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.
This is a preview of subscription content, log in to check access
L.H.K. thanks the ONR for the support for this work through the ONR grant N00014-06-10287. L.H.K. is very thankful to George L. Mellor for pointing out that the IW fluctuations observed in the DM experiments could have been generated at the very beginning by the initial passage of the grid.
Batchelor GK, Townsend AA (1948) Decay of isotropic turbulence in the initial period. Proc Royal Soc A 193:539–566Google Scholar
Baumert H, Peters H (2000) Second moment closures and length scales for weakly stratified turbulent shear flows. J Geophys Res 105:6453–6468CrossRefGoogle Scholar
Baumert H, Peters H (2004) Turbulence closure, steady state, and collapse into waves. J Phys Oceanogr 34:505–512CrossRefGoogle Scholar
Baumert H, Simpson J, Sundermann J (eds) (2004) Marine turbulence: theories, observations and models. Cambridge University Press, Cambridge, UKGoogle Scholar
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
Burchard H (2002) Applied turbulence modeling in marine waters. Springer, Berlin Heidelberg New YorkGoogle Scholar
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
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
Dickey TD (1977) An experimental study of decaying and diffusing turbulence in neutral and stratified fluids, Ph.D. dissertation. Princeton University, pp 133Google Scholar
Dickey TD, Mellor GL (1980) Decaying turbulence in neutral and stratified fluids. J Fluid Mech 99:13–31CrossRefGoogle Scholar
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
Hopfinger EJ (1987) Turbulence in stratified fluids: a review. J Geophys Res 92:5287–5303Google Scholar
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