Subgrid scale stress models for the large-eddy simulation of rotating turbulent flows

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Abstract
The modeling of the subgrid scale stresses is considered from a theoretical standpoint with a view toward developing models that are more suitable for the large-eddy simulation of rotating turbulent flows. It is proven, as a rigorous consequence of the Navier-Stokes equations, that such models must be generally invariant under the extended Galilean group and must be frame-indifferent in the limit of two-dimensional turbulence which can be approached in a rapidly rotating framework. Furthermore, it is shown that a significant increase in the rotation rate must be accompanied by a substantial reduction in the energy dissipation rate of the turbulence. Vorticity subgrid scale stress models as well as several other commonly used models are shown to be in serious violation of one or more of these constraints and, hence, are not generally suitable for the description of rotating flows. Alternative models with the correct physical properties are discussed and compared.