Discretization induced statistical artifacts in large-eddy simulation

Two effects of numerical discretization on the statistical properties of large-eddy simulation (LES) are discussed. First, we demonstrate the impact of numerical dispersion error on the energy cascade in LES. It is shown that dispersion error causes a phase decoherence between triad interacting wavemodes, leading to a reduction in the mean energy transfer rate for these scales and a corresponding reduction in the energy spectrum. The second result concerns the commutator between the filtering and differentiation operators, which arises as a result of inhomogeneous filtering/resolution in a LES. A statistical description of the commutator is derived for a general filter in terms of the energy spectrum, which can serve as a target for commutation models and determines the importance of the commutator relative to other turbulent processes. Both issues are explored through multiscale asymptotic analyses and simulations of homogeneous isotropic turbulence.