The Effect of Subfilter-Scale Physics on Regularization Models |
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Authors: | Jonathan Pietarila Graham Darryl D Holm Pablo Mininni Annick Pouquet |
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Affiliation: | 1.Max-Planck-Institut für Sonnensystemforschung,Katlenburg-Lindau,Germany;2.Department of Applied Mathematics & Statistics,The Johns Hopkins University,Baltimore,USA;3.Department of Mathematics,Imperial College London,London,UK;4.National Center for Atmospheric Research,Boulder,USA;5.Departamento de Física, Facultad de Ciencias Exactas y Naturales,Universidad de Buenos Aires,Buenos Aires,Argentina |
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Abstract: | 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 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-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. |
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Keywords: | |
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