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. 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 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.

Sub-grid effects of the Voigt viscoelastic regularization of a singular dyadic model of turbulence

“…We would also like to point out some very interesting results concerning the sub-grid effects of α regularization of three-dimensional flows obtained in [18,19]. It is our intention to compare the three-dimensional simulations of the Voigt model with those observed in [18,19] in a future work.…”

High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model

“…[27] with 1536 3 spatial resolution. By "equivalent grid," we mean the following: a comparison with the 1536 3 DNS with η = ν = 2 × 10 −4 was carried solving the LAMHD equations on grids of 256 3 , 384 3 , and 512 3 points to validate the results of the model [19,23]. The runs presented here, with 1024…”

“…There are numerous methods that have been devised over the years (see, e.g., recent reviews for fluids [18] and for MHD [19]). Among them, the Lagrangian averaged MHD model (LAMHD hereafter) developed in [20] (see also [21]) seems promising in that it allows to perform a quasi-DNS, in the sense that the Reynolds number is known and that the inertial range is extended, compared to a DNS performed on the same grid without the model, thanks to a different formulation of the equations that preserves the invariants, albeit in a different norm (see below).…”