  We study the sub-grid scale characteristics of a vorticity-transport-based
approach for large-eddy simulations. In particular, we consider a
multi-dimensional upwind scheme for the vorticity transport equations and
establish its properties in the under-resolved regime. The asymptotic behavior
of key turbulence statistics of velocity gradients, vorticity, and invariants
is studied in detail. Modified equation analysis indicates that dissipation can
be controlled locally via non-linear limiting of the gradient employed for the
vorticity reconstruction on the cell face such that low numerical diffusion is
obtained in well-resolved regimes and high numerical diffusion is realized in
under-resolved regions. The enstrophy budget highlights the remarkable ability
of the truncation terms to mimic the true sub-grid scale dissipation and
diffusion. The modified equation also reveals diffusive terms that are similar
to several commonly employed sub-grid scale models including tensor-gradient
and hyper-viscosity models. Investigations on several canonical turbulence flow
cases show that large-scale features are adequately represented and remain
consistent in terms of spectral energy over a range of grid resolutions.
Numerical dissipation in under-resolved simulations is consistent and can be
characterized by diffusion terms discovered in the modified equation analysis.
A minimum state of scale separation necessary to obtain asymptotic behavior is
characterized using metrics such as effective Reynolds number and effective
grid spacing. Temporally-evolving jet simulations, characterized by large-scale
vortical structures, demonstrate that high Reynolds number vortex-dominated
flows are captured when criteria is met and necessitate diffusive non-linear
limiting of vorticity reconstruction be employed to realize accuracy in
under-resolved simulations.
