The turbulent stress tenser in large-eddy simulation is examined from a theoretical point of view. Realizability conditions for the components of this tenser are derived, which hold if and only if the filter function is positive. The spectral cut-off, one of the filters frequently used in large-eddy simulation, is not positive. Consequently, the turbulent stress tenser based on spectrally filtered fields does not satisfy the realizability conditions, which leads to negative values of the generalized turbulent kinetic energy k. Positive filters, e.g. Gaussian or top-hat, always give rise to a positive k. For this reason, subgrid models which require positive values for k should be used in conjunction 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 model for this tenser also satisfies these conditions. With respect to this point of view several subgrid models are discussed. 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.
