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1
Cho, H. C., und F. C. Chou. „Rivulet Instability with Effect of Coriolis Force“. Journal of Mechanics 22, Nr. 3 (September 2006): 221–27. http://dx.doi.org/10.1017/s1727719100000861.
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AbstractThe effect of Coriolis force on the rivulet (fingering) instability, the onset of rivulet phenomena during spin coating, is investigated by flow visualization experiments incorporating with dimensional analysis. This study demonstrates that the Coriolis force will affect significantly the critical radius of rivulet instability and the deflection angle of instability rivulet. For the cases of low Bond number, the effect of Coriolis force is a stabilizing factor, and the dimensionless critical radius increases slightly with increasing rotational Reynolds number Reω. In the case of high Bond number, the effect of Coriolis force becomes a destabilizing factor while Reω < 1, and a characteristic length is found by balancing the viscous force with the surface tension. For Reω > 1, the radial Corilois force, which is always pointing inward, plays a stabilizing role with magnitude Reω2.
2
Khiri, Rachid. „Coriolis effect on convection for a low Prandtl number fluid“. International Journal of Non-Linear Mechanics 39, Nr. 4 (Juni 2004): 593–604. http://dx.doi.org/10.1016/s0020-7462(02)00225-1.
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3
Nakabayashi, Koichi, und Osami Kitoh. „Low Reynolds number fully developed two-dimensional turbulent channel flow with system rotation“. Journal of Fluid Mechanics 315 (25.05.1996): 1–29. http://dx.doi.org/10.1017/s0022112096002303.
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Theoretical and experimental studies have been performed on fully developed twodimensional turbulent channel flows in the low Reynolds number range that are subjected to system rotation. The turbulence is affected by the Coriolis force and the low Reynolds number simultaneously. Using dimensional analysis, the relevant parameters of this flow are found to be Reynolds number Re* = u*D/v (u* is the friction velocity, D the channel half-width) and Ωv/u2* (Ω is the angular velocity of the channel) for the inner region, and Re* and ΩD/u* for the core region. Employing these parameters, changes of skin friction coefficients and velocity profiles compared to nonrotating flow can be reasonably well understood. A Coriolis region where the Coriolis force effect predominates is shown to exist in addition to conventional regions such as viscous and buffer regions. A flow regime diagram that indicates ranges of these regions as a function of Re* and |Ω|v/u2* is given from which the overall flow structure in a rotating channel can be obtained.Experiments have been made in the range of 56 ≤ Re* ≤ 310 and -0.0057 ≤ Ωv/u2* ≤ 0.0030 (these values correspond to Re = 2UmD/v from 1700 to 10000 and rotation number R0 = 2|Ω|D/Um up to 0.055; Um is bulk mean velocity). The characteristic features of velocity profiles and the variation of skin friction coefficients are discussed in relation to the theoretical considerations.
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Ivers, D. J., A. Jackson und D. Winch. „Enumeration, orthogonality and completeness of the incompressible Coriolis modes in a sphere“. Journal of Fluid Mechanics 766 (04.02.2015): 468–98. http://dx.doi.org/10.1017/jfm.2015.27.
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AbstractWe consider incompressible flows in the rapid-rotation limit of small Rossby number and vanishing Ekman number, in a bounded volume with a rigid impenetrable rotating boundary. Physically the flows are inviscid, almost rigid rotations. We interpret the Coriolis force, modified by a pressure gradient, as a linear operator acting on smooth inviscid incompressible flows in the volume. The eigenfunctions of the Coriolis operator $\boldsymbol{{\mathcal{C}}}$ so defined are the inertial modes (including any Rossby modes) and geostrophic modes of the rotating volume. We show $\boldsymbol{{\mathcal{C}}}$ is a bounded operator and that $-\text{i}\boldsymbol{{\mathcal{C}}}$ is symmetric, so that the Coriolis modes of different frequencies are orthogonal. We prove that the space of incompressible polynomial flows of degree $N$ or less in a sphere is invariant under $\boldsymbol{{\mathcal{C}}}$. The symmetry of $-\text{i}\boldsymbol{{\mathcal{C}}}$ thus implies the Coriolis operator is non-defective on the finite-dimensional space of spherical polynomial flows. This enables us to enumerate the Coriolis modes, and to establish their completeness using the Weierstrass polynomial approximation theorem. The fundamental tool, which is required to establish invariance of spherical polynomial flows under $\boldsymbol{{\mathcal{C}}}$ and completeness, is that the solution of the polynomial Poisson–Neumann problem, i.e. Poisson’s equation with a Neumann boundary condition and polynomial data, in a sphere is a polynomial. We also enumerate the Coriolis modes in a sphere, with careful consideration of the geostrophic modes, directly from the known analytic solutions.
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Kumar, Vivek, und Martin Anklin. „Numerical simulations of Coriolis flow meters for low Reynolds number flows“. MAPAN 26, Nr. 3 (September 2011): 225–35. http://dx.doi.org/10.1007/s12647-011-0021-6.
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6
Chan, Kwing L. „‘Negative’ surface differential rotation in stars having low Coriolis numbers (slow rotation or high turbulence)“. Proceedings of the International Astronomical Union 5, S264 (August 2009): 219–21. http://dx.doi.org/10.1017/s1743921309992663.
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AbstractA general picture of differential rotation in cool stars is that they are ‘solar-like’, with the equator spinning faster than the poles. Such surface differential rotation profiles have also been demonstrated by some three-dimensional simulations. In our numerical investigation of rotating convection (both regional and global), we found that this picture is not universally applicable. The equator may spin substantially slower than the poles (Ωequator − Ωpole)/Ω can reach −50%). The key parameter that determines the transition in behavior is the Coriolis number (inverse Rossby number). ‘Negative’ differential rotation of the equator (relative to the mean rotation) occurs if the Coriolis number is below a critical value.
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Eley, R., C. H. J. Fox und S. McWilliam. „The dynamics of a vibrating-ring multi-axis rate gyroscope“. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 214, Nr. 12 (01.12.2000): 1503–13. http://dx.doi.org/10.1243/0954406001523443.
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A novel, multi-axis rate sensor based on the vibration properties of a ring structure is presented. Vibrating ring structures have been used successfully to detect rates applied about the axis perpendicular to the plane of the ring using Coriolis coupling between in-plane displacements. The presented multi-axis sensor is capable of detecting rate applied about three mutually perpendicular axes using Coriolis coupling between in-plane and out-of-plane displacements. The steady state amplitude of the induced displacements are proportional to the applied rate. Coriolis coupling is only present for certain combinations of in-plane and out-of-plane displacement patterns, which allows a number of feasible concepts for two- and three-axis rate sensitivity.
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Oke, Abayomi S., Winifred N. Mutuku, Mark Kimathi und Isaac L. Animasaun. „Insight into the dynamics of non-Newtonian Casson fluid over a rotating non-uniform surface subject to Coriolis force“. Nonlinear Engineering 9, Nr. 1 (13.10.2020): 398–411. http://dx.doi.org/10.1515/nleng-2020-0025.
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AbstractCasson fluid model is the most accurate mathematical expression for investigating the dynamics of fluids with non-zero plastic dynamic viscosity like that of blood. Despite huge number of published articles on the transport phenomenon, there is no report on the increasing effects of the Coriolis force. This report presents the significance of increasing not only the Coriolis force and reducing plastic dynamic viscosity, but also the Prandtl number and buoyancy forces on the motion of non-Newtonian Casson fluid over the rotating non-uniform surface. The relevant body forces are derived and incorporated into the Navier-Stokes equations to obtain appropriate equations for the flow of Newtonian Casson fluid under the action of Coriolis force. The governing equations are non-dimensionalized using Blasius similarity variables to reduce the nonlinear partial differential equations to nonlinear ordinary differential equations. The resulting system of nonlinear ordinary differential equations is solved using the Runge-Kutta-Gills method with the Shooting technique, and the results depicted graphically. An increase in Coriolis force and non-Newtonian parameter decreases the velocity profile in the x-direction, causes a dual effect on the shear stress, increases the temperature profiles, and increases the velocity profile in the z-direction.
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Riahi, D. H. „The effect of Coriolis force on nonlinear convection in a porous medium“. International Journal of Mathematics and Mathematical Sciences 17, Nr. 3 (1994): 515–36. http://dx.doi.org/10.1155/s0161171294000761.
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Nonlinear convection in a porous medium and rotating about vertical axis is studied in this paper. An upper bound to the heat flux is calculated by the method initiated first by Howard [6] for the case of infinite Prandtl number.ForTa≪0(1), the rotational effect is not significant. For0(1)≪Ta≪0(RlogR), the Nusselt number decreases with increasingTafor a given Rayleigh numberR. The flow has always a finite number of modes, but with increasingTain this region, the number of modes decreases. The functional dependence of the Nusselt number onRandTais found to have discontinuities as the number of modesN*reduces toN*−1. For0(RlogR)≪Ta≪0(R), the Nusselt number is proportional toRTa(logRTa). The stabilizing effect of rotation is so strong that the optimal solution has left with only one horizontal mode. ForTa=0(R), the Nusselt number becomes0(1)and the convection is inhibited entirely by rotation forTa>1π2R.
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Chan, Kwing L. „A finite-difference convective model for Jupiter's equatorial jet“. Proceedings of the International Astronomical Union 2, S239 (August 2006): 230–32. http://dx.doi.org/10.1017/s174392130700049x.
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AbstractWe present results of a numerical model for studying the dynamics of Jupiter's equatorial jet. The computed domain is a piece of spherical shell around the equator. The bulk of the region is convective, with a thin radiative layer at the top. The shell is spinning fast, with a Coriolis number = ΩL/V on the order of 50. A prominent super-rotating equatorial jet is generated, and secondary alternating jets appear in the higher latitudes. The roles of terms in the zonal momentum equation are analyzed. Since both the Reynolds number and the Taylor number are large, the viscous terms are small. The zonal momentum balance is primarily between the Coriolis and the Reynolds stress terms.
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Salinas, Jorge S., Thomas Bonometti, Marius Ungarish und Mariano I. Cantero. „Rotating planar gravity currents at moderate Rossby numbers: fully resolved simulations and shallow-water modelling“. Journal of Fluid Mechanics 867 (20.03.2019): 114–45. http://dx.doi.org/10.1017/jfm.2019.152.
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The flow of a gravity current of finite volume and density $\unicode[STIX]{x1D70C}_{1}$ released from rest from a rectangular lock (of height $h_{0}$) into an ambient fluid of density $\unicode[STIX]{x1D70C}_{0}$ (${<}\unicode[STIX]{x1D70C}_{1}$) in a system rotating with $\unicode[STIX]{x1D6FA}$ about the vertical $z$ is investigated by means of fully resolved direct numerical simulations (DNS) and a theoretical model (based on shallow-water and Ekman layer spin-up theories, including mixing). The motion of the dense fluid includes several stages: propagation in the $x$-direction accompanied by Coriolis acceleration/deflection in the $-y$-direction, which produces a quasi-steady wedge-shaped structure with significant anticyclonic velocity $v$, followed by a spin-up reduction of $v$ accompanied by a slow $x$ drift, and oscillation. The theoretical model aims to provide useful insights and approximations concerning the formation time and shape of wedge, and the subsequent spin-up effect. The main parameter is the Coriolis number, ${\mathcal{C}}=\unicode[STIX]{x1D6FA}h_{0}/(g^{\prime }h_{0})^{1/2}$, where $g^{\prime }=(\unicode[STIX]{x1D70C}_{1}/\unicode[STIX]{x1D70C}_{0}-1)g$ is the reduced gravity. The DNS results are focused on a range of relatively small Coriolis numbers, $0.1\leqslant {\mathcal{C}}\leqslant 0.25$ (i.e. Rossby number $Ro=1/(2{\mathcal{C}})$ in the range $2\leqslant Ro\leqslant 5$), and a large range of Schmidt numbers $1\leqslant Sc<\infty$; the Reynolds number is large in all cases. The current spreads out in the $x$ direction until it is arrested by the Coriolis effect (in ${\sim}1/4$ revolution of the system). A complex motion develops about this state. First, we record oscillations on the inertial time scale $1/\unicode[STIX]{x1D6FA}$ (which are a part of the geostrophic adjustment), accompanied by vortices at the interface. Second, we note the spread of the wedge on a significantly longer time scale; this is an indirect spin-up effect – mixing and entrainment reduce the lateral (angular) velocity, which in turn decreases the Coriolis support to the $\unicode[STIX]{x2202}h/\unicode[STIX]{x2202}x$ slope of the wedge shape. Contrary to non-rotating gravity currents, the front does not remain sharp as it is subject to (i) local stretching along the streamwise direction and (ii) convective mixing due to Kelvin–Helmholtz vortices generated by shear along the spanwise direction and stemming from Coriolis effects. The theoretical model predicts that the length of the wedge scales as ${\mathcal{C}}^{-2/3}$ (in contrast to the Rossby radius $\propto 1/{\mathcal{C}}$ which is relevant for large ${\mathcal{C}}$; and in contrast to ${\mathcal{C}}^{-1/2}$ for the axisymmetric lens).
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van der Laan, Maarten Paul, Mark Kelly, Rogier Floors und Alfredo Peña. „Rossby number similarity of an atmospheric RANS model using limited-length-scale turbulence closures extended to unstable stratification“. Wind Energy Science 5, Nr. 1 (26.03.2020): 355–74. http://dx.doi.org/10.5194/wes-5-355-2020.
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Abstract. The design of wind turbines and wind farms can be improved by increasing the accuracy of the inflow models representing the atmospheric boundary layer. In this work we employ one-dimensional Reynolds-averaged Navier–Stokes (RANS) simulations of the idealized atmospheric boundary layer (ABL), using turbulence closures with a length-scale limiter. These models can represent the mean effects of surface roughness, Coriolis force, limited ABL depth, and neutral and stable atmospheric conditions using four input parameters: the roughness length, the Coriolis parameter, a maximum turbulence length, and the geostrophic wind speed. We find a new model-based Rossby similarity, which reduces the four input parameters to two Rossby numbers with different length scales. In addition, we extend the limited-length-scale turbulence models to treat the mean effect of unstable stratification in steady-state simulations. The original and extended turbulence models are compared with historical measurements of meteorological quantities and profiles of the atmospheric boundary layer for different atmospheric stabilities.
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Kloosterziel, R. C., G. F. Carnevale und P. Orlandi. „Equatorial inertial instability with full Coriolis force“. Journal of Fluid Mechanics 825 (19.07.2017): 69–108. http://dx.doi.org/10.1017/jfm.2017.377.
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The zonally symmetric inertial instability of oceanic near-equatorial flows is studied through high-resolution numerical simulations. In homogeneous upper layers, the instability of surface-confined westward currents implies potentially fast downward mixing of momentum with a predictable final equilibrium. With increasing Reynolds number, latitudinal scales along the surface associated with the instability become ever smaller and initially the motions are ever more concentrated underneath the surface. The results suggest that even if the upper layer is stratified, it may still be necessary to include the full Coriolis force in the dynamics rather than use the traditional $\unicode[STIX]{x1D6FD}$-plane approximation.
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Schwaiger, T., T. Gastine und J. Aubert. „Force balance in numerical geodynamo simulations: a systematic study“. Geophysical Journal International 219, Supplement_1 (26.04.2019): S101—S114. http://dx.doi.org/10.1093/gji/ggz192.
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SUMMARY Dynamo action in the Earth’s outer core is expected to be controlled by a balance between pressure, Coriolis, buoyancy and Lorentz forces, with marginal contributions from inertia and viscous forces. Current numerical simulations of the geodynamo, however, operate at much larger inertia and viscosity because of computational limitations. This casts some doubt on the physical relevance of these models. Our work aims at finding dynamo models in a moderate computational regime which reproduce the leading-order force balance of the Earth. By performing a systematic parameter space survey with Ekman numbers in the range 10−6 ≤ E ≤ 10−4, we study the variations of the force balance when changing the forcing (Rayleigh number, Ra) and the ratio between viscous and magnetic diffusivities (magnetic Prandtl number, Pm). For dipole-dominated dynamos, we observe that the force balance is structurally robust throughout the investigated parameter space, exhibiting a quasi-geostrophic (QG) balance (balance between Coriolis and pressure forces) at zeroth order, followed by a first-order Magneto-Archimedean-Coriolis (MAC) balance between the ageostrophic Coriolis, buoyancy and Lorentz forces. At second order, this balance is disturbed by contributions from inertia and viscous forces. Dynamos with a different sequence of the forces, where inertia and/or viscosity replace the Lorentz force in the first-order force balance, can only be found close to the onset of dynamo action and in the multipolar regime. To assess the agreement of the model force balance with that expected in the Earth’s core, we introduce a parameter quantifying the distance between the first- and second-order forces. Analysis of this parameter shows that the strongest-field dynamos can be obtained close to the onset of convection (Ra close to critical) and in situations of reduced magnetic diffusivity (high Pm). Decreasing the Ekman number gradually expands this regime towards higher supercriticalities and lower values of Pm. Our study illustrates that most classical numerical dynamos are controlled by a QG-MAC balance, while cases where viscosity and inertia play a dominant role are the exception rather than the norm.
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LI, BU-YANG, NAN-SHENG LIU und XI-YUN LU. „DIRECT NUMERICAL SIMULATION OF TURBULENT FLOWS IN A VERTICAL ROTATING OPEN-CHANNEL“. Modern Physics Letters B 19, Nr. 28n29 (20.12.2005): 1443–46. http://dx.doi.org/10.1142/s0217984905009614.
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Direct numerical simulation (DNS) is carried out to study turbulence characteristics in a vertical rotating open-channel with the rotation number N τ = 0-0.12 and the Reynolds number Re τ = 180 based on the wall friction velocity of non-rotating case and the channel depth. Here, two typical rotation regimes are identified. As 0 < N τ < 0.06, the turbulence statistics correlated with the spanwise velocity fluctuation are enhanced since the shear rate of spanwise mean flow induced by Coriolis force increases; however, the other statistics are suppressed. As N τ > 0.06, the turbulence statistics are suppressed significantly because the effect of Coriolis force plays as a dominant role.
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Chang, Shyy Woei, Tong-Minn Liou, Jui-Hung Hung und Wen-Hsien Yeh. „Heat Transfer in a Radially Rotating Square-Sectioned Duct With Two Opposite Walls Roughened by 45Deg Staggered Ribs at High Rotation Numbers“. Journal of Heat Transfer 129, Nr. 2 (02.05.2006): 188–99. http://dx.doi.org/10.1115/1.2409988.
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This paper describes an experimental study of heat transfer in a radially rotating square duct with two opposite walls roughened by 45deg staggered ribs. Air coolant flows radially outward in the test channel with experiments to be undertaken that match the actual engine conditions. Laboratory-scale heat transfer measurements along centerlines of two rib-roughened surfaces are performed with Reynolds number (Re), rotation number (Ro), and density ratio (Δρ∕ρ) in the ranges of 7500–15,000, 0–1.8, and 0.076–0.294. The experimental rig permits the heat transfer study with the rotation number considerably higher than those studied in other researches to date. The rotational influences on cooling performance of the rib-roughened channel due to Coriolis forces and rotating buoyancy are studied. A selection of experimental data illustrates the individual and interactive impacts of Re, Ro, and buoyancy number on local heat transfer. A number of experimental-based observations reveal that the Coriolis force and rotating buoyancy interact to modify heat transfer even if the rib induced secondary flows persist in the rotating channel. Local heat transfer ratios between rotating and static channels along the centerlines of stable and unstable rib-roughened surfaces with Ro varying from 0.1 to 1.8 are in the ranges of 0.6–1.6 and 1–2.2, respectively. Empirical correlations for periodic flow regions are developed to permit the evaluation of interactive and individual effects of ribflows, convective inertial force, Coriolis force, and rotating buoyancy on heat transfer.
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Watson, J. KG. „l-Type doubling: Herzberg versus Nielsen“. Canadian Journal of Physics 79, Nr. 2-3 (01.02.2001): 521–32. http://dx.doi.org/10.1139/p00-094.
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In 1942 Gerhard Herzberg demonstrated the existence of l-type doubling in a number of bending fundamental levels of linear molecules. He attributed the doubling partly to asymmetric-top effects and partly to Coriolis interactions with the stretching modes, but Harald Nielsen and Wave Shaffer claimed that it is a purely Coriolis effect. The dispute, which was due mainly to errors in theoretical calculations, lasted for several years. This paper presents a summary of the controversy, based on published papers and letters exchanged between the main participants. PACS No.: 33.10
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Vadasz, P. „Three-Dimensional Free Convection in a Long Rotating Porous Box: Analytical Solution“. Journal of Heat Transfer 115, Nr. 3 (01.08.1993): 639–44. http://dx.doi.org/10.1115/1.2910734.
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A three-dimensional analytical solution to the steady-state free convection problem in a long rotating porous box is presented for large values of the porous media Ekman number. The convection results from differential heating of the horizontal walls leading to temperature gradients orthogonal to the centrifugal body force. The solution to the nonlinear set of partial differential equations was obtained through an asymptotic expansion of the dependent variables in terms of two small parameters representing the reciprocal Ekman number in porous media and the aspect ratio of the domain. The results are focused towards the Coriolis effect on the flow. Secondary circulation was obtained in a plane orthogonal to the leading free convection plane. The results show that the Coriolis effect on free convection is controlled by a combined dimensionless group representing the ratio of the centrifugal Rayleigh number to the porous media Ekman number.
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Abdel-Wahab, Samer, und Danesh K. Tafti. „Large Eddy Simulation of Flow and Heat Transfer in a 90 deg Ribbed Duct With Rotation: Effect of Coriolis and Centrifugal Buoyancy Forces“. Journal of Turbomachinery 126, Nr. 4 (01.10.2004): 627–36. http://dx.doi.org/10.1115/1.1791648.
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Results from large eddy simulations (LES) of fully developed flow in a 90 deg ribbed duct are presented with rib pitch-to-height ratio P/e=10 and a rib height-to-hydraulic-diameter ratio e/Dh=0.1. Three rotation numbers Ro=0.18, 0.36, and 0.68 are studied at a nominal Reynolds number based on bulk velocity of 20 000. Centrifugal buoyancy effects are included at two Richardson numbers of Ri=12, 28 (Buoyancy parameter, Bo=0.12 and 0.30) for each rotation case. Heat transfer augmentation on the trailing side of the duct due to the action of Coriolis forces alone asymptotes to a value of 3.7±5% by Ro=0.2. On the other hand, augmentation ratios on the leading surface keep decreasing with an increase in rotation number with values ranging from 1.7 at Ro=0.18 to 1.2 at Ro=0.67. Secondary flow cells augment the heat transfer coefficient on the smooth walls by 20% to 30% over a stationary duct. Centrifugal buoyancy further strengthens the secondary flow cells in the duct cross-section which leads to an additional increase of 10% to 15%. Buoyancy also accentuates the augmentation of turbulence near the trailing wall of the duct and increases the heat transfer augmentation ratio 10% to 20% over the action of Coriolis forces alone. However, it does not have any significant effect at the leading side of the duct. The overall effect of buoyancy on heat transfer augmentation for the ribbed duct is found to be less than 10% over the effect of Coriolis forces alone. Friction on the other hand is augmented 15% to 20% at the highest buoyancy number studied. Comparison with available experiments in the literature show excellent agreement.
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Saleh, H., und I. Hashim. „Magnetohydrodynamic Natural Convection in a Rotating Enclosure“. Advances in Applied Mathematics and Mechanics 8, Nr. 2 (27.01.2016): 279–92. http://dx.doi.org/10.4208/aamm.2013.m419.
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AbstractMagnetohydrodynamic natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this article. The governing equations are in velocity, pressure and temperature formulation and solved using the staggered grid arrangement together with MAC method. The governing parameters considered are the Hartmann number, 0≤Ha≤70, the inclination angle of the magnetic field, 0°≤θ 90°, the Taylor number, 8.9 x 104≤Ta≤1.1 x 106 and the centrifugal force is smaller than the Coriolis force and the both forces were kept below the buoyancy force. It is found that a sufficiently large Lorentz force neutralizes the effect of buoyancy, inertial and Coriolis forces. Horizontal or vertical direction of the magnetic field was most effective in reducing the global heat transfer.
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Kawata, Takuya, und P. Henrik Alfredsson. „Scale interactions in turbulent rotating planar Couette flow: insight through the Reynolds stress transport“. Journal of Fluid Mechanics 879 (26.09.2019): 255–95. http://dx.doi.org/10.1017/jfm.2019.668.
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In turbulent planar Couette flow under anticyclonic spanwise system rotation, large-scale roll-cell structures arise due to a Coriolis-force-induced instability. The structures are superimposed on smaller-scale turbulence, and with increasing angular velocity ($\unicode[STIX]{x1D6FA}_{z}$) such roll cells dominate the flow field and small-scale turbulence is instead suppressed in a certain rotation number range $0<Ro\lesssim 0.1$ ($Ro=2\unicode[STIX]{x1D6FA}_{z}h/U_{w}$, where $h$ is the channel half-width, $U_{w}$ the wall velocity). At low rotation numbers around $Ro\approx 0.02$ both large-scale roll cells and smaller-scale turbulence coexist. In the present study, we investigate interaction between these structures through a scale-by-scale analysis of the Reynolds stress transport. We show that at low rotation numbers $Ro\approx 0.01$ the turbulence productions by the mean flow gradient and the Coriolis force occur at different scales and thereby the turbulent energy distribution over a wide range of scales is maintained. On the other hand at higher rotation numbers $Ro\gtrsim 0.05$, a zero-absolute-vorticity state is established and production of small scales from the mean shear disappears although large-scale turbulence production is maintained through the Coriolis force. At high enough Reynolds numbers, where scale separation between the near-wall structures and the roll cells is relatively distinct, transition between these different $Ro$ regimes is found to occur rather abruptly around $Ro\approx 0.02$, resulting in a non-monotonic behaviour of the wall shear stress as a function of $Ro$. It is also shown that at such an intermediate rotation number the roll cells interact with smaller scales by moving near-wall structures towards the core region of the channel, by which the Reynolds stress is transported from relatively small scales near the wall towards larger scales in the channel centre. Such Reynolds stress transport by scale interaction becomes increasingly significant as the Reynolds number increases, and results in a reversed mean velocity gradient at the channel centre at high enough Reynolds numbers.
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Bons, J. P., und J. L. Kerrebrock. „1998 Heat Transfer Committee Best Paper Award: Complementary Velocity and Heat Transfer Measurements in a Rotating Cooling Passage With Smooth Walls“. Journal of Turbomachinery 121, Nr. 4 (01.10.1999): 651–62. http://dx.doi.org/10.1115/1.2836717.
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An experimental investigation was conducted on the internal flowfield of a simulated smooth-wall turbine blade cooling passage. The square cross-sectioned passage was manufactured from quartz for optical accessibility. Velocity measurements were taken using Particle Image Velocimetry for both heated and non-heated cases. Thin film resistive heaters on all four exterior walls of the passage allowed heat to be added to the coolant flow without obstructing laser access. Under the same conditions, an infrared detector with associated optics collected wall temperature data for use in calculating local Nusselt number. The test section was operated with radial outward flow and at values of Reynolds number and Rotation number typical of a small turbine blade. The density ratio was 0.27. Velocity data for the non-heated case document the evolution of the Coriolis-induced double vortex. The vortex has the effect of disproportionately increasing the leading side boundary layer thickness. Also, the streamwise component of the Coriolis acceleration creates a considerably thinned side wall boundary layer. Additionally, these data reveal a highly unsteady, turbulent flowfield in the cooling passage. Velocity data for the heated case show a strongly distorted streamwise profile indicative of a buoyancy effect on the leading side. The Coriolis vortex is the mechanism for the accumulation of stagnant flow on the leading side of the passage. Heat transfer data show a maximum factor of two difference in the Nusselt number from trailing side to leading side. A first-order estimate of this heat transfer disparity based on the measured boundary layer edge velocity yields approximately the same factor of two. A momentum integral model was developed for data interpretation, which accounts for coriolis and buoyancy effects. Calculated streamwise profiles and secondary flows match the experimental data well. The model, the velocity data, and the heat transfer data combine to strongly suggest the presence of separated flow on the leading wall starting at about five hydraulic diameters from the channel inlet for the conditions studied.
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Or, A. C. „Chaotic transitions of convection rolls in a rapidly rotating annulus“. Journal of Fluid Mechanics 261 (25.02.1994): 1–19. http://dx.doi.org/10.1017/s0022112094000224.
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Drifting convection rolls in a rapidly rotating cylindrical annulus with conical endwalls exhibit different transitional modes to chaotic flows at different Prandtl numbers. Three transition sequences for Prandtl numbers 0.3, 1.0 and 7.0 are studied for a moderately large Coriolis parameter and a wavenumber near the critical value using an initial-value code. As the Rayleigh number increases, each transition sequence first leads to a vacillating flow, and then to an aperiodic flow, the route of which is Prandtl-number dependent. From the low Prandtl number to the high Prandtl number, the transitions take different routes of torus folding, period doubling, and mode-locking intermittency.
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Berman, J., und L. F. Mockros. „Mass Transfer to Fluids Flowing Through Rotating Nonaligned Straight Tubes“. Journal of Biomechanical Engineering 108, Nr. 4 (01.11.1986): 342–49. http://dx.doi.org/10.1115/1.3138626.
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Relatively inefficient heat/mass transfer is characteristic of tubular devices if the Reynolds number is low. One method of improving the heat/mass transfer efficiency of such devices is by inducing transverse laminar secondary circulations that are superimposed on the primary flow field; the resulting transverse velocity components lead to fluid mixing and hence augmented mass transfer in the tube lumen. The present work is a theoretical and experimental investigation of the enhanced transport in rotating, nonaligned, straight tubes, a method of transport enhancement that utilizes Coriolis acceleration to create transverse fluid mixing. This technique couples the transport advantages of coiled tubes with the design advantages of straight tubes. The overall mass balance equation is numerically solved for transfer into fluids flowing steadily through rotating nonaligned straight tubes. This solution, for small Coriolis disturbances, incorporates a third order perturbation solution for the primary and secondary flow fields. For sufficiently small Coriolis disturbances the bulk concentration increase is found to be uniquely determined by the value of a single similarity parameter. As the Coriolis disturbance is increased, however, two additional parameters are required to accurately characterize the mass transfer. In general, increasing the Coriolis accelerations results in an increase in mass transfer. There are solution regimes, however, in which increasing this acceleration can lead to a decrease in mass transfer efficiency. This interesting phenomena, which has important design implications, appears to result from velocity-weighting effects on the exiting sample. Experiments, involving the measurement of oxygen transferred into water and blood, produced data that agree with the theoretical predictions.
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Ernst, Wolfgang E., und Stefan Rakowsky. „Rotational structure of the B–X system of Na3 from high-resolution resonant two-photon ionization spectroscopy“. Canadian Journal of Physics 72, Nr. 11-12 (01.11.1994): 1307–14. http://dx.doi.org/10.1139/p94-166.
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First investigations of the [Formula: see text] system of Na3 at rotational resolution are reported. Using resonant two-photon ionization and optical-optical double resonance spectroscopy, two vibronic bands were assigned and rotationally analyzed. In the B state, the three sodium nuclei perform a nearly free pseudorotational motion in the moat of a pseudo-Jahn–Teller potential that is characterized by a vibronic angular momentum quantum number j. In states with J > 0, each rotational level is split by Coriolis interaction. Rotational and Coriolis coupling parameters were determined and are discussed in terms of the dynamics of the vibronic coupling in this floppy molecule.
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LIANG, C. F., P. PARIS, CH BRIANÇON und R. K. SHELINE. „REFLECTION ASYMMETRIC SHAPE IN 221Ra“. International Journal of Modern Physics A 05, Nr. 08 (20.04.1990): 1551–60. http://dx.doi.org/10.1142/s0217751x90000696.
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Mass separated sources of 225Th were used to study the level structure of 221Ra following alpha decay. Fluorination techniques were used to obtain the selectivity in atomic number. The low lying levels in 221Ra are interpreted in terms of K=5/2± and 3/2± parity doublet bands which occur naturally from reflection asymmetric models. The anomalous spin sequences in the K= 3/2± bands of 221Ra are interpreted in terms of their Coriolis coupling with K=1/2± bands with large decoupling parameters. The low-lying parity doublet bands in 221Ra, 223Ra and 225Ra, and particularly the Coriolis coupling of their K=3/2± bands, are compared and contrasted.
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Razavi, Esmail, Hosseinali Soltanipour und Parisa Choupani. „Second law analysis of laminar forced convection in a rotating curved duct“. Thermal Science 19, Nr. 1 (2015): 95–107. http://dx.doi.org/10.2298/tsci120606034r.
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In this paper, flow characteristics, heat transfer and entropy generation in a rotating curved duct are studied numerically. The continuity, Navier-Stokes and energy equations are solved using control volume method. The effects of Dean number, non-dimensional wall heat flux, and force ratio (the ratio of Coriolis to centrifugal forces) on the entropy generation due to friction and heat transfer irreversibility and also overall entropy generation are presented. Optimal thermal operating conditions (based on dimensionless parameters) are determined from the viewpoint of thermodynamics second law. The comparison of numerical results at different force ratios indicates that for any fixed Dean number or non-dimensional heat flux, the minimal frictional entropy generation occurs when the Coriolis and centrifugal forces have the same value but in the opposite direction. For a specific non-dimensional heat flux, there is a force ratio with maximum heat transfer irreversibility which depends on Dean number. Based on optimal analysis, the optimal force ratio with minimal total entropy generation depends on heat flux and Dean number.
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Matsson, O. John E., und P. Henrik Alfredsson. „Curvature- and rotation-induced instabilities in channel flow“. Journal of Fluid Mechanics 210 (Januar 1990): 537–63. http://dx.doi.org/10.1017/s0022112090001392.
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In a curved channel streamwise vortices, often called Dean vortices, may develop above a critical Reynolds number owing to centrifugal effects. Similar vortices can occur in a rotating plane channel due to Coriolis effects if the axis of rotation is normal to the mean flow velocity and parallel to the walls. In this paper the flow in a curved rotating channel is considered. It is shown from linear stability theory that there is a region for which centrifugal effects and Coriolis effects almost cancel each other, which increases the critical Reynolds number substantially. The flow visualization experiments carried out show that a complete cancellation of Dean vortices can be obtained for low Reynolds number. The rotation rate for which this occurs is in close agreement with predictions from linear stability theory. For curved channel flow a secondary instability of travelling wave type is found at a Reynolds number about three times higher than the critical one for the primary instability. It is shown that rotation can completely cancel the secondary instability.
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Lucas, Carine, James C. McWilliams und Antoine Rousseau. „On nontraditional quasi-geostrophic equations“. ESAIM: Mathematical Modelling and Numerical Analysis 51, Nr. 2 (27.01.2017): 427–42. http://dx.doi.org/10.1051/m2an/2016041.
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In this article, we work on nontraditional models where the so-called traditional approximation on the Coriolis force is removed. In the derivation of the quasi-geostrophic equations, we carefully consider terms in δ/ε, where δ (aspect ratio) and ε (Rossby number) are both small numbers. We provide here some rigorous crossed-asymptotics with regards to these parameters, prove some mathematical results and compare QHQG and QG models.
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Audusse, E., V. Dubos, A. Duran, N. Gaveau, Y. Nasseri und Y. Penel. „Numerical approximation of the shallow water equations with coriolis source term“. ESAIM: Proceedings and Surveys 70 (2021): 31–44. http://dx.doi.org/10.1051/proc/202107003.
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We investigate in this work a class of numerical schemes dedicated to the non-linear Shallow Water equations with topography and Coriolis force. The proposed algorithms rely on Finite Volume approximations formulated on collocated and staggered meshes, involving appropriate diffusion terms in the numerical fluxes, expressed as discrete versions of the linear geostrophic balance. It follows that, contrary to standard Finite-Volume approaches, the linear versions of the proposed schemes provide a relevant approximation of the geostrophic equilibrium. We also show that the resulting methods ensure semi-discrete energy estimates. Numerical experiments exhibit the efficiency of the approach in the presence of Coriolis force close to the geostrophic balance, especially at low Froude number regimes.
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Rudraiah, N., und O. P. Chandna. „Effects of Coriolis force and nonuniform temperature gradient on the Rayleigh–Benard convection“. Canadian Journal of Physics 64, Nr. 1 (01.01.1986): 90–99. http://dx.doi.org/10.1139/p86-013.
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The effects of the Coriolis force and a nonuniform temperature gradient on the onset of the Rayleigh–Benard convection in a thin, horizontal, rotating fluid layer is studied using linear-stability analysis. It is shown analytically that the method and rate of heating, the Coriolis force, and the nature of the bounding surfaces of the fluid layer significantly influence the value of the Rayleigh number at the onset of marginal convection. The mechanism for suppressing or augmenting convection is discussed in detail. The Galerkin technique employed here is much easier to use than that the method of Chandrasekhar (5). The analytical results obtained from using this procedure are compared with the published experimental data and the results obtained from numerical procedures; good agreement is found.
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Brethouwer, G., Y. Duguet und P. Schlatter. „Turbulent–laminar coexistence in wall flows with Coriolis, buoyancy or Lorentz forces“. Journal of Fluid Mechanics 704 (02.07.2012): 137–72. http://dx.doi.org/10.1017/jfm.2012.224.
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AbstractDirect numerical simulations of subcritical rotating, stratified and magneto-hydrodynamic wall-bounded flows are performed in large computational domains, focusing on parameters where laminar and turbulent flow can stably coexist. In most cases, a regime of large-scale oblique laminar-turbulent patterns is identified at the onset of transition, as in the case of pure shear flows. The current study indicates that this oblique regime can be shifted up to large values of the Reynolds number $\mathit{Re}$ by increasing the damping by the Coriolis, buoyancy or Lorentz force. We show evidence for this phenomenon in three distinct flow cases: plane Couette flow with spanwise cyclonic rotation, plane magnetohydrodynamic channel flow with a spanwise or wall-normal magnetic field, and open channel flow under stable stratification. Near-wall turbulence structures inside the turbulent patterns are invariably found to scale in terms of viscous wall units as in the fully turbulent case, while the patterns themselves remain large-scale with a trend towards shorter wavelength for increasing $\mathit{Re}$. Two distinct regimes are identified: at low Reynolds numbers the patterns extend from one wall to the other, while at large Reynolds number they are confined to the near-wall regions and the patterns on both channel sides are uncorrelated, the core of the flow being highly turbulent without any dominant large-scale structure.
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Steeneveld, G. J., B. J. H. van de Wiel und A. A. M. Holtslag. „Diagnostic Equations for the Stable Boundary Layer Height: Evaluation and Dimensional Analysis“. Journal of Applied Meteorology and Climatology 46, Nr. 2 (01.02.2007): 212–25. http://dx.doi.org/10.1175/jam2454.1.
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Abstract The performance of diagnostic equations for the stable boundary layer height h is evaluated with four observational datasets that represent a broad range of latitudes, land use, and surface roughness. In addition, large-eddy simulation results are used. Special care is given to data-quality selection. The diagnostic equations evaluated are so-called multilimit equations as derived by Zilitinkevich and coworkers in a number of papers. It appears that these equations show a serious negative bias, especially for h < 100 m, and it was found that the parameters involved could not be determined uniquely with calibration. As an alternative, dimensional analysis is used here to derive a formulation for h that is more robust. The formulation depends on the surface friction velocity u*, surface buoyancy flux Bs, Coriolis parameter, and the free-flow stability N. The relevance of the Coriolis parameter for the boundary layer height estimation in practice is also discussed. If the Coriolis parameter is ignored, two major regimes are found: h ∼ u*/N for weakly stable conditions and h ∼ (|Bs|/N 3)1/2 for moderate to very stable conditions.
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Prabhu, S. V., Neelabh Arora und R. P. Vedula. „Effect of Channel Orientation and Rib Pitch-to-Height Ratio on Pressure Drop in a Rotating Square Channel with Ribs on Two Opposite Surfaces“. International Journal of Rotating Machinery 2005, Nr. 1 (2005): 67–76. http://dx.doi.org/10.1155/ijrm.2005.67.
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The effect of channel orientation and rib pitch-to-height ratio on the pressure drop distribution in a rib-roughened channel is an important issue in turbine blade cooling. The present investigation is a study of the overall pressure drop distribution in a square cross-sectioned channel, with rib turbulators, rotating about an axis normal to the free stream. The ribs are configured in a symmetric arrangement on two opposite surfaces with a rib angle of90∘to the mainstream flow. The study has been conducted for three Reynolds numbers, namely, 13 000, 17 000, and 22 000 with the rotation number varying from 0–0.38. Experiments have been carried out for various rib pitch-to-height ratios(P/e)with a constant rib height-to-hydraulic diameter ratio(e/D)of0.1. The test section in which the ribs are placed on the leading and trailing surfaces is considered as the base case (orientation angle=0∘, Coriolis force vector normal to the ribbed surfaces). The channel is turned about its axis in steps of15∘to vary the orientation angle from0∘to90∘. The overall pressure drop does not change considerably under conditions of rotation for the base case. However, for the other cases tested, it is observed that the overall pressure drop increases with an increase in the rotation number for a given orientation angle and also increases with an increase in the orientation angle for a given rotation number. This change is attributed to the variation in the separation zone downstream of the ribs due to the presence of the Coriolis force—local pressure drop data is presented which supports this idea. At an orientation angle of90∘(ribs on the top and bottom surfaces, Coriolis force vector normal to the smooth surfaces), the overall pressure drop is observed to be maximum during rotation. The overall pressure drop for a case with a rib pitch-to-height ratio of5on both surfaces is found to be the highest among all the rib pitch-to-height ratios covered in this study with the maximum increase in the overall pressure drop being as high as five times the corresponding no-rotation case at the highest rotation number of0.38and90∘orientation angle.
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Wagner, J. H., B. V. Johnson und F. C. Kopper. „Heat Transfer in Rotating Serpentine Passages With Smooth Walls“. Journal of Turbomachinery 113, Nr. 3 (01.07.1991): 321–30. http://dx.doi.org/10.1115/1.2927879.
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Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large-scale, multipass, smooth-wall heat transfer model with both radially inward and outward flow. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature ratio, Rossby number, Reynolds number, and radius-to-passage hydraulic diameter ratio. These four parameters were varied over ranges that are typical of advanced gas turbine engine operating conditions. It was found that both Coriolis and buoyancy effects must be considered in turbine blade cooling designs and that the effect of rotation on the heat transfer coefficients was markedly different depending on the flow direction. Local heat transfer coefficients were found to decrease by as much as 60 percent and increase by 250 percent from no-rotation levels. Comparisons with a pioneering stationary vertical tube buoyancy experiment showed reasonably good agreement. Correlation of the data is achieved employing dimensionless parameters derived from the governing flow equations.
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Nitheesh, George, und M. Govardhan. „Computational Studies of Turbulent Flows in Rotating Radial and 200 Backward Swept Diverging Channels“. Advanced Materials Research 1016 (August 2014): 540–45. http://dx.doi.org/10.4028/www.scientific.net/amr.1016.540.
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Computational study is carried out in radial and 200 backward swept diverging channels rotating about the axial direction. Centrifugal and Coriolis forces, which are developed due to the rotation, affect the secondary flows and flow pattern inside the channel. Reynolds number of Re=36000 with Rotation numbers ranging from 0.0 and 1.5 are chosen for investigation. The variation of velocity and turbulence kinetic energy is studied at several locations of the curved channels. Positive Richardson numbers on the suction side indicates stabilizations of the flow. The stabilization effect increases with increasing Rotation numbers at both the channels.
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Sarja, A., P. Singh und S. V. Ekkad. „Parallel rotation for negating Coriolis force effect on heat transfer“. Aeronautical Journal 124, Nr. 1274 (31.01.2020): 581–96. http://dx.doi.org/10.1017/aer.2020.1.
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ABSTRACTGas turbine blades feature multi-pass internal cooling channels, through which relatively colder air bled from the compressor is routed to cool internal walls. Under rotation, due to the influence of Coriolis force and centrifugal buoyancy, heat transfer at the trailing side enhances and that at the leading side reduces, for a radially outward flow. This non-uniform temperature distribution results in increased thermal stress, which is detrimental to blade life. In this study, a rotation configuration is presented which can negate the Coriolis force effect on heat and fluid flow, thereby maintaining uniform heat transfer on leading and trailing walls. A straight, smooth duct of unit aspect ratio is considered to demonstrate the concept and understand the fluid flow within the channel and its interaction with the walls. The new design is compared against the conventional rotation design. Numerical simulations under steady-state condition were carried out at a Reynolds number of 25000, where the Rotation numbers were varied as 0, 0.1, 0.15, 0.2, 0.25. Realisable version of k-$\varepsilon$ model was used for turbulence modelling. It was observed that new rotation (parallel) configuration’s heat transfer on leading and trailing sides were near similar, and trailing side was marginally higher compared to leading side. An interesting phenomenon of secondary Coriolis effect is reported which accounts for the minor differences in heat transfer augmentation between leading and trailing walls. Due to centrifugal buoyancy, the fluid is pushed towards the radially outward wall, resulting in a counter-rotating vortex pair, which also enhances the heat transfer on leading and trailing walls when compared to stationary case.
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Orvedahl, Ryan J., Nicholas A. Featherstone und Michael A. Calkins. „Large-scale magnetic field saturation and the Elsasser number in rotating spherical dynamo models“. Monthly Notices of the Royal Astronomical Society: Letters 507, Nr. 1 (13.08.2021): L67—L71. http://dx.doi.org/10.1093/mnrasl/slab097.
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ABSTRACT Numerical simulations are used to investigate large-scale (mean) magnetic field generation in rotating spherical dynamos. Beyond a certain threshold, we find that the magnitude of the mean magnetic field becomes nearly independent of the system rotation rate and buoyancy forcing. The analysis suggests that this saturation arises from the Malkus-Proctor mechanism in which a Coriolis-Lorentz force balance is achieved in the zonal component of the mean momentum equation. When based on the large-scale magnetic field, the Elsasser number is near unity in the saturated regime. The results show that the large and small magnetic field saturate via distinct mechanisms in rapidly rotating dynamos, and that only the axisymmetric component of the magnetic field appears to follow an Elsasser number scaling.
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Benisek, Miroslav, Dejan Ilic, Djordje Cantrak und Ivan Bozic. „Investigation of the turbulent swirl flows in a conical diffuser“. Thermal Science 14, suppl. (2010): 141–54. http://dx.doi.org/10.2298/tsci100630026b.
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Results of the theoretical and experimental investigations of the turbulent mean swirl flows characteristics change along straight conical diffuser of incompressible fluid (air) are presented in this paper. The main swirl flow characteristics review is given. In addition: the specific swirl flow energy, the energy loss, the mean circulation, the swirl flow parameter, the ratio between the swirl and axial flow loss coefficients change along the diffuser are presented. Among other values: the Boussinesq number, outlet Coriolis coefficient and swirl flow loss coefficient dependences on inlet swirl flow parameter are also given. The swirl flow specific energy and outlet Coriolis coefficient calculation procedure are presented in this paper, as well as experimental test bed and measuring procedures. The swirl flow fields were induced by the axial fan impeller. Various swirl parameters were achieved by the impeller openings and rotational speeds.
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McDermott, B. R., und P. A. Davidson. „On the helicity characteristics and induced emf of magnetic-Coriolis wave packets“. Geophysical Journal International 223, Nr. 2 (18.08.2020): 1398–411. http://dx.doi.org/10.1093/gji/ggaa373.
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SUMMARY In a rapidly rotating Boussinesq fluid, buoyant anomalies radiate low-frequency inertial wave packets that disperse along the rotation axis. The wave packets lead to axially elongated vortices, which propagate negative (positive) kinetic helicity upwards (downwards) with respect to the rotation vector. The kinetic helicity carried by the inertial wave packets is near-maximal relative to the velocity and vorticity fields. In classical mean-field theory, kinetic helicity is often associated with the α-effect, which is thought to be an important ingredient for planetary dynamos. The modification of inertial wave packets in the presence of a transverse uniform magnetic field is investigated here, motivated by small-scale dynamics in planetary cores, where a large-scale magnetic field affects fluid motions. We study numerically the dispersion of wave packets from an isolated buoyant source and from a random layer of buoyant anomalies, while varying the Lehnert number Le—the ratio of the frequencies of Alfvén and inertial waves. We find that for Le < 0.1, the vortices are columnar and continue to segregate kinetic helicity so that it is negative (positive) above (below) the buoyant source. Importantly, the wave packets induce an α-effect, which remains strong and coherent for Earth-like values of the Lehnert number (Le < 0.1). The interaction of wave packets emitted by multiple neighbouring buoyant sources results in an α-effect that is stronger than the α-effect induced by wave packets launched from an isolated buoyant source, and we provide an analytical explanation for this. The coherence of the α-effect induced by the wave packets, for Earth-like values of the Lehnert number, lends support to the α2 dynamo model driven by helical waves.
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PRASANNA, A. R., und BANIBRATA MUKHOPADHYAY. „EFFECT OF CORIOLIS FORCE ON ACCRETION FLOWS AROUND ROTATING COMPACT OBJECT“. International Journal of Modern Physics D 12, Nr. 01 (Januar 2003): 157–72. http://dx.doi.org/10.1142/s0218271803002457.
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Using the generalised set of fluid equations that include the "Coriolis force" along with the centrifugal and pressure gradient forces, we have reanalysed the class of self-similar solutions, with the pseudo-Newtonian potential. We find that the class of solutions is well behaved for almost the entire parameter space except for a few selected combinations of γ and α for the co-rotating flow. The analysis of the Bernoulli number shows that whereas it remains positive for co-rotating flow for f > 1/3, for the counter-rotating flow it does admit both positive and negative values, indicating the possibility of energy transfer in either direction.
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CARNEVALE, G. F., P. ORLANDI, YE ZHOU und R. C. KLOOSTERZIEL. „Rotational suppression of Rayleigh–Taylor instability“. Journal of Fluid Mechanics 457 (09.04.2002): 181–90. http://dx.doi.org/10.1017/s0022112002007772.
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It is demonstrated that the growth of the mixing zone generated by Rayleigh–Taylor instability can be greatly retarded by the application of rotation, at least for low Atwood number flows for which the Boussinesq approximation is valid. This result is analysed in terms of the effect of the Coriolis force on the vortex rings that propel the bubbles of fluid in the mixing zone.
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Siegel, R. „Analysis of Buoyancy Effect on Fully Developed Laminar Heat Transfer in a Rotating Tube“. Journal of Heat Transfer 107, Nr. 2 (01.05.1985): 338–44. http://dx.doi.org/10.1115/1.3247420.
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Laminar heat transfer is analyzed in a tube rotating about an axis perpendicular to the tube axis. The solution applies for flow that is either radially outward from the axis of rotation, or radially inward toward the axis of rotation. The conditions are fully developed, and there is uniform heat addition at the tube wall. The analysis is performed by expanding velocities and temperature in power series using the Taylor number as a perturbation parameter. Coriolis and buoyancy forces caused by tube rotation are included, and the solution is calculated through second-order terms. The secondary flow induced by the Coriolis terms always tends to increase the heat transfer coefficient; this effect can dominate for small wall heating. For radial inflow, buoyancy also tends to improve heat transfer. For radial outflow, however, buoyancy tends to reduce heat transfer; for large wall heating this effect can dominate, and there is a net reduction in heat transfer coefficient.
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Basarab, Mikhail, und Boris Lunin. „Solving the Coriolis Vibratory Gyroscope Motion Equations by Means of the Angular Rate B-Spline Approximation“. Mathematics 9, Nr. 3 (02.02.2021): 292. http://dx.doi.org/10.3390/math9030292.
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The exact solution of the movement equation of the Coriolis vibratory gyroscope (CVG) with a linear law of variation of the angular rate of rotation of the base is given. The solution is expressed in terms of the Weber functions (the parabolic cylinder functions) and their asymptotic representations. On the basis of the obtained solution, an analytical solution to the equation of the ring dynamics in the case of piecewise linear approximation of an arbitrary angular velocity profile on a time grid is derived. The piecewise linear solution is compared with the more rough piecewise constant solution and the dependence of the error of such approximations on the sampling step in time is estimated numerically. The results obtained make it possible to significantly reduce the number of operations when it is necessary to study long-range dynamics of oscillations of the system, as well as quantitatively and qualitatively control the convergence of finite-difference schemes for solving the movement equations of the Coriolis vibratory gyroscope.
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Malik, Mujeeb R. „The neutral curve for stationary disturbances in rotating-disk flow“. Journal of Fluid Mechanics 164 (März 1986): 275–87. http://dx.doi.org/10.1017/s0022112086002550.
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The neutral curve for stationary vortex disturbances in rotating-disk flow is computed up to a Reynolds number of 107 using the sixth-order system of linear stability equations which includes the effects of streamline curvature and Coriolis force. It is found that the neutral curve has two minima: one at R = 285.36 (upper branch) and the other at R = 440.88 (lower branch). At large Reynolds numbers, the upper branch tends to Stuart's asymptotic solution while the lower branch tends to a solution that is associated with the wave angle corresponding to the direction of zero mean wall shear.
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Kang, Jianhong, Tongqiang Xia und Yingke Liu. „Heat Transfer and Flows of Thermal Convection in a Fluid-Saturated Rotating Porous Medium“. Mathematical Problems in Engineering 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/905458.
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Thermal convection at the steady state for high Rayleigh number in a rotating porous half space is investigated. Taking into account the effect of rotation, Darcy equation is extended to incorporate the Coriolis force term in a rotating reference frame. The velocity and temperature fields of thermal convection are obtained by using the homotopy analysis method. The influences of Taylor number and Rayleigh number on the Nusselt number, velocity profile, and temperature distribution are discussed in detail. It is found that the Nusselt number decreases rapidly with the increase of Taylor number but tends to have an asymptotic value. Besides, the rotation can give rise to downward flow in contrast with the upward thermal convection.
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Soong, Chyi-Yeou. „Prandtl Number Effects on Mixed Convection Between Rotating Coaxial Disks“. International Journal of Rotating Machinery 2, Nr. 3 (1996): 161–66. http://dx.doi.org/10.1155/s1023621x96000036.
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Prandtl number characterizes the competition of viscous and thermal diffusion effects and, therefore, is an influential factor in thermal-fluid flows. In the present study, the Prandtl number effects on non-isothermal flow and heat transfer between two infinite coaxial disks are studied by using a similarity model for rotation-induced mixed convection. To account for the buoyancy effects, density variation in Coriolis and centrifugal force terms are considered by invoking Boussinesq approximation and a linear density-temperature relation. Co-rotating disks(Ω2=Ω1)and rotor-stator system(Ω1≠Ω2=0)are considered to investigate the free and mixed convection flows, respectively. For Reynolds number, Re, up to 1000 and the buoyancy parameter, B=βΔT, of the range of|B|≤0.05, the flow and heat transfer characteristics with Prandtl numbers of 100, 7, 0.7, 0.1, and 0.01 are examined. The results reveal that the Prandtl number shows significant impact on the fluid flow and heat transfer performance. In the typical cases of mixed convection in a rotor-stator system with|B|=0.05, the effects in buoyancy-opposed flowsB=0.05are more pronounced than that in buoyancy-assisted ones.
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Thuburn, J., C. J. Cotter und T. Dubos. „A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids“. Geoscientific Model Development 7, Nr. 3 (20.05.2014): 909–29. http://dx.doi.org/10.5194/gmd-7-909-2014.
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Abstract. A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.
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Thuburn, J., C. J. Cotter und T. Dubos. „A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed sphere grids“. Geoscientific Model Development Discussions 6, Nr. 4 (17.12.2013): 6867–925. http://dx.doi.org/10.5194/gmdd-6-6867-2013.
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Abstract. A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.
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Ostilla-Mónico, Rodolfo, Erwin P. van der Poel, Roberto Verzicco, Siegfried Grossmann und Detlef Lohse. „Exploring the phase diagram of fully turbulent Taylor–Couette flow“. Journal of Fluid Mechanics 761 (18.11.2014): 1–26. http://dx.doi.org/10.1017/jfm.2014.618.
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AbstractDirect numerical simulations of Taylor–Couette flow, i.e. the flow between two coaxial and independently rotating cylinders, were performed. Shear Reynolds numbers of up to $3\times 10^{5}$, corresponding to Taylor numbers of $\mathit{Ta}=4.6\times 10^{10}$, were reached. Effective scaling laws for the torque are presented. The transition to the ultimate regime, in which asymptotic scaling laws (with logarithmic corrections) for the torque are expected to hold up to arbitrarily high driving, is analysed for different radius ratios, different aspect ratios and different rotation ratios. It is shown that the transition is approximately independent of the aspect and rotation ratios, but depends significantly on the radius ratio. We furthermore calculate the local angular velocity profiles and visualize different flow regimes that depend both on the shearing of the flow, and the Coriolis force originating from the outer cylinder rotation. Two main regimes are distinguished, based on the magnitude of the Coriolis force, namely the co-rotating and weakly counter-rotating regime dominated by Rayleigh-unstable regions, and the strongly counter-rotating regime where a mixture of Rayleigh-stable and Rayleigh-unstable regions exist. Furthermore, an analogy between radius ratio and outer-cylinder rotation is revealed, namely that smaller gaps behave like a wider gap with co-rotating cylinders, and that wider gaps behave like smaller gaps with weakly counter-rotating cylinders. Finally, the effect of the aspect ratio on the effective torque versus Taylor number scaling is analysed and it is shown that different branches of the torque-versus-Taylor relationships associated to different aspect ratios are found to cross within 15 % of the Reynolds number associated to the transition to the ultimate regime. The paper culminates in phase diagram in the inner versus outer Reynolds number parameter space and in the Taylor versus inverse Rossby number parameter space, which can be seen as the extension of the Andereck et al. (J. Fluid Mech., vol. 164, 1986, pp. 155–183) phase diagram towards the ultimate regime.