Abstract
Abstract. 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. This is observed, for example, in the highly energetic tidal flow near a sill in Knight Inlet. The new model further exhibits a turbulent length scale proportional to the Ozmidov scale, as observed in the ocean, and predicts the ratio between the turbulent Thorpe and Ozmidov length scales well within the range observed in the ocean.
Highlights
1.1 Motivation and goalBetween strong turbulence in the surface and benthic boundary layers and weak and to some degree intermittent turbulence in the interior, the oceans harbor dynamically different regimes of turbulent flows
On the other hand, mixing in the interior of the ocean is dominantly driven by internal gravity waves, and the prevailing model of this mixing has its root in nonlinear wave-wave interaction theory
We only treat the two limits of (i) internal wave-driven mixing in the absence of mean shear and (ii) mean-shear driven mixing in the absence of wave-generated turbulence
Summary
Between strong turbulence in the surface and benthic boundary layers and weak and to some degree intermittent turbulence in the interior, the oceans harbor dynamically different regimes of turbulent flows. On the one hand, mixing in boundary layers and mean shear flows, such as, for example, in tidal domains or in the Equatorial Undercurrent (EUC), is commonly represented by turbulence closure models. These models have their root in the turbulence theory of neutrally stratified flows and are completely ignorant of the presence of internal waves. A more sophisticated approach than a background diffusivity is clearly needed to account for turbulence in geophysical flows This conclusion is supported by an examination of a K-ε closure applied to the permanently stratified and strongly sheared tidal flow of the Hudson River by Peters and Baumert (2007). We show below that our new model is constructed such that it exhibits the most important results of DL00
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