Galilean invariance of subgrid-scale stress models in the large-eddy simulation of turbulence

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Abstract
The modelling of the subgrid-scale stresses in the large-eddy simulation of turbulence is examined from a theoretical standpoint. While there are a variety of approaches that have been proposed, it is demonstrated that one of the more recent models gives rise to equations of motion for the large eddies of turbulence which are not Galilean-invariant. Consequently, this model cannot be of any general applicability, since it is inconsistent with the basic physics of the problem, which requires that the description of the turbulence be the same in all inertial frames of reference. Alternative models that have been proposed which are properly invariant are discussed and compared.