Wave turbulence in rapidly rotating flows

Journal of Fluid Mechanics

Volumn 562, Issue , 2006, Pages 83-121

  Bellet, F ^a   Godeferd, F S ^a   Scott, J F ^a   Cambon, Claude ^a  

^a ECOLE CENTRALE DE LYON   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; KINETIC ENERGY; REYNOLDS NUMBER; ROTATIONAL FLOW;

ASYMPTOTIC QUASI-NORMAL MARKOVIAN (AQNM) MODEL; LINEAR WAVE REGIME; ROSSBY NUMBER; STATISTICAL CLOSURE MODEL; WAVE TURBULENCE;

TURBULENT FLOW;

ANISOTROPY; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; KINETIC ENERGY; REYNOLDS NUMBER; ROTATIONAL FLOW; TURBULENT FLOW;

NUMERICAL MODEL; REYNOLDS NUMBER; ROSSBY NUMBER; ROTATING FLOW; TURBULENCE; TURBULENT FLOW;

EID: 33748281602     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112006000929     Document Type: Article

References (49)

1. Babin, A., Mahalov, A. & Nicolaenko, B. 1997 Regularity and integrability of three-dimensional Euler and Navier-Stokes equations for uniformly rotating fluids. Asympt. Anal. 15 (2), 103-150.
2. Babin, A., Mahalov, A. & Nicolaenko, B. 1999 Global regularity of three-dimensional rotating Navier-Stokes equations for resonant domains. Indiana Univ. Maths J. 48 (3), 1133-1176.
3. Babin, A., Mahalov, A. & Nicolaenko, B. 2001 3D Navier-Stokes and Euler equations with initial data characterized by uniformly large vorticity. Indiana Univ. Maths J. 50, 1-35.
4. Bardina, J., Ferziger, J. & Rogallo, R. S. 1985 Effect of rotation on isotropic turbulence: Computation and modelling. J. Fluid Mech. 154, 321-326.
5. Bartello, P., Métais, O. & Lesieur, M. 1994 Coherent structures in rotating three-dimensional turbulence. J. Fluid Mech. 173, 1-29.
6. Bellet, F. 2003 Étude asymptotique de la turbulence d'ondes en rotation. PhD thesis, École Centrale de Lyon.
7. Benney, D. J. & Newell, A. C. 1969 Random wave closures. Stud. Appl. Maths 48, 29-53.
8. Benney, D. J. & Saffman, P. G. 1966 Nonlinear interaction of random waves in a dispersive medium. Proc. R. Soc. Lond. A 289, 301-320.
9. Caillol, P. & Zeitlin, V. 2000 Kinetic equations and stationary energy spectra of weakly nonlinear internal gravity waves. Dyn. Atmos. Oceans 32, 81-112.
10. Cambon, C. 1982 Étude spectrale d'un champ turbulent incompressible soumis à des effets couplés de déformation et de rotation imposés extérieurement. PhD thesis, Univ. Lyon I, France.
11. Cambon, C., Godeferd, F. S., Nicolleau, F. C. G. A. & Vassilicos, J. C. 2004a Turbulent diffusion in rapidly rotating flows with and without stable stratification. J. Fluid Mech. 499, 231-255.
12. Cambon, C. & Jacquin, L. 1989 Spectral approach to non-isotropic turbulence subjected to rotation. J. Fluid Mech 202, 295-317.
13. Cambon, C., Jacquin, L. & Lubrano, J.-L. 1992 Toward a new reynolds stress model for rotating turbulence. Phys. Fluids A 4 (4), 812-824.
14. Cambon, C., Mansour, N. N. & Godeferd, F. S. 1997 Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303-332.
15. Cambon, C., Rubinstein, R. & Godeferd, F. S. 2004b Advances in wave turbulence: Rapidly rotating flows. New J. Phys. 6 (73).
16. Cambon, C. & Scott, J. F. 1999 Linear and nonlinear models of anisotropic turbulence. Annu. Rev. Fluid Mech. 31, 1-53.
17. Comte-Bellot, G. & Corrsin, S. 1971 Simple eulerian time-correlation of full and narrow-band velocity signals in grid-generated isotropic turbulence. J. Fluid Mech. 48, 273-337.
18. Craya, A. D. D. 1958 Contribution à l'analyse de la turbulence associée à des vitesses moyennes. PST 345. Ministère de l'air, France.
19. Galtier, S. 2003 A weak inertial wave turbulence theory. Phys. Rev. E 68, 015301-1-4.
20. Galtier, S., Nazarenko, S., Newell, A. C. & Pouquet, A. 2000 A weak turbulence theory for incompressible MHD. J. Plasma Phys. 63, 447-488.
21. Godeferd, F. S. & Cambon, C. 1994 Detailed investigation of energy transfers in homogeneous stratified turbulence. Phys. Fluids 6 (6), 2084-2100.
22. Godeferd, F. S. & Staquet, C. 2003 Statistical modelling and direct numerical simulations of decaying stably-stratified turbulence. Part 2. Large-scale and small-scale anisotropy. J. Fluid Mech. 486, 115-159.
23. Godeferd, F. S. & Lollini, L. 1999 Direct numerical simulations of turbulence with confinement and rotation. J. Fluid Mech. 393, 257-308.
24. Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press; reprinted 1990 by Breukelen Press, Brookline, MA.
25. Hossain, M. 1994 Reduction in the dimensionality of turbulence due to a strong rotation. Phys. Fluids 6, 1077-1080.
26. Jacquin, L., Leuchter, O., Cambon, C. & Mathieu, J. 1990 Homogeneous turbulence in the presence of rotation. J. Fluid Mech. 220, 1-52.
27. Kraichnan, R. H. 1958 The structure of isotropic turbulence at very high reynolds numbers. J. Fluid Mech. 5, 497-543.
28. Leith, C. E. 1971 Atmospheric predicability and two dimensional turbulence. J. Atmos. Sci. 28, 145-161.
29. Lvov, Y. & Tabak, E. 2001 Hamiltonian formalism and the garrett-munk spectrum of internal waves in the ocean. Phys. Rev. Lett. 87, 168501.
30. McEwan, A. D. 1970 Inertial oscillations in a rotating fluid cylinder. J. Fluid Mech. 40, 603-640.
31. Monin, A. & Yaglom, A. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence (2 vols.). MIT Press.
32. Morinishi, Y., Nakabayashi, K. & Ren, S. Q. 2001a Dynamics of anisotropy on decaying homogeneous turbulence subjected to system rotation. Phys. Fluids 13, 2912.
33. Morinishi, Y., Nakabayashi, K. & Ren, S. Q. 2001b A new dns algorithm for rotating homogeneous turbulence. Intl J. Heat Fluid Flow 22, 30-38.
34. Mowbray, D. E. & Rarity, D. E. 1967 A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J. Fluid Mech. 28, 1-16.
35. Orszag, S. A. 1969 Numerical methods for the simulation of turbulence. Phys. Fluids, Suppl. II 12, 250-257.
36. Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363.
37. Pouquet, A., Lesieur, M., André, J. C. & Basdevant, C. 1975 Evolution of high Reynolds number two-dimensional turbulence. J. Fluid Mech. 75, 305-319.
38. Reynolds, W. C. & Kassinos, S. 1995 One-point modeling for rapidly deformed homogeneous turbulence. Proc. R. Soc. Lond. A 451, 87-104.
39. Riley, J. J., Metcalfe, R. W. & Weissman, M. A. 1981 Direct numerical simulations of homogeneous turbulence in density-stratified fluids. In Proc AIP Conf. on Nonlinear Properties of Internal Waves (ed. B. West), pp. 79-112. American Institute of Physics.
40. Smith, L. & Lee, Y. 2005 On near resonances and symmetry breaking in forced rotating flows at moderate rossby number. J. Fluid Mech. 535, 111-142.
41. Smith, L. & Waleffe, F. 1999 Transfer of energy to two-dimensional large scales in forced, rotating three-dimensionnal turbulence. Phys. Fluids 11 (6), 1608-1622.
42. Smith, L. & Waleffe, F. 2002 Generation of slow large scales in forced rotating stratified turbulence. J. Fluid Mech. 451, 145-168.
43. Squires, K. D., Chasnov, J. R., Mansour, N. N. & Cambon, C. 1994 The asymptotic state of rotating homogeneous turbulence at high Reynolds number. In Application of Direct and Large Eddy Simulation to Transition and Turbulence. Chania, Crete, Greece.
44. Staquet, C. & Sommeria, J. 2002 Internal gravity waves: From instabilities to turbulence. Annu. Rev. Fluid Mech. 34, 559-593.
45. Turner, L. 1999 Macroscopic structures of inhomogeneous, Navier-Stokes turbulence. Phys. Fluids 11, 2367-2380.
46. Waleffe, F. 1993 Inertial transfers in the helical decomposition. Phys. Fluids A 5, 677-685.
47. Yang, X. & Domaradzki, J. A. 2004 LES of decaying rotating turbulence. Phys. Fluids 16, 4088-4104.
48. Zakharov, V. E., Lvov, V. & Falkovich, G. 1992 Wave turbulence. Springer.
49. Zhou, Y. 1995 A phenomenological treatment of rotating turbulence. Phys. Fluids 7, 2092.