Ocean Science www.ocean-sci.net 1812-0784 1812-0792 5 1 2009 10.5194/os-5-47-2009 http://www.ocean-sci.net/5/47/2009/ http://www.ocean-sci.net/5/47/2009/os-5-47-2009.html http://www.ocean-sci.net/5/47/2009/os-5-47-2009.pdf 47 58 2009-03-06 Turbulence closure: turbulence, waves and the wave-turbulence transition – Part 1: Vanishing mean shear H. Z. Baumert H. Peters hpeters@esr.org Freie Universität, Dept. Mathematics and Computer Science, Berlin, and Institute for Applied Marine and Limnic Studies, Hamburg, Germany Earth and Space Research, Seattle, USA This paper extends a turbulence closure-like model for stably stratified flows into a new dynamic domain in which turbulence is generated by internal gravity waves rather than mean shear. The model turbulent kinetic energy (TKE, K) balance, its first equation, incorporates a term for the energy transfer from internal waves to turbulence. This energy source is in addition to the traditional shear production. The second variable of the new two-equation model is the turbulent enstrophy (Ω). Compared to the traditional shear-only case, the Ω-equation is modified to account for the effect of the waves on the turbulence time and space scales. This modification is based on the assumption of a non-zero constant flux Richardson number in the limit of vanishing mean shear when turbulence is produced exclusively by internal waves. This paper is part 1 of a continuing theoretical development. It accounts for mean shear- and internal wave-driven mixing only in the two limits of mean shear and no waves and waves but no mean shear, respectively. The new model reproduces the wave-turbulence transition analyzed by D'Asaro and Lien (2000b). At small energy density E of the internal wave field, the turbulent dissipation rate (ε) scales like ε~E2. This is what is observed in the deep sea. With increasing E, after the wave-turbulence transition has been passed, the scaling changes to ε~E1. 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