  Implicitly filtered large-eddy simulation (LES) is by nature numerically
under-resolved. With the sole exception of Fourier-spectral methods, discrete
numerical derivative operators cannot accurately represent the dynamics of all
of the represented scales. Since the resolution scale in an LES usually lies in
the inertial range, these poorly represented scales are dynamically significant
and errors in their dynamics can affect all resolved scales. This Letter is
focused on characterizing the effects of numerical dispersion error by studying
the energy cascade in LES of convecting homogeneous isotropic turbulence.
Numerical energy and transfer spectra reveal that energy is not transferred at
the appropriate rate to wavemodes where significant dispersion error is
present. This leads to a deficiency of energy in highly dispersive modes and an
accompanying pile up of energy in the well resolved modes, since dissipation by
the subgrid model is diminished. An asymptotic analysis indicates that
dispersion error causes a phase decoherence between triad interacting
wavemodes, leading to a reduction in the mean energy transfer rate for these
scales. These findings are relevant to a wide range of LES, since turbulence
commonly convects through the grid in practical simulations. Further, these
results indicate that the resolved scales should be defined to not include the
dispersive modes.
