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

Modeling of anisotropic turbulent flows with either magnetic fields or imposed rotation