Ocean Dynamics

, Volume 57, Issue 2, pp 151–156 | Cite as

On leakage of energy from turbulence to internal waves in the oceanic mixed layer

Original paper

Abstract

In this paper, we address the question of energy leakage from turbulence to internal waves (IWs) in the oceanic mixed layer (OML). If this leakage is substantial, then not only does this have profound implications as far as the dynamics of the OML is concerned, but it also means that the equation for the turbulence kinetic energy (TKE) used in OML models must include an appropriate sink term, and traditional models must be modified accordingly. Through comparison with the experimental data on grid-generated turbulence in a stably stratified fluid, we show that a conventional two-equation turbulence model without any IW sink term can explain these observations quite well, provided that the fluctuating motions that persist long after the decay of grid-generated turbulence are interpreted as being due to IW motions generated by the initial passage of the grid through the stably stratified fluid and not during turbulence decay. We conclude that there is no need to postulate an IW sink term in the TKE equation, and conventional models suffice to model mixing in the OML.

Keywords

Turbulence Turbulent mixing Oceanic mixed layer Stably stratified fluid Internal waves Turbulence kinetic energy 

References

  1. Batchelor GK, Townsend AA (1948) Decay of isotropic turbulence in the initial period. Proc Royal Soc A 193:539–566Google Scholar
  2. Baumert H, Peters H (2000) Second moment closures and length scales for weakly stratified turbulent shear flows. J Geophys Res 105:6453–6468CrossRefGoogle Scholar
  3. Baumert H, Peters H (2004) Turbulence closure, steady state, and collapse into waves. J Phys Oceanogr 34:505–512CrossRefGoogle Scholar
  4. Baumert H, Simpson J, Sundermann J (eds) (2004) Marine turbulence: theories, observations and models. Cambridge University Press, Cambridge, UKGoogle Scholar
  5. Browand FK, Guyomar D, Yoon SC (1987) The behavior of a turbulent front in a stratified fluid: experiments with an oscillating grid. J Geophys Res 92:5329–5341Google Scholar
  6. Burchard H (2002) Applied turbulence modeling in marine waters. Springer, Berlin Heidelberg New YorkGoogle Scholar
  7. Burchard H, Bolding K (2001) Comparative analysis of four second-moment turbulence closure models for the oceanic mixed layer. J Phys Oceanogr 31:1943–1968CrossRefGoogle Scholar
  8. Comte-Bellot G, Corrsin S (1966) The use of contraction to improve the isotropy of grid-generated turbulence. J Fluid Mech 25:657–687CrossRefGoogle Scholar
  9. Dickey TD (1977) An experimental study of decaying and diffusing turbulence in neutral and stratified fluids, Ph.D. dissertation. Princeton University, pp 133Google Scholar
  10. Dickey TD, Mellor GL (1980) Decaying turbulence in neutral and stratified fluids. J Fluid Mech 99:13–31CrossRefGoogle Scholar
  11. Gad-El-Hak M, Corrsin S (1974) Measurements of the nearly isotropic turbulence behind a uniform jet grid. J Fluid Mech 62:115–143CrossRefGoogle Scholar
  12. Hopfinger EJ (1987) Turbulence in stratified fluids: a review. J Geophys Res 92:5287–5303Google Scholar
  13. Itsweire EC, Helland KN, Van Atta CW (1986) The evolution of grid-generated turbulence in a stably stratified fluid. J Fluid Mech 162:299–338CrossRefGoogle Scholar
  14. Kantha LH (2003) On an improved model for the turbulent PBL. J Atmos Sci 60:2239–2246CrossRefGoogle Scholar
  15. Kantha LH (2004) The length scale equation in turbulence models. Nonlinear Process Geophys 11:83–97Google Scholar
  16. Kantha LH (2005) Comments on “Turbulence closure, steady state, and collapse into waves” by H. Baumert and H. Peters. J Phys Oceanogr 35:131–134CrossRefGoogle Scholar
  17. Kantha L, Carniel S (2003) Comments on “A generic length scale equation for geophysical turbulence models” by L. Umlauf and H. Burchard. J Mar Res 61:693–702CrossRefGoogle Scholar
  18. Kantha LH, Clayson CA (1994) An improved mixed layer model for geophysical applications. J Geophys Res 99:25235–25266CrossRefGoogle Scholar
  19. Kantha LH, Clayson CA (2000) Small scale processes in geophysical flows. Academic Press, New YorkGoogle Scholar
  20. Kato H, Phillips OM (1969) On the penetration of a turbulent layer into a stratified fluid. J Fluid Mech 37:643–655CrossRefGoogle Scholar
  21. Kistler AL, Vrebalovich T (1966) Grid turbulence at large Reynolds numbers. J Fluid Mech 26:37–47CrossRefGoogle Scholar
  22. Kolmogoroff AN (1941) The local structure of turbulence in incompressible viscous fluid for very large Reynolds number (in Russian). Dokl Akad Nauk SSSR 30:301–310Google Scholar
  23. Lange RE (1974) Decay of turbulence in stratified salt water. Ph.D. thesis, University of California, San DiegoGoogle Scholar
  24. Lin JT, Veenhuizen SD (1974) Measurements of the decay of grid-generated turbulence in a stably stratified fluid (abstract). Bull Am Phys Soc 19:1142–1143Google Scholar
  25. Mellor GL (2001) One-dimensional, ocean surface layer modeling: a problem and a solution. J Phys Oceanogr 31:790–809CrossRefGoogle Scholar
  26. Mellor GL, Blumberg AF (2004) Wave breaking and ocean surface thermal response. J Phys Oceanogr 34:693–698CrossRefGoogle Scholar
  27. Mellor GL, Yamada T (1982) Development of a turbulence closure model for geophysical fluid problems. Rev Geophys Space Phys 20:851–875Google Scholar
  28. Pao YH (1973) Measurements of internal waves and turbulence in two-dimensional stratified shear flows. Bound Layer Met 5:177–193CrossRefGoogle Scholar
  29. Riley JJ, Lelong M-P (2000) Fluid motions in the presence of strong stable stratification. Annu Rev Fluid Mech 32:613–657CrossRefGoogle Scholar
  30. Rohr J, Van Atta CW (1987) Mixing efficiency in stably stratified growing turbulence. J Geophys Res 92:5481–5488CrossRefGoogle Scholar
  31. Rohr JJ, Itsweire EC, Helland KN, Van Atta CW (1988) Growth and decay of turbulence in a stably stratified shear flow. J Fluid Mech 195:77–111CrossRefGoogle Scholar
  32. Schedvin J, Stegen G, Gibson CH (1974) Universal similarity at high grid Reynolds numbers. J Fluid Mech 65:561–579CrossRefGoogle Scholar
  33. Staquet C, Goderferd FS (1998) Statistical modeling and numerical simulation of decaying stably stratified turbulence. Part 1. Flow energetics. J Fluid Mech 360:295–340CrossRefGoogle Scholar
  34. Stillinger DC, Helland KN, Van Atta CW (1983) Experiments on the transition of homogeneous turbulence to internal waves in stratified fluid. J Fluid Mech 131:91–122CrossRefGoogle Scholar
  35. Uberoi MS, Wallis S (1967) Effect of grid geometry on turbulence decay. J Fluid Mech 10:1216–1224Google Scholar
  36. Umlauf L, Burchard H (2003) A generic length scale equation for geophysical turbulence models. J Mar Res 61:235–265CrossRefGoogle Scholar
  37. Van Atta CW (1999) On parameterizing turbulence growth rates and fluxes in nonequilibrium stably stratified turbulent shear flows. J Mar Syst 21:103–112CrossRefGoogle Scholar
  38. Van Atta CW, Chen WY (1968) Correlation measurements in grid turbulence using digital harmonic analysis. J Fluid Mech 34:497–515CrossRefGoogle Scholar
  39. Wyatt LA (1955) Energy and spectra in decaying homogeneous turbulence. Ph.D. thesis, University of ManchesterGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Aerospace Engineering Sciences, CB 431University of ColoradoBoulderUSA
  2. 2.Department of MeteorologyFlorida State UniversityTallahasseeUSA

Personalised recommendations