Turbulence closure: Turbulence, waves and the wave-turbulence transition - Part 1: Vanishing mean shear

Ocean Science

Volumn 5, Issue 1, 2009, Pages 47-58

  Baumert, H Z ^a,b   Peters, H ^c  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

^b Institute for Applied Marine and Limnic Studies   (Germany)

^c EARTH AND SPACE RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEEP SEA; GRAVITY WAVE; INTERNAL WAVE; KINETIC ENERGY; RICHARDSON NUMBER; STRATIFIED FLOW; TURBULENCE;

EID: 71149097159     PISSN: 18120784     EISSN: 18120792     Source Type: Journal    
DOI: 10.5194/os-5-47-2009     Document Type: Article

References (47)

1. Abarbanel, H. D. I., Holm, D. D., Marsden, J. E., and Ratio, T.: Richardson number criterion for the nonlinear stability of threedimensional stratified flow, Phys. Rev. Lett., 26, 2352-2355, 1984.
2. Baumert, H.: A Novel Two-Equation Turbulence Closure for high Reynolds numbers. Part B: Spatially Non-Uniform Conditions, in: Marine Turbulence, Theories, Observations and Models, edited by Baumert, H., Simpson, J., and Sündermann, J., Cambridge University Press, Cambridge, UK, 4, 31-43, 2005.
3. Baumert, H. and Peters, H.: Second Moment Closures and Length Scales for Stratified Turbulent Shear Flows, J. Geophys. Res., 105, 6453-6468, 2000.
4. Baumert, H. and Peters, H.: Turbulence Closure, Steady State, and Collapse into Waves, J. Phys. Oceanogr., 34, 505-512, 2004
5. Baumert, H. and Peters, H.: A Novel Two-Equation Turbulence Closure for high Reynolds numbers. Part A: Homogeneous, Non- Rotating Stratified Shear Layers, in: Marine Turbulence, Theories, Observations and Models, edited by Baumert, H., Simpson, J., and Sündermann, J., Cambridge University Press, Cambridge, UK, 14-30, 2005.
6. Canuto, V. M., Howard, A., Cheng, Y., and Dubovikov, M. S.: Ocean turbulence I: One-point closure model. Momentum and heat vertical diffusivities, J. Phys. Oceanogr., 31, 1413-1426, 2001.
7. Crawford,W. R.: A Comparison of Length Scales and Decay Times of Turbulence in Stratified Flows, J. Phys. Oceanogr., 16, 1847-1854, 1986.
8. D'Asaro, E. A. and Lien, R. C.: Lagrangian measurements of waves and turbulence in stratifed flows, J. Phys. Oceanogr., 30, 641-655, 2000a.
9. D'Asaro, E. A. and Lien, R. C.: The Wave-Turbulence Transition for Stratified Flows, J. Phys. Oceanogr., 30, 1669-1678, 2000b.
10. Dickey, T. D. and Mellor, G. L.: Decaying Turbulence in Neutral and Stratified Fluids, J. Fluid Mech., 99, 37-48, 1980.
11. Dillon, T. M.: Vertical Overturns: A Comparison of Thorpe and Ozmidov Length Scales, J. Geophys. Res., 87, 9601-9613, 1982.
12. Foken, T.: 50 years of the Monin-Obukhov similarity theory, Bound.-Lay. Meteorol., 119, 431-447, 2006.
13. Fritts, D. and Alexander, J.: Middle atmosphere gravity wave dynamics, Rev. Geophys., 41, 1-64, 2003.
14. Fritts, D. C.: A review of gravity wave saturation processes, effects and variability in the middle atmosphere, Pure Appl. Geophys., 130, 242-371, 1989.
15. Galperin, B., Sukoriansky, S., and Anderson, P. S.: On the critical Richardson number in stably stratified turbulence, Atmos. Sci. Lett., 8, 65-69, 2007.
16. Garrett, C. J. R. and Munk, W. H.: Space-Time Scales of Internal Waves, Geophys. Astrophys. Fluid Dyn., 3, 225-264, 1972.
17. Garrett, C. J. R. and Munk, W. H.: Space-Time Scales of Internal Waves: A Progress Report, J. Geophys. Res., 80, 291-297, 1975.
18. Gill, A. E.: Atmosphere-Ocean Dynamics, Academic Press, New York, 662 pp., 1982.
19. Gregg, M. C.: Scaling of Turbulent Dissipation in the Thermocline, J. Geophys. Res., 94, 9686-9697, 1989.
20. Gregg, M. C., Winkel, D. P., and Sanford, T. B.: Varieties of Fully Resolved Spectra of Vertical Shear, J. Phys. Oceanogr., 23, 124-141, 1993.
21. Henyey, F. S., Wright, J., and Flatté, S. M.: Energy and Action Flow Through the Internal Wave Field: An Eikonal Approach, J. Geophys. Res., 91, 8487-8495, 1986.
22. Howard, L. N.: Notes on a paper of John W. Miles, J. Fluid. Mech., 10, 509-512, 1961.
23. Li, M., Zhong, L., and Boicourt, W. C.: Simulations of Chesapeake Bay estuary: Sensitivity to turbulence mixing parameterizations and comparison with observations, J. Geophys. Res.- Oceans, 110, C12004, doi:10.1029/2004JC002585, 2005. (Pubitemid 43169355)
24. MacKinnon, J. A. and Gregg, M. C.: Mixing on the Late-Summer New England Shelf - Solibores, Shear, and Stratification, J. Phys. Oceanogr., 33, 1476-1492, 2003.
25. McComas, C. H. and Müller, P.: The Dynamic Balance of Internal Waves, J. Phys. Oceanogr., 11, 970-986, 1981.
26. Mellor, G. L. and Yamada, T.: A Hierarchy of Turbulence Closure models for Planetary Boundary Layers, J. Atmos. Sci., 31, 1791 - 1806, 1974.
27. Mellor, G. L. and Yamada, T.: Development of a Turbulence Closure Model for Geophysical Fluid Problems, Rev. Geophys., 20(4), 851-875, 1982.
28. Miles, J. W.: On the stability of heterogeneous shear flow, J. Fluid. Mech., 10, 496-508, 1961.
29. Moum, J. N.: The Quest for Kρ - Prelimiary Results From Direct Measurements of Turbulent Fluxes in the Ocean, J. Phys. Oceanogr., 20, 1980-1984, 1990.
30. Moum, J. N.: Efficiency of Mixing in the Main Thermocline, J. Geophys. Res., 101, 12 057-12 070, 1996a.
31. Moum, J. N.: Energy-Containing Scales of Stratified Turbulence, J. Geophys. Res., 101, 14 095-14 109, 1996b.
32. Oakey, N. S.: Determination of the Rate of Dissipation of Turbulent Energy From Simultaneous Temperature and Velocity Shear Microstructure Measurements, J. Phys. Oceanogr., 12, 256-271, 1982.
33. Osborn, T. R.: Estimates of the Local Rate of Vertical Diffusion from Dissipation Measurements, J. Phys. Oceanogr., 10, 83-89, 1980.
34. Peters, H. and Baumert, H. Z.: Validating a Turbulence Closure Against Estuarine Microstructure Measurements, Ocean Modelling, 19, 183-203, 2007.
35. Polzin, K., Toole, J. M., and Schmitt, R. W.: Finescale Parameterizations of Turbulent Dissipation, J. Phys. Oceanogr., 25, 306-328, 1995.
36. Richardson, L. F.: Weather prediction by numerical processes, Cambridge Univ. P., London, 236 pp., 1922.
37. Rodi, W.: Examples of Calculation Methods for Flow and Mixing in Stratified Fluids, J. Geophys. Res., 92, 5305-5328, 1987.
38. Rohr, J. J., Itsweire, E. C., Helland, K. N., and Van Atta, C. W.: Growth and Decay of Turbulence in a Stably Stratified Shear Flow, J. Fluid Mech., 195, 77-111, 1988.
39. Schumann, U. and Gerz, T.: Turbulent Mixing in Stably Stratified Shear Flows, J. Appl. Meteorol., 34, 33-48, 1995.
40. Shih, L. H., Koseff, J. R., Ferziger, J. H., and Rehmann, C. R.: Scaling and Parameterization of Stratified Homogeneous Turbulent Shear Flow, J. Fluid Mech., 412, 1-20, 2000.
41. Sukoriansky, S.: On the critical Richardson number in stably stratified turbulence, Atmospheric Science Letters, 8(3), 65-69, 2007.
42. Sukoriansky, S., Galperin, B., and Perov, V.: A quasi-normal scale elimination model of turbulence and its application to stably stratified flows, Nonlinear. Proc. Geoph., 13, 9-22, 2006.
43. Tjernström, M.: Turbulence length scales in stably stratied flows analyzed from slant aircraft proiles, J. Climate, 32, 948-963, 1993.
44. Weinstock, J.: Vertical Turbulence Diffusivity for Weak and Strong Stable Stratification, J. Geophys. Res., 86, 9925-9928, 1981.
45. Wijesekera, H.W. and Dillon, T. M.: Shannon Entropy as an Indicator of Age for Turbulent Overturns in the Oceanic Thermocline, J. Geophys. Res., 102, 3279-3291, 1997.
46. Wilcox, D. C.: Turbulence modeling for CFD, DCW Industries, Inc., La Canada, CA, 2nd edn., 540 pp., 1998.
47. Zilitinkevich, S. S., Elperin, T., Kleeorin, N., and Rogachevskii, I.: Energy- and flux-budget (EFB) turbulence closure model for the stably stratified flows. Part I: Steady-state, homogeneous regimes, Bound.-Lay. Meteorol., 125, 167-191, 2007.