Stratified turbulence in the atmosphere and oceans: a new subgrid model

Abstract

Turbulence in a stratified medium is studied with emphasis on stable stratification, as it occurs in the atmosphere and oceans, and on the construction of a subgrid model (SGS) for use in large eddy simulation (LES). The two basic assumptions of all SGS models are 1) that the unresolved scales are isotropic and 2) that they can be described by a Kolmogorov spectrum and are no longer valid in a stably stratified medium. First, Weinstock's model is used to find that the energy dissipation rate ε decreases with stability. By contrast, the dissipation rate εθ of temperature variance increases with stability. Second, because fo the higher anisotropy of stably stratified flows, even the most complete SGS model presently in use must be enalrged to include new higher-order terms. A new second-order closure model presently in use must be enlarged to include new higher-order temrs. A new second-order closure model is proposed in which the three components of the flux μ̄īθ̄ can be obtained by inverting a 3 × 3 matrix and μ̄īμ̄j̄ can be obtained by inverting a 6 × 6 matrix. An approximate procedure is suggested, however, to avoid the 6 × 6 matrix inversion and yet account for anisotropic production. Preliminary results indicate that the (total) kinetic energy dissipation length scale increase with stability, in accordance with LES results but in disagreement with Deardorff's model that suggested a decrease of all dissipation scales in presence of stratification. -from Authors