REALIZABILITY CONDITIONS FOR THE TURBULENT STRESS TENSER IN LARGE-EDDY SIMULATION

The turbulent stress tenser in large-eddy simulation is examined from a theoretical point of view. Realizability conditions for the componen ts of this tenser are derived, which hold if and only if the filter fu nction is positive. The spectral cut-off, one of the filters frequentl y used in large-eddy simulation, is not positive. Consequently, the tu rbulent stress tenser based on spectrally filtered fields does not sat isfy the realizability conditions, which leads to negative values of t he generalized turbulent kinetic energy k. Positive filters, e.g. Gaus sian or top-hat, always give rise to a positive k. For this reason, su bgrid models which require positive values for k should be used in con junction with e.g. the Gaussian or top-hat filter rather than with the spectral cut-off filter. If the turbulent stress tenser satisfies the realizability conditions, it is natural to require that the subgrid m odel for this tenser also satisfies these conditions. With respect to this point of view several subgrid models are discussed. For eddy-visc osity models a lower bound for the generalized turbulent kinetic energ y follows as a necessary condition. This result provides an inequality for the model constants appearing in a 'Smagorinsky-type' subgrid mod el for compressible flows.