The effect of subfilter-scale physics on regularization models

Abstract

The subfilter-scale (SFS) physics of regularization models are investigated to understand the regularizations’ performance as SFS models. The strong suppression of spectrally local SFS interactions and the conservation of small-scale circulation in the Lagrangian-averaged Navier-Stokes α−model (LANS−α) is found to lead to the formation of rigid bodies. These contaminate the superfilter-scale energy spectrum with a scaling that approaches k ⁺¹ as the SFS spectra is resolved. The Clark−α and Leray−α models, truncations of LANS−α, do not conserve small-scale circulation and do not develop rigid bodies. LANS−α, however, is closest to Navier-Stokes in intermittency properties. For magnetohydrodynamics (MHD), the presence of the Lorentz force as a source (or sink) for circulation and as a facilitator of both spectrally nonlocal large to small scale interactions as well as local SFS interactions prevents the formation of rigid bodies in Lagrangian-averaged MHD (LAMHD−α). We find LAMHD−α performs well as a predictor of superfilter-scale energy spectra and of intermittent current sheets at high Reynolds numbers. We expect it may prove to be a generally applicable MHD-LES.

The National Center for Atmospheric Research is sponsored by the National Science Foundation