Realizability conditions for the turbulent stress tensor in large-eddy simulation

In this paper, the turbulent stress tensor in large-eddy simulation is examined from a theoretical point of view. Derived are realizability conditions for the components of this tensor, which hold true if and only if the filter function is positive. For eddy-viscosity models, a lower bound for the generalized turbulent kinetic energy follows as a necessary condition. This result provides an inequality for the model constants appearing in a 'Smagorinsky-type' subgrid model for compressible flows.