Galilean invariance of shallow cumulus convection large-eddy simulations

In large-eddy simulations (LES) a computational-domain translation velocity can be used to improve performance by allowing longer time-step intervals. The continuous equations are Galilean invariant. However, standard finite-difference-based discretizations not discretely invariant with the error being proportional product of local and truncation error. Even though such numerical errors expected small, it is shown that in LES buoyant convection turbulent large-scale flow organization modulate amplify invariance global statistics observed well-resolved direct (DNS). single-phase under an inversion, nearly do depend on order accuracy finite difference approximation. contrast, cloudy convection, show strong dependence frame reference respect becomes negligible as increased from second sixth present LES. Schemes low resolving power produce large dispersion surface-fixed amplified anisotropies, updrafts rising non-turbulent free troposphere cumulus-cloud layers. Interestingly, simulations, second-order discretization proper yield comparable high-order scheme frame.