An Algebraic Model for Subgrid-Scale Turbulence in Stratified Flows

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Abstract
Some aspects of the large eddy simulation method as applied to stratified flows are discussed and an algebraic model for subgrid-scale (SGS) turbulence is proposed. Differential equations for the SGS Reynolds stresses and turbulent heat fluxes are derived and new terms, which appear as a result of filtering nonlinear terms, are discussed. With the introduction of certain simplifying assumptions, the set of differential equations is reduced to a system of algebraic equations. The behavior of the solution of this system is studied for the special case of a locally two-dimensional structure for the large-scale field. Under certain assumptions the form of the algebraic equations for the SGS quantities is similar to the form of the equations for the corresponding “conventional” turbulent quantities. This allows comparison of the predictions made by the present SGS model to the results from “conventional” models and experimental data. The proposed model predicts that, for highly stratified flows, SGS turbulence is totally suppressed if the large-scale field is characterized by pure shear. In the presence of stretching, SGS turbulence approaches a constant level asymptotically as the intensity of stratification increases.

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