Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 2. Large-scale and small-scale anisotropy

Journal of Fluid Mechanics

Volumn 486, Issue , 2003, Pages 115-159

  Godeferd, F S ^a   Staquet, C ^b  

^a LABORATOIRE DE MÉCANIQUE DES FLUIDES ET D ACOUSTIQUE   (France)

^b LEGI   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; COMPUTER SIMULATION; KINETIC ENERGY; REYNOLDS NUMBER;

VORTEX STRUCTURES;

TURBULENT FLOW;

ANISOTROPIC MEDIUM; MATHEMATICAL ANALYSIS; MODELING; STATISTICAL ANALYSIS; STRATIFIED FLOW; TURBULENCE;

EID: 0037962022     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003004531     Document Type: Article

References (61)

1. ANDRÉ, J. C. & LESIEUR, M. 1977 Influence of helicity on high Reynolds number isotropic turbulence. J. Fluid Mech. 81, 187-207.
2. BARRY, M. E., IVEY, G. N., WINTERS, K. B. & IMBERGER, J. 2001 Measurements of diapycnal diffusivities in stratified fluids. J. Fluid Mech. 442, 267-291.
3. BATCHELOR, G. K. 1946 The theory of axisymmetric turbulence. Proc. R. Soc. Lond. A 186, 480-502.
4. BATCHELOR, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.
5. BILLANT, P. & CHOMAZ, J.-M. 2001 Self-similarity of strongly stratified inviscid flows. Phys. Fluid 13, 1645-1651.
6. BOURUET-AUBERTOT, P., KOUDELLA, C., STAQUET, C. & WINTERS, K. B. 2001 Particle dispersion and mixing by breaking internal gravity waves: two-dimensional numerical experiments. Dyn. Atmos. Oceans 33, 95-134.
7. BOUSSINESQ, J. 1901 Théorie Analytique de la Chaleur. Gauthier-Villars, Paris.
8. BRYAN, F. 1987 Parameter sensitivity of primitive equation ocean general circulation models. J. Phys. Oceanogr. 17, 970-985.
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. 1989 Spectral Approach to Axisymmetric Turbulence in a Stratified Fluid. Advances in Turbulence 2 (ed. H.-H. Fernholz & H. E. Fiedler). Springer.
11. CAMBON, C. 2001 Turbulence and vortex structures in rotating and stratified flows. Eur. J. Mech. B Fluids 20, 489-510.
12. CAMBON, C., MANSOUR, N. N. & GODEFERD, F. S. 1997 Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303-332.
13. CANUTO, C., HUSSAINI, M. Y., QUARTERONI, A. & ZANG, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.
14. CRAYA, A. D. 1958 Contribution à l'analyse de la turbulence associée à des vitesses moyennes. PST 345. Ministère de I'Air, France.
15. FINCHAM, A. M., MAXWORTHY, T. & SPEDDING, G. R. 1996 Energy dissipation and vortex structure in freely-decaying stratified grid-turbulence. Dyn. Atmos. Oceans 23, 155-169.
16. GARGETT, A. E., OSBORN, T. R. & NASMYTH, P. W. 1984 Local isotropy and the decay of turbulence in a stratified fluid. J. Fluid Mech. 144, 231-280.
17. GODEFERD, F. S. & CAMBON, C. 1994 Detailed investigation of energy transfers in homogeneous stratified turbulence. Phys. Fluids 6, 2084-2100.
18. HANAZAKI, H. & HUNT, J. C. R. 1996 Linear processes in unsteady stably stratified turbulence. J. Fluid Mech. 318, 303-337.
19. VANHAREN, L., STAQUET, C. & CAMBON, C. 1996 Decaying stratified turbulence: comparison between a two-point closure EDQNM model and direct numerical simulations. Dyn. Atmos. Oceans 23, 217-245.
20. HERRING, J. R. 1974 Approach of axisymmetric turbulence to isotropy. Phys. Fluids 17, 859-872.
21. HERRING, J. R. & KRAICHNAN, R. H. 1971 Comparison of some approximations for isotropic turbulence. In Statistical Models and Turbulence, Lecture Notes in Physics, vol. 12 (ed. J. Ehlers, K. Hepp & H. A. Weidenmller). Springer.
22. HERRING, J. R. & METAIS, O. 1989 Numerical experiments in forced stably stratified turbulence. J. Fluid Mech. 202, 97-115.
23. HOLLIDAY, D. & MCINTYRE, M. E. 1981 On potential energy density in an incompressible stratified fluid. J. Fluid Mech. 107, 221-225.
24. HUQ, P. & STRETCH, D. D. 1995 Critical dissipation rates in density stratified turbulence. Phys. Fluids 7, 1034-1039.
25. ITSWEIRE, E. C., HELLAND, K. N. & VAN ATTA, C. W. 1986 The evolution of grid-generated tubulence in a stably stratified fluid. J. Fluid Mech. 162, 299-338.
26. LELONG, M. P. & RILEY, J. J. 1991 Internal wave-vortical mode interactions in strongly stratified flows. J. Fluid Mech. 232, 119.
27. LESIEUR, M. 1990 Turbulence in Fluids, 2nd Edn. Kluwer.
28. LESIEUR, M. & METAIS, O. 1996 New trends in large-eddy simulations of turbulence. Annu. Rev. Fluid Mech. 28, 45 82.
29. LIENHARD, J. H. & VAN ATTA, C. W. 1990 The decay of turbulence in thermally stratified flow. J. Fluid Mech. 210, 57 112.
30. LILLY, D. K. 1983 Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 40, 749 761.
31. LIN, J.-T. & PAO, Y.-H. 1979 Wakes in stratified fluids. Annu. Rev. Fluid Mech. 11, 317-338.
32. LORENZ, E. 1955 Available potential energy and the maintenance of the general circulation. Tellus 7, 157 167.
33. MCINTYRE, M. E. & NORTON, W. A. 1990 Dissipative wave-mean interactions and the transports of vorticity or potential vorticity. J. Fluid Mech. 212, 403 435; and Corrigendum 220, 693.
34. METAIS, O. & HERRING, J. R. 1989 Numerical simulations of freely evolving turbulence in stably stratified fluids. J. Fluid Mech. 202, 117-148.
35. ORSZAG, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363.
36. OSBORN, T. R. & COX, C. S. 1972 Oceanic fine structure. Geophys. Fluid Dyn. 3, 321-345.
37. PICCIRILLO, P. & VAN ATTA, C. W. 1997 The evolution of uniformly sheared thermally stratified turbulent flow. J. Fluid Mech. 334, 61-86.
38. RAMSDEN, D. & HOLLOWAY, G. 1992 Energy transfers across an internal wave-vortical mode spectrum. J. Geophys. Res. 97, 3659-3668.
39. REYNOLDS, W. C. & KASSINOS, S. 1995 One-point modelling of rapidly deformed homogeneous turbulence. Osborne Reynolds Centenary Volume. Proc. R. Soc. Lond. A 451, 87 104.
40. RILEY, J. J. & LELONG, M.-P. 2000 Fluid motions in the presence of strong stable stratification. Annu. Rev. Fluid Mech. 32, 613 657.
41. 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 Wave (ed. B. J. West), pp. 79 112. American Institute of Physics.
42. ROGALLO, R. S. 1981 Numerical experiments in homogeneous turbulence. NASA Tech. Mem. 81315.
43. 2m]) fluctuations in the stratosphere. Proc. Euromech Colloquium 339 (ed. C. Staquet).
44. SIEGEL, D. A. & DOMARADZKI, J. A. 1994 Large Eddy Simulation of Decaying Stratified Turbulence. J. Phys. Oceangr. 24, 1353 1386.
45. SOMMERIA, J. 2002 Two-dimensional turbulence. Les Houches. Ecole d'Été de Physique Théorique, vol. 74. Springer.
46. STAQUET, C. 2000 Mixing in a stably stratified shear layer: two- and three-dimensional numerical experiments. Fluid Dyn. Res. 27, 367 -404.
47. STAQUET, C. & GODEFERD, F. S. 1998 Statistical modelling and direct numerical simulations of decaying stably stratified turbulence. Part 1. Energetics. J. Fluid Mech. 360, 295-340.
48. STILLINGER, D. C., HELLAND, K. N. & VAN ATTA, C. 1983 Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid. J. Fluid Mech. 131, 91 122.
49. THORODDSEN, S. T. & VAN ATTA, C. W. 1992 The influence of stable stratification on small-scale anisotropy and dissipation in turbulence. J. Geophys. Res. 97 (C3), 3647 3658.
50. THORODDSEN, S. T. & VAN ATTA, C. W. 1996 Experiments on density-gradient anisotropies and scalar dissipation of turbulence in a stably stratified fluid. J. Fluid Mech. 322, 383 409.
51. THORPE, S. A. 1977 Turbulence and mixing in a scottish loch. Phil. Trans. R. Soc. Lond. 286, 125 181.
52. THUAL, O. 1992 Zero-Prandtl-number convection. J. Fluid Mech. 240, 229 258.
53. TOOLE, J. M. 1998 Turbulent Mixing in the Ocean: Intensity, Causes, and Consequences. In Ocean Modeling and Parameterization (ed. E. P. Chassignet & J. Verron) pp. 171 190. Kluwer.
54. TOWNSEND, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
55. VINCENT, A. & MENEGUZZI, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid Mech. 225, 1 20.
56. WINTERS, K. B., LOMBARD, P. N., RILEY, J. J. & D'ASARO, E. A. 1995 Available potential energy and mixing in stratified fluids. J. Fluid Mech. 289, 115 128.
57. YAMAZAKI, H. & OSBORN, T. 1990 Dissipation estimates for stratified turbulence. J. Geophys. Res. 95, 9739 9744.
58. YAMAZAKI, H. & OSBORN, T. 1993a Correction to "Dissipation estimates for stratified turbulence". J. Geophys. Res. 98(12), 605.
59. YAMAZAKI, H. & OSBORN, T. 1993b Direct estimation of heat flux in a seasonal thermocline. J. Phys. Oceanogr. 23, 503-516.
60. YEUNG, P. K., BRASSEUR, J. G. & WANG, Q. 1995 Dynamics of direct large-small scale couplings in coherently forced turbulence: concurrent physical- and Fourier-space views. J. Fluid Mech. 283, 43-95.
61. YOON, K. & WARHAFT, Z. 1990 The evolution of grid-generated turbulence under conditions of stable thermal stratification. J. Fluid Mech. 215, 601-638.