Magnitude control of commutator errors

Non-uniform filtering of the Navier-Stokes equations expresses itself, next to the turbulent stresses, in additional closure terms known as commutator errors. These terms require explicit subgrid modeling if the non-uniformity of the filter is sufficiently pronounced. We derive expressions for the magnitude of the mean flux, the turbulent stress flux and the commutator error for individual Fourier modes. This gives rise to conditions for the spatial variations in the filter-width and the filter-skewness subject to which the magnitude of the commutator errors can be controlled. These conditions are translated into smoothness requirements of the computational grid, that involve ratios of first -, second - and third order derivatives of the grid mapping.