On the critical Richardson number in stably stratified turbulence

Atmospheric Science Letters

Volumn 8, Issue 3, 2007, Pages 65-69

  Galperin, Boris ^a   Sukoriansky, Semion ^b   Anderson, Philip S ^c  

^a UNIVERSITY OF SOUTH FLORIDA   (United States)

^b BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^c BRITISH ANTARCTIC SURVEY   (United Kingdom)

Author keywords

Critical Richardson number; Stable stratification; Turbulence

Indexed keywords

INTERNAL WAVE; LAMINAR FLOW; OBSERVATIONAL METHOD; RICHARDSON NUMBER; STRATIFICATION; TURBULENCE; VERTICAL MIXING;

EID: 38749139908     PISSN: None     EISSN: 1530261X     Source Type: Journal    
DOI: 10.1002/asl.153     Document Type: Article

References (52)

1. Abarbanel H, Holm D, Marsden J, Ratiu T. 1984. Richardson number criterion for the nonlinear stability of three-dimensional stratified flow. Physical Review Letters 52: 2352-2355.
2. Andreas E. 2002. Parametric scalar transfer over snow and ice: A review. Journal of Hydrometeorology 3: 417-432.
3. Blanke B, Delecluse P. 1993. Variability of the tropical Atlantic ocean simulated by a general circulation model with two different mixed-layer physics. Journal of Physical Oceanography 23: 1363-1388.
4. Canuto V. 1998. Turbulence in stars. II. Shear, stable stratification, and radiative losses. Astrophysics Journal 508: 767-779.
5. Canuto V. 2002a. Critical Richardson numbers and gravity waves. Astronomy and Astrophysics 384: 1119-1123.
6. Canuto V. 2002b. Diffusion in stars: the case of gravity waves, rigid rotation and stable stratification. Monthly Notices of the Royal Astronomical Society 337: 713-719.
7. Canuto V, Howard A, Cheng Y, Dubovikov M. 2001. Ocean turbulence. Part I: One-point closure model momentum and heat vertical diffusivities. Journal of Physical Oceanography 31: 1413-1426.
8. Drazin P. 1977. On the instability of an internal gravity ware. Proceedings of the Royal Society of London Series A 356: 411-432.
9. Gage K. 1971. The effect of stable thermal stratification on the stability of viscous parallel flows. Journal of Fluid Mechanics 47: 1-20.
10. Garcia-Lopez R, Spruit H. 1991. Li depletion in F stars by internal gravity waves. Astrophysical Journal 377(1): 268-277.
11. Gregg M, Sanford T, Whikel D. 2003. Reduced mixing from the breaking of internal waves in equatorial waters, Nature 422: 513-515.
12. Howard L. 1961. Note on a paper of John W. Miles. Journal of fluid Mechanics 10: 509-512.
13. Itsweire E, Helland K. 1989. Spectra and energy-transfer in stably stratified turbulence. Journal of Fluid Mechanics 207: 419-452.
14. Izakov M. 2003. Estimating the role of different sources of turbulent energy in the atmosphere of Venus. Solar System Research 37: 489-496.
15. Kimura Y, Herring J. 1996. Diffusion in stably stratified turbulence. Journal of Fluid Mechanics 328: 253-263.
16. Laval J-P, McWilliams J, Dubrulle B. 2003. Forced stratified turbulence: Successive transitions with Reynolds number. Physical Review E 68: 036308.
17. Lettau H. 1979. Wind and temperature profile prediction for diabatic surface layers including strong inversion cases. Boundary-Layer Meteorology 17: 443-464.
18. Lewellen W. 1977. Use of invariant modeling. In Handbook of Turbulence, Volume I-Fundamentals and Applications. Plenum Press: New York; 237-280.
19. Ligniéres F, Califano F, Mangeney A. 1999. Shear layer instability in a highly diffusive stably stratified atmosphere. Astronomy and Astrophysics 349: 1027-1036.
20. Lilly DK. The representation of small-scale turbulence in numerical simulations experiments, Proc. IBM Scientific Symp. on Envir. Science, pp 195-210, 1967.
21. Maeder A, Meynet G. 1996. Diffusive mixing by shears in rotating stars. Astronomy and Astrophysics 313: 140-144.
22. Mahrt L. 1998. Stratified atmospheric boundary layers and breakdown of models. Theoritical and Computational Fluid Dynamics 11: 263-279.
23. Mahrt L, Vickers D. 2006. Extremely weak mixing in stable conditions. Boundary-Layer Meteorology 119: 19-39.
24. Majda A, Shefter M. 1998. Elementary stratified flows with instability at large Richardson number. Journal of Fluid Mechanics 376: 319-350.
25. Martin P. 1985. Simulation of the mixed layer at OWS November and Papa with several models. Journal of Geophysical Research 90: 903-916.
26. Mathis S, Palacios A, Zahn J-P. 2004. On shear-induced turbulence in rotating stars. Astronomy and Astrophysics 425: 243-247.
27. Mauritsen T, Svensson G. 2007. Observations of stably stratified shear-driven atmospheric turbulence at low and high Richardson numbers. Journal of the Atmospheric Sciences 64: 645-655.
28. Meier M. 2001. On the parameterization of mixing in three-dimensional Baltic Sea models. Journal of Geophysical Research 106: 30997-31016.
29. Mellor G. 1973. Analytic prediction of the properties of stratified planetary surface layers. Journal of the Atmospheric Sciences 30: 1061-1069.
30. Mellor G, Yamada T. 1982. Development of a turbulence closure model for geophysical fluid problems. Reviews of Geophysics and Space Physics 20: 851-875.
31. Métais O, Herring J. 1989. Numerical studies of freely decaying homogeneous stratified turbulence. Journal of Fluid Mechanics 202a: 117-148.
32. Meunier P, Diamessis P, Spedding G. 2006. Self-preservation in stratified momentum wakes. Physics of Fluids 18: 106601.
33. Miles J. 1961. On the stability of heterogeneous shear flows. Journal of Fluid Mechanics 10: 496-508.
34. Monin A, Yaglom A. Statistical Fluid Mechanics. Mechanics of Turbulence, Vol. 1. The MIT Press, Cambridge, Massachusetts; 1975.
35. Monti P, Fernando HJS, Princevac M, Chan WC, Kowalewski TA, Pardyjak ER. 2002. Observations of flow and turbulence in the nocturnal boundary layer over a slope. Journal of the Atmospheric Sciences 59: 2513-2534.
36. Osborn T. 1980. Estimates of the local rate of vertical diffusion from dissipation measurements. Journal of Physical Oceanography 10: 83-89.
37. Polzin K, Ferrari R. 2004. Isopycnal dispersion in NATRE. Journal of Physical Oceanography 34: 247-257.
38. Rafkin S, Haberle R, Michaels T. 2001. The Mars regional atinospheric modeling system: Model description and selected simulations. Icarus 151: 228-256.
39. Ristorcelli J. 1997. Toward a turbulence constitutive relation for geophysical flows. Theoretical and Computational Fluid Dynamics 9: 207-221.
40. Schatzman E, Zahn J-P, Morel P. 2000. Shear turbulence beneath the solar tachocline. Astronomy and Astrophysics 364: 876-878.
41. Smagorinsky J. 1963. General circulation experiments with the primitive equations. Monthly Weather Review 91: 99-164.
42. Spedding G. 1997. The evolution of initially turbulent bluff-body wakes at high internal Froude number. Journal of Fluid Mechanics 337: 283-301.
43. Spedding G. 2001. Anisotropy in turbulence profiles of stratified wakes. Physics of Fluids 13: 2361-2372.
44. Strang E, Fernando HJS. 2001. Vertical mixing and transports through a stratified shear layer. Journal of Physical Oceanography 31: 2026-2048.
45. Sukoriansky S, Galperin B, Staroselsky I. 2005. A quasinormal scale elimination model of turbulent flows with stable stratification. Physics of Fluids 17: 085107.
46. Sukoriansky S, Galperin B, Perov V. 2006. A quasi-normal scale elimination model of turbulence and its application to stably stratified flows. Nonlinear Processes in Geophysics 13: 9-22.
47. Webster C. 1964. An experimental study of turbulence in a density stratified shear flow. Journal of Fluid Mechanics 19: 221-245.
48. Weinstock J. 1978. Vertical turbulent-diffusion in a stably stratified fluid. Journal of the Atmospheric Sciences 35: 1022-1027.
49. Yagüe C, Maqueda G, Rees J. 2001. Characteristics of turbulence in the lower atmosphere at Halley IV station, Antarctica. Dynamics of Atmospheres and Oceans 34: 205-223.
50. h, for the stable atmospheric boundary layer. Nonlinear Processes in Geophysics 13: 185-203.
51. Yamamoto G. 1975. Generalization of the KEYPS formula in diabatic conditions and related discussion on the critical Richardson number. Journal of the Meteorological Society of Japan 53: 189-195.
52. Zhang J, Steele M. 2007. Effect of vertical mixing on the Atlantic Water layer circulation in the Arctic Ocean. Journal of Geophysical Research 112: C04S04, DOI: 10.1029/2006JC003732.