic and hypersonic speeds, not covered by Roshko.

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24

Zang, Huaping, Jingzhe Li, Chenglong Zheng, et al. "The Generation of Equal-Intensity and Multi-Focus Optical Vortices by a Composite Spiral Zone Plate." Photonics 11, no. 5 (2024): 466. http://dx.doi.org/10.3390/photonics11050466.

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We propose a new vortex lens for producing multiple focused coaxial vortices with approximately equal intensities along the optical axis, termed equal-intensity multi-focus composite spiral zone plates (EMCSZPs). In this typical methodology, two concentric conventional spiral zone plates (SZPs) of different focal lengths were composited together and the alternate transparent and opaque zones were arranged with specific m-bonacci sequence. Based on the Fresnel–Kirchhoff diffraction theory, the focusing properties of the EMCSZPs were calculated in detail and the corresponding demonstration experiment was been carried out to verify our proposal. The investigations indicate that the EMCSZPs indeed exhibit superior performance, which accords well with our physical design. In addition, the topological charges (TCs) of the multi-focus vortices can be flexibly selected and controlled by optimizing the parameters of the zone plates. These findings which were demonstrated by the performed experiment may open new avenues towards improving the performance of biomedical imaging, quantum computation and optical manipulation.

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Ramos, Juan I. "Finite Difference Methods Based on the Kirchhoff Transformation and Time Linearization for the Numerical Solution of Nonlinear Reaction–Diffusion Equations." Computation 12, no. 11 (2024): 218. http://dx.doi.org/10.3390/computation12110218.

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Four formulations based on the Kirchhoff transformation and time linearization for the numerical study of one-dimensional reaction–diffusion equations, whose heat capacity, thermal inertia and reaction rate are only functions of the temperature, are presented. The formulations result in linear, two-point boundary-value problems for the temperature, energy or heat potential, and may be solved by either discretizing the second-order spatial derivative or piecewise analytical integration. In both cases, linear systems of algebraic equations are obtained. The formulation for the temperature is extended to two-dimensional, nonlinear reaction–diffusion equations where the resulting linear two-dimensional operator is factorized into a sequence of one-dimensional ones that may be solved by means of any of the four formulations developed for one-dimensional problems. The multidimensional formulation is applied to a two-dimensional, two-equation system of nonlinearly coupled advection–reaction–diffusion equations, and the effects of the velocity and the parameters that characterize the nonlinear heat capacities and thermal conductivity are studied. It is shown that clockwise-rotating velocity fields result in wave stretching for small vortex radii, and wave deceleration and thickening for counter-clockwise-rotating velocity fields. It is also shown that large-core, clockwise-rotating velocity fields may result in large transient periods, followed by time intervals of apparent little activity which, in turn, are followed by the propagation of long-period waves.

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Candelier, Fabien, Mathieu Porez, and Frederic Boyer. "Note on the swimming of an elongated body in a non-uniform flow." Journal of Fluid Mechanics 716 (January 28, 2013): 616–37. http://dx.doi.org/10.1017/jfm.2012.560.

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AbstractThis paper presents an extension of Lighthill’s large-amplitude elongated-body theory of fish locomotion which enables the effects of an external weakly non-uniform potential flow to be taken into account. To do so, the body is modelled as a Kirchhoff beam, made up of elliptical cross-sections whose size may vary along the body, undergoing prescribed deformations consisting of yaw and pitch bending. The fluid velocity potential is decomposed into two parts corresponding to the unperturbed potential flow, which is assumed to be known, and to the perturbation flow. The Laplace equation and the corresponding Neumann’s boundary conditions governing the perturbation velocity potential are expressed in terms of curvilinear coordinates which follow the body during its motion, thus allowing the boundary of the body to be considered as a fixed surface. Equations are simplified according to the slenderness of the body and the weakness of the non-uniformity of the unperturbed flow. These simplifications allow the pressure acting on the body to be determined analytically using the classical Bernoulli equation, which is then integrated over the body. The model is finally used to investigate the passive and the active swimming of a fish in a Kármán vortex street.

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HAZEL, ANDREW L., and MATTHIAS HEIL. "Three-dimensional airway reopening: the steady propagation of a semi-infinite bubble into a buckled elastic tube." Journal of Fluid Mechanics 478 (March 10, 2003): 47–70. http://dx.doi.org/10.1017/s0022112002003452.

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We consider the steady propagation of an air finger into a buckled elastic tube initially filled with viscous fluid. This study is motivated by the physiological problem of pulmonary airway reopening. The system is modelled using geometrically nonlinear Kirchhoff–Love shell theory coupled to the free-surface Stokes equations. The resulting three-dimensional fluid–structure-interaction problem is solved numerically by a fully coupled finite element method.The system is governed by three dimensionless parameters: (i) the capillary number, Ca=μU/σ*, represents the ratio of viscous to surface-tension forces, where μ is the fluid viscosity, U is the finger's propagation speed and σ* is the surface tension at the air–liquid interface; (ii) σ=σ*/(RK) represents the ratio of surface tension to elastic forces, where R is the undeformed radius of the tube and K its bending modulus; and (iii) A∞=A*∞/(4R2), characterizes the initial degree of tube collapse, where A*∞ is the cross-sectional area of the tube far ahead of the bubble.The generic behaviour of the system is found to be very similar to that observed in previous two-dimensional models (Gaver et al. 1996; Heil 2000). In particular, we find a two-branch behaviour in the relationship between dimensionless propagation speed, Ca, and dimensionless bubble pressure, p*b/(σ*/R). At low Ca, a decrease in p*b is required to increase the propagation speed. We present a simple model that explains this behaviour and why it occurs in both two and three dimensions. At high Ca, p*b increases monotonically with propagation speed and p*b/(σ*/R) ∝ Ca for sufficiently large values of σ and Ca. In a frame of reference moving with the finger velocity, an open vortex develops ahead of the bubble tip at low Ca, but as Ca increases, the flow topology changes and the vortex disappears.An increase in dimensional surface tension, σ*, causes an increase in the bubble pressure required to drive the air finger at a given speed; p*b also increases with A*∞ and higher bubble pressures are required to open less strongly buckled tubes. This unexpected finding could have important physiological ramifications. If σ* is sufficiently small, steady airway reopening can occur when the bubble pressure is lower than the external (pleural) pressure, in which case the airway remains buckled (non-axisymmetric) after the passage of the air finger. Furthermore, we find that the maximum wall shear stresses exerted on the airways during reopening may be large enough to damage the lung tissue.

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Miyazaki, Takeshi, and Hideshi Hanazaki. "Baroclinic instability of Kirchhoff's elliptic vortex." Journal of Fluid Mechanics 261 (February 25, 1994): 253–71. http://dx.doi.org/10.1017/s0022112094000339.

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The linear instability of Kirchhoff's elliptic vortex in a vertically stratified rotating fluid is investigated using the quasi-geostrophic, f-plane approximation. Any elliptic vortex is shown to be unstable to baroclinic disturbances of azimuthal wavenumber m = 1 (bending mode) and m = 2 (elliptical deformation). The axial wavenumber of the unstable bending mode approaches Λc = 1.7046 in the limit of small ellipticity, indicating that it is a short-wave baroclinic instability. The instability occurs when the bending wave rotates around the vortex axis with angular velocity identical to the rotation rate of the undisturbed elliptic vortex. On the other hand, the wavenumber of the elliptical deformation mode approaches zero in the same limit, showing that it is a long-wave sideband instability.

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Miyazaki, Takeshi, Takeshi Imai, and Yasuhide Fukumoto. "Three‐dimensional instability of Kirchhoff’s elliptic vortex." Physics of Fluids 7, no. 1 (1995): 195–202. http://dx.doi.org/10.1063/1.868719.

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Miyazaki, Takeshi, and Hideshi Hanazaki. "Corrigenda: Baroclinic instability of Kirchhoff's elliptic vortex." Journal of Fluid Mechanics 274 (September 10, 1994): 405. http://dx.doi.org/10.1017/s002211209400217x.

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Xiong, Jiaming, Song Sang, Youwei Du, Chaojie Gan, Ao Zhang, and Fugang Liu. "Kinematic Stability Analysis of Anchor Cable Structures in Submerged Floating Tunnel under Combined Parametric–Vortex Excitation." Journal of Marine Science and Engineering 12, no. 9 (2024): 1478. http://dx.doi.org/10.3390/jmse12091478.

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The submerged floating tunnel is a marine transportation infrastructure that links two shorelines. The tunnel tube body’s buoyancy exceeds gravity, with anchoring ensuring equilibrium. Anchoring reliability is crucial. This study presents a three-way coupled kinematic model for the mooring structure, formulated on Hamilton’s principle and Kirchhoff’s assumption. It explores the impact of the tube body’s buoyancy-to-weight ratio and the sea current’s angle of incidence on mooring motion response. By solving the motion analysis model, Hill’s equation system is derived to assess the parameter instability of the anchor cable structure. The coefficient of excitation instability intervals for the submerged floating tunnel is determined and validated. The findings indicate the following: (1) Increasing the float-weight ratio reduces displacement response amplitudes in all directions, bringing downstream and transverse currents closer to their initial positions; (2) Changes in current direction angles result in decreased downstream excitation strength and increased transverse displacement response with the same excitation direction; (3) The instability interval visualization effectively predicts anchor cable structure instability under parametric excitation. Structures within the instability region are deemed unstable, while those outside are considered stable.

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32

Ceci, Stefano, and Christian Seis. "On the dynamics of point vortices for the two-dimensional Euler equation with L ^p vorticity." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, no. 2226 (2022). http://dx.doi.org/10.1098/rsta.2021.0046.

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We study the evolution of solutions to the two-dimensional Euler equations whose vorticity is sharply concentrated in the Wasserstein sense around a finite number of points. Under the assumption that the vorticity is merely L p integrable for some p > 2 , we show that the evolving vortex regions remain concentrated around points, and these points are close to solutions to the Helmholtz–Kirchhoff point vortex system. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.

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33

McPhail, Michael, and Michael Krane. "Aeroacoustic source prediction using material surfaces bounding the flow." Fluid Dynamics Research, May 9, 2022. http://dx.doi.org/10.1088/1873-7005/ac6e02.

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Abstract This article presents an extension of Liepmann's characterization of an aeroacoustic source in terms of the motion of a bounding surface containing the source region. Rather than using an arbitrary surface, we express the problem in terms of bounding material surfaces, identified by Lagrangian Coherent Structures (LCS), which demarcate flow into regions with distinct dynamics. The sound generation of the flow is written in terms of the motion of these material surfaces using the Kirchhoff integral equation, so that the flow noise problem now appears like that of a deforming body. This approach provides a natural connection between the flow topology, as revealed through LCS analysis, and sound generation mechanisms. As examples, we examine two-dimensional cases of corotating vortices and leap-frogging vortex pairs and compare estimated sound sources to vortex sound theory.

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Ahmedou, Mohameden, Thomas Bartsch, and Tim Fiernkranz. "Equilibria of vortex type Hamiltonians on closed surfaces." Topological Methods in Nonlinear Analysis, February 26, 2023, 1–18. http://dx.doi.org/10.12775/tmna.2023.003.

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We prove the existence of critical points of vortex type Hamiltonians \[ H(p_1,\ldots, p_N) = \sum_{{i,j=1}\atop{i\ne j}} ^N \Gamma_i\Gamma_jG(p_i,p_j)+\Psi(p_1,\dots,p_N) \] on a closed Riemannian surface $(\Sigma,g)$ which is not homeomorphic to the sphere or the projective plane. Here $G$ denotes the Green function of the Laplace-Beltrami operator in $\Sigma$, $\Psi\colon \Sigma^N\to\mathbb{R}$ may be any function of class ${\mathcal C}^1$, and $\Gamma_1,\dots,\Gamma_N\in\mathbb{R}\setminus\{0\}$ are the vorticities. The Kirchhoff-Routh Hamiltonian from fluid dynamics corresponds to $\Psi(p) = -\sum\limits_{i=1}^N \Gamma_i^2h(p_i,p_i)$ where $h\colon \Sigma\times\Sigma\to\mathbb{R}$ is the regular part of the Laplace-Beltrami operator. We obtain critical points $p=(p_1,\dots,p_N)$ for arbitrary $N$ and vorticities $(\Gamma_1,\dots,\Gamma_N)$ in $\mathbb{R}^N\setminus V$ where $V$ is an explicitly given algebraic variety of codimension 1.

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35

Edgar Moafo Wembe, Boris, Olivier Cots, and Bernard Bonnard. "A Zermelo navigation problem with a vortex singularity." ESAIM: Control, Optimisation and Calculus of Variations, August 25, 2020. http://dx.doi.org/10.1051/cocv/2020058.

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Helhmoltz-Kirchhoff equations of motions of vortices of an incompressible fluid in the plane define a dynamics with singularities and this leads to a Zermelo navigation problem describing the ship travel in such a field where the control is the heading angle. Considering one vortex, we define a time minimization problem, geometric frame being the extension of Randers metrics in the punctured plane, with rotational symmetry. Candidates as minimizers are parameterized thanks to the Pontryagin Maximum Principle as extremal solutions of a Hamiltonian vector field. We analyze the time minimal solution to transfer the ship between two points where during the transfer the ship can be either in a strong current region in the vicinity of the vortex or in a weak current region. Analysis is based on a micro-local classification of the extremals using mainly the integrability properties of the dynamics due to the rotational symmetry. The discussion is complex and related to the existence of an isolated extremal (Reeb) circle due to the vortex singularity. Explicit computation of cut points where the extremal curves cease to be optimal is given and the spheres are described in the case where at the initial point the current is weak.

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36

Miyoshi, Hiroyuki, Hiroki Miyazako, and Takaaki Nara. "Free energy formulae for confined nematic liquid crystals based on analogies with Kirchhoff–Routh theory in vortex dynamics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 480, no. 2300 (2024). http://dx.doi.org/10.1098/rspa.2024.0405.

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Active nematics are influenced by alignment angle singularities called topological defects. The localization of these defects is of major interest for biological applications. The total distortion of alignment angles due to defects is evaluated using Frank free energy, which is one of the criteria used to determine the location and stability of these defects. Previous work used the line integrals of a complex potential associated with the alignments for the energy calculation (Miyazako and Nara 2022 R. Soc. Open Sci . 9 , 211663 (doi: 10.1098/rsos.211663 )), which has a high computational cost. We propose analytical formulae for the free energy in the presence of multiple topological defects in confined geometries. The formulae derived here are an analogue of Kirchhoff–Routh functions in vortex dynamics. The proposed formulae are explicit with respect to the defect locations and conformal maps, which enable the explicit calculation of the energy extrema. The formulae are applied to calculate the locations of defects in so-called doublets and triplets by solving simple polynomial formulae. A stability analysis is also conducted to detect whether defect pairs with charges ± 1 / 2 are stable or unstable in triplet regions. Our numerical results are shown to match the experimental results (Ienaga et al. 2023 Soft Matter 19 , 5016–5028. (doi: 10.1039/d3sm00071k )).

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37

Zang, Huaping, Baozhen Wang, Chenglong Zheng, et al. "Performance analysis of single-focus phase singularity based on elliptical reflective annulus quadrangle-element coded spiral zone plates." Chinese Physics B, June 14, 2023. http://dx.doi.org/10.1088/1674-1056/acde4f.

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Abstract Optical vortices generated by the conventional vortex lens are usually disturbed by the undesired higher order foci which may lead to additional artifacts and thus degrade contrast sensitivity. Herein, in this work, we propose an efficient methodology to combine the merit of elliptical reflective zone plates (ERZPs) and the advantage of spiral zone plates (SZPs) in establishing a specific single optical element, termed elliptical reflective annulus quadrangle-element coded spiral zone plates (ERAQSZPs) to generate single-focus phase singularity. Differing from the abrupt reflectance of the ERZPs, series of randomly distributed nanometer apertures are adopted to realize the sinusoidal reflectance. Typically, according to our physical design, the ERAQSZPs are fabricated on a bulk substrate, therefore, the new idea can significantly reduce the difficulty in the fabrication process. Based on the Kirchhoff diffraction theory and convolution theorem, the focusing performance of ERAQSZPs was calculated. The results reveal that, apart from the capability of generating optical vortices, ERAQSZPs can also integrate the function of focusing, energy selection, higher order foci elimination as well as high spectral resolution together. In addition, the focusing properties can be further improved by appropriately adjusting the parameters such as zone number and the size of the consisted primitives. These findings are expected to direct a new direction towards improving the performance of optical capture, x-ray fluorescence spectra, and forbidden transition.

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38

Elgammi, Moutaz, and Tonio Sant. "A Modified Beddoes–Leishman Model for Unsteady Aerodynamic Blade Load Computations on Wind Turbine Blades." Journal of Solar Energy Engineering 138, no. 5 (2016). http://dx.doi.org/10.1115/1.4034241.

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A modified version of the Beddoes–Leishman (B-L) dynamic stall model is presented. A novel approach was applied for deriving the effective flow separation points using two-dimensional (2D) static wind tunnel test data in conjunction with Kirchhoff's model. The results were then fitted in a least-squares sense using a new nonlinear model that gives a better fit for the effective flow separation point under a wide range of operating conditions with fewer curve fitting coefficients. Another model, based on random noise generation, was also integrated within the B-L model to simulate the effects of vortex shedding more realistically. The modified B-L model was validated using 2D experimental data for the S809 and NACA 4415 aerofoils under both steady and unsteady (oscillating) conditions. The model was later embedded in a free-wake vortex model to estimate the unsteady aerodynamic loads on the NREL Phase VI rotor blades consisting of S809 aerofoils when operating under yawed rotor conditions. The results in this study confirm the effectiveness of the proposed modifications to the B-L method under both 2D and three-dimensional (3D) (rotating) conditions.

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39

Shashikanth, Banavara N. "Application of Kirchhoff’s equations of motion to the dynamically coupled system of a rigid body with a completely-liquid-filled cavity." Mathematics and Mechanics of Solids, February 17, 2023, 108128652311513. http://dx.doi.org/10.1177/10812865231151391.

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This paper considers the dynamical problem of a rigid body with a cavity that is completely filled by a liquid. The dynamically coupled motion of the rigid body and the liquid is examined in the absence of any external forces or torques. This problem is not new, but the paper draws attention to the fact that Kirchhoff’s equation of motion, which was derived for the dynamically coupled motion of a homogeneous rigid body fully immersed in a liquid, applies to this problem as well. The methodology is explained. Details of a simple, idealized planar example, in which a vorticity field in the form of a single point vortex is also added to the fluid flow field, are presented. In principle, this simple model could be extended to an elastodynamic model to study the dynamically coupled motion of an elastic body and a cavity completely filled with liquid in the framework of linear elasticity.

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