  We present two models for turbulent flows with periodic boundary conditions
and with either rotation, or a magnetic field in the magnetohydrodynamics (MHD)
limit. One model, based on Lagrangian averaging, can be viewed as an
invariant-preserving filter, whereas the other model, based on spectral
closures, generalizes the concepts of eddy viscosity and eddy noise. These
models, when used separately or in conjunction, may lead to substantial savings
for modeling high Reynolds number flows when checked against high resolution
direct numerical simulations (DNS), the examples given here being run on grids
of up to 1536^3 points.
