The Effect of Subfilter-Scale Physics on Regularization Models

The subfilter-scale (SFS) physics of regularization models are investigated to understand the regularizations’ performance as SFS models. Suppression of spectrally local SFS interactions and 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. All three models are found to be stable at high Reynolds number. Differences between L2 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 Lagrangianaveraged MHD (LAMHD-α). LAMHD-α performs well as a predictor of superfilter-scale energy spectra and of intermittent current sheets at high Reynolds numbers. It may prove generally applicable as a MHD-LES. The National Center for Atmospheric Research is sponsored by the National Science Foundation. J. Pietarila Graham ( ) Max-Planck-Institut für Sonnensystemforschung, Katlenburg-Lindau, Germany e-mail: [email protected] J. Pietarila Graham Department of Applied Mathematics & Statistics, The Johns Hopkins University, Baltimore, MD, USA D.D. Holm Department of Mathematics, Imperial College London, London, UK P. Mininni · A. Pouquet National Center for Atmospheric Research, Boulder, CO, USA P. Mininni Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Buenos Aires, Argentina 22 J Sci Comput (2011) 49:21–34