  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 alpha-model
(LANS-alpha) 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-alpha and Leray-alpha
models, truncations of LANS-alpha, do not conserve small-scale circulation and
do not develop rigid bodies. LANS-alpha, however, is closest to Navier-Stokes
in intermittency properties. All three models are found to be stable at high
Reynolds number. Differences between L^2 and H^1 norm models are clarified. 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-alpha). We find
LAMHD-alpha 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.
