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Coherent structures in rotating three-dimensional turbulence

Published online by Cambridge University Press:  26 April 2006

Peter Bartello ,
Olivier Métais  and
Marcel Lesieur
Peter Bartello
Affiliation:
LEGI - IMG, Institut National Polytechnique de Grenoble and Université Joseph Fourier, BP 53 X, 38041 Grenoble Cedex, France Present address: Recherche en prévision numérique, Service de l’Environnement Atmosphérique, Dorval (Québec), Canada H9P 1J3
Olivier Métais
Affiliation:
LEGI - IMG, Institut National Polytechnique de Grenoble and Université Joseph Fourier, BP 53 X, 38041 Grenoble Cedex, France
Marcel Lesieur
Affiliation:
LEGI - IMG, Institut National Polytechnique de Grenoble and Université Joseph Fourier, BP 53 X, 38041 Grenoble Cedex, France
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Abstract

Numerical simulations investigating the formation and stability of quasi-two-dimensional coherent vortices in rotating homogeneous three-dimensional flow are described. In a numerical study of shear flows Lesieur, Yanase & Métais (1991) found that cyclones (respectively anticyclones) with |ω2D| ∼ O(2Ω), where ω2D is the vorticity and Ω is the rotation rate, are stabilized (respectively destabilized) by the rotation. A study of triply periodic pseudo-spectral simulations (643) was undertaken in order to investigate the vorticity asymmetry in homogeneous turbulence. Specifically, we examine (i) the possible three-dimensionalization of initially two-dimensional vortices and (ii) the emergence of quasi-two-dimensional structures in initially-isotropic three-dimensional turbulence. Direct numerical simulations of the Navier—Stokes equations are compared with large-eddy simulations employing a subgridscale model based on the second-order velocity structure function evaluated at the grid separation and with simulations employing hyperviscosity.

Isolated coherent two-dimensional vortices, obtained from a two-dimensional decay simulation, were superposed with a low-amplitude three-dimensional perturbation, and used to initialize the first set of simulations. With Ω = 0, a three-dimensionalization of all vortices was observed. This occurred first in the small scales in conjunction with the formation of longitudinal hairpin vortices with vorticity perpendicular to that of the initial quasi-two-dimensional flow. In agreement with centrifugal stability arguments, when 2Ω = [ω2D]rms a rapid destabilization of anticyclones was observed to occur, whereas the initial two-dimensional cyclonic vortices persisted throughout the simulation. At larger Ω, both cyclones and anticyclones remained two-dimensional, consistent with the Taylor—Proudman theorem. A second set of simulations starting from isotropic three-dimensional fields was initialized by allowing a random velocity field to evolve (Ω = 0) until maximum energy dissipation. When the simulations were continued with 2Ω = [ω · Ω]rms/Ω, the three-dimensional flow was observed to organize into two-dimensional cyclonic vortices. At larger Ω, two-dimensional anticyclones also emerged from the initially-isotropic flow. The consequences for a variety of industrial and geophysical applications are clear. For quasi-two-dimensional eddies whose characteristic circulation times are of the order ofder of Ω−1, rotation induces a complete disruption of anticyclonic vortices, while stabilizing cyclonic ones.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 273 , 25 August 1994 , pp. 1 - 29
Copyright
© 1994 Cambridge University Press

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References

André, J. C. & Lesieur, M. 1977 Influence of helicity on high Reynolds number isotropic turbulence. J. Fluid Mech. 81, 187–207.Google Scholar
Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. 1984 High-order velocity structure functions in turbulent shear flows. J. Fluid Mech. 140, 63–89.Google Scholar
Bardina, J., Ferziger, J. H. & Rogallo, R. S. 1985 Effect of rotation on isotropic turbulence: computation and modelling. J. Fluid Mech. 154, 321–336.Google Scholar
Basdevant, C., Legras, B., Sadourny, R. & Béland, M. 1981 A study of barotropic model flows: Intermittency, waves and predictability. J. Atmos. Sci. 38, 2305–2326.Google Scholar
Basdevant, C. & Sadourny, R. 1983 Modélisation des échelles virtuelles dans la simulation numérique des écoulements turbulents bidimensionels. J. Mec. Theor. Appl., Numéro Spécial, 243–269.Google Scholar
Bidokhti, A. A. & Tritton, D. J. 1992 The structure of a turbulent free shear layer in a rotating fluid. J. Fluid Mech. 241, 469–502.Google Scholar
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177–191.Google Scholar
Cambon, C. & Jacquin, L. 1989 Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech. 202, 295–317.Google Scholar
Chollet, J.-P. & Lesieur, M. 1981 Parameterization of small scales of three-dimensional isotropic turbulence utilizing spectral closures. J. Atmos. Sci. 38, 2747–2757.Google Scholar
Comte, P., Lesieur, M. & Lamballais, E. 1992 Large- and small-scale stirring of vorticity and a passive scalar in a three-dimensional temporal mixing layer. Phys. Fluids A 4, 2761–2778.Google Scholar
Dang, K. & Roy, P. 1985a Numerical simulation of homogeneous turbulence. In Proc. Workshop on Macroscopic Modelling of Turbulent Flows and Fluid Mixtures. Springer.
Dang, K. & Roy, P. 1985b Direct and large eddy simulation of homogeneous turbulence submitted to solid body rotation. In Proc. 5th Symp. on Turbulent Shear Flows. Springer.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Flores, C. 1993 Étude numérique de l’influence d’une rotation sur les écoulements cisaillés libres. PhD thesis, National Polytechnic Institute, Grenoble.
Fornberg, B. 1977 A numerical study of 2-D turbulence. J. Comput. Phys. 25, 1–31.Google Scholar
Greenspan, H. P. 1969 The Theory of Rotating Fluids. Cambridge University Press.
Hart, J. E. 1971 Instability and secondary motion in a rotating channel flow. J. Fluid Mech. 45, 341–351.Google Scholar
Herring, J. R. & Métais, O. 1989 Numerical experiments in forced stably stratified turbulence. J. Fluid Mech. 202, 97–115.Google Scholar
Holloway, G. 1979 On the spectral evolution of strongly interacting waves. Geophys. Astrophys. Fluid Dyn. 11, 271–287.Google Scholar
Hopfinger, E. J., Browand, F. K. & Gagne, Y. 1982 Turbulence and waves in a rotating tank. J. Fluid Mech. 125, 505–534.Google Scholar
Jacquin, L., Leuchter, O., Cambon, C. & Mathieu, J. 1990 Homogeneous turbulence in the presence of rotation. J. Fluid Mech. 220, 1–52.Google Scholar
Kloosterziel, R. C. & van Heijst, G. J. F. 1991 An experimental study of unstable barotropic vortices in a rotating fluid. J. Fluid Mech. 223, 1–24.Google Scholar
Kristoffersen, R. & Andersson, H. F. 1993 Direct simulations of low-Reynolds-number turbulent flow in a rotating channel. J. Fluid Mech. 256, 163–197.Google Scholar
Lesieur, M. 1990 Turbulence in Fluids, 2nd Edn. Martinus Nijhoff.
Lesieur, M., Yanase, S. & Métais, O. 1991 Stabilizing and destabilizing effects of a solid-body rotation on quasi-two-dimensional shear layers. Phys. Fluids A 3, 403–407.Google Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.Google Scholar
Mansour, N. N., Cambon, C. & Speziale, C. G. 1991a Single point modelling of initially isotropic turbulence under uniform rotation. In Annual Research Briefs. Center for Turbulence Research, NASA-Ames Research Center - Stanford University.
Mansour, N. N., Cambon, C. & Speziale, C. G. 1992 Theoretical and computational study of rotating isotropic turbulence. In Studies in Turbulence (ed. T. B. Gatski, S. Sarkar & C. G. Speziale). Springer.
Mansour, N. N., Shih, T.-H. & Reynolds, W. C. 1991b The effects of rotation on initially anisotropic homogeneous flows. Phys. Fluids A 3, 2421–2425.Google Scholar
Métais, O. & Lesieur, M. 1992 Spectral large-eddy simulation of isotropic and stably-stratified turbulence. J. Fluid Mech. 235, 157–194.Google Scholar
Métais, O., Yanase, S., Flores, C., Bartello, P. & Lesieur, M. 1992 Reorganization of coherent vortices in shear layers under the action of solid-body rotation. In Turbulent Shear Flows 8, pp. 415–430. Springer.
Mory, M. & Caperan, P. 1987 On the genesis of quasi-steady vortices in a rotating turbulent flow. J. Fluid Mech. 185, 121–136.Google Scholar
Orszag, S. A. 1971 Numerical simulation of incompressible flows within simple boundaries. I Galerkin (spectral) representations. Stud. Appl. Maths 50, 293–327.Google Scholar
Rayleigh, Lord 1916 On the dynamics of revolving fluids. Proc. R. Soc. Lond. A 93, 148–154.Google Scholar
Reynolds, W. C. 1989 Effects of rotation on homogeneous turbulence. In Proc. of the Tenth Australasian Fluid Mechanics Conference. University of Melbourne, Australia.
Reynolds, W. C. 1991 Towards a structure-based turbulence model. In Studies in Turbulence (ed. T. B. Gatski, S. Sarkar & C. G. Speziale). Springer.
Roy, Ph. 1986 Simulation numérique d’un champ turbulent homogène incompressible soumis à des gradients de vitesse moyenne. Thèse de Doctorat d’État, Université de Nice.
Siggia, E. D. 1981 Numerical study of small scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375–406.Google Scholar
Smyth, W. D. & Peltier, W. R. 1994 three-dimensionalization of barotropic vortices on the f-plane. J. Fluid Mech. in press.Google Scholar
Teissèdre, C. & Dang, K. 1987 Anisotropic behaviour of rotating homogeneous turbulence by numerical simulation. In Proc. AIAA 19th Fluid Dynamics, Plasma Dynamics and Lasers Conference, 1987 Honolulu, Hawaii.
Tritton, D. J. 1992 Stabilization and destabilization of turbulent shear flow in a rotating fluid. J. Fluid Mech. 241, 503–523.Google Scholar
van Atta, C. W. & Park, J. 1972 Statistical self-similarity and inertial subrange turbulence. In Statistical Models and Turbulence (ed. M. Rosenblatt & C. W. Van Atta). Lecture Notes in Physics, vol. 12. Springer.
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1–20.Google Scholar
Waleffe, F. 1993 Inertial transfers in the helical decomposition. Phys. Fluids A 5, 677–685.Google Scholar
Yanase, S., Flores, C., Métais, O. & Riley, J. J. 1993 Rotating free shear flows Part 1: Linear stability analysis. Phys. Fluids A 5, 2725–2737.Google Scholar