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 H1 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.

[1]  Parviz Moin,et al.  Large-eddy simulation of conductive flows at low magnetic Reynolds number , 2004 .

[2]  S. Boldyrev,et al.  Numerical measurements of the spectrum in magnetohydrodynamic turbulence. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  S. SRIDHAR,et al.  TOWARD A THEORY OF INTERSTELLAR TURBULENCE. I. WEAK ALFVENIC TURBULENCE , 2009 .

[4]  C. Meneveau,et al.  Scale-Invariance and Turbulence Models for Large-Eddy Simulation , 2000 .

[5]  Edriss S. Titi,et al.  On the statistical properties of the 3D incompressible Navier-Stokes-Voigt model , 2009, 0901.0474.

[6]  G. Taylor,et al.  Mechanism of the production of small eddies from large ones , 1937 .

[7]  R D Richtmyek,et al.  Survey of the Stability of Linear Finite Difference Equations , 2022 .

[8]  E. Titi,et al.  Invariant measures for the 3D Navier-Stokes-Voigt equations and their Navier-Stokes limit , 2009, 0910.1386.

[9]  Annick Pouquet,et al.  Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottlenecks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  S. Frankel,et al.  Regularization-based sub-grid scale (SGS) models for large eddy simulations (LES) of high-Re decaying isotropic turbulence , 2009 .

[11]  P. Mininni,et al.  Lack of universality in decaying magnetohydrodynamic turbulence. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  L. Berselli,et al.  On the consistency of the Rational Large Eddy Simulation model , 2004 .

[13]  T. A. Zang,et al.  Spectral methods for fluid dynamics , 1987 .

[14]  Annick Pouquet,et al.  Numerical solutions of the three-dimensional magnetohydrodynamic alpha model. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Jerrold E. Marsden,et al.  Numerical simulations of the Lagrangian averaged Navier-Stokes equations for homogeneous isotropic turbulence , 2003 .

[16]  Uriel Frisch,et al.  Dynamo action in a family of flows with chaotic streamlines , 1986 .

[17]  S. Sridhar,et al.  Toward a theory of interstellar turbulence. 2. Strong Alfvenic turbulence , 1994 .

[18]  Pablo D. Mininni,et al.  High-order low-storage explicit Runge-Kutta schemes for equations with quadratic nonlinearities , 2008, 0808.1883.

[19]  Bernardus J. Geurts,et al.  Interacting errors in large-eddy simulation: a review of recent developments , 2006 .

[20]  Jean-Luc Guermond,et al.  On the use of the notion of suitable weak solutions in CFD , 2008 .

[21]  Darryl D. Holm,et al.  Leray and LANS-α modelling of turbulent mixing , 2005, nlin/0504038.

[22]  Sabatino Sofia,et al.  A subgrid‐scale resistivity for magnetohydrodynamics , 1994 .

[23]  Darryl D. Holm,et al.  Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes alpha model and their large-eddy-simulation potential. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Darryl D. Holm,et al.  Three regularization models of the Navier–Stokes equations , 2007, Physics of Fluids.

[25]  Robert H. Kraichnan,et al.  Inertial‐Range Spectrum of Hydromagnetic Turbulence , 1965 .

[26]  Edriss S. Titi,et al.  On the Higher-Order Global Regularity of the Inviscid Voigt-Regularization of Three-Dimensional Hydrodynamic Models , 2009, 0910.3354.

[27]  Approximate Deconvolution Models for Magnetohydrodynamics , 2010 .

[28]  Volker John.  An assessment of two models for the subgrid scale tensor in the rational LES model , 2005 .

[29]  William Layton,et al.  APPROXIMATION OF THE LARGER EDDIES IN FLUID MOTIONS II: A MODEL FOR SPACE-FILTERED FLOW , 2000 .

[30]  A Pouquet,et al.  Spectral modeling of magnetohydrodynamic turbulent flows. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  Daniele Carati,et al.  Dynamic gradient-diffusion subgrid models for incompressible magnetohydrodynamic turbulence , 2002 .

[32]  M. Lesieur,et al.  Parameterization of Small Scales of Three-Dimensional Isotropic Turbulence Utilizing Spectral Closures , 1981 .

[33]  P. Mininni,et al.  Nonlocal interactions in hydrodynamic turbulence at high Reynolds numbers: the slow emergence of scaling laws. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[34]  M. Gurtin,et al.  Impact of the inherent separation of scales in the Navier-Stokes- alphabeta equations. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Darryl D. Holm,et al.  The Navier–Stokes-alpha model of fluid turbulence , 2001, nlin/0103037.

[36]  Pablo D. Mininni,et al.  MHD simulations and astrophysical applications , 2005 .

[37]  P. D. Mininni,et al.  A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows , 2005 .

[38]  Darryl D. Holm.  Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics. , 2002, Chaos.

[39]  G. Doolen,et al.  Large-scale disruptions in a current-carrying magnetofluid , 1986, Journal of Plasma Physics.

[40]  An alternative interpretation for the Holm alpha model , 2002, physics/0207056.

[41]  Thomas J. R. Hughes,et al.  The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence , 2001 .

[42]  Jean-François Pinton,et al.  Simulation of induction at low magnetic Prandtl number. , 2004, Physical review letters.

[43]  Darryl D. Holm,et al.  The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories , 1998, chao-dyn/9801015.

[44]  Darryl D. Holm,et al.  Camassa-Holm Equations as a Closure Model for Turbulent Channel and Pipe Flow , 1998, chao-dyn/9804026.

[45]  Darryl D. Holm,et al.  On the Clark–α model of turbulence: global regularity and long-time dynamics , 2004, nlin/0412007.

[46]  G. Eyink,et al.  Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter , 2009, 0909.2451.

[47]  Darryl D. Holm.  Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics , 2001 .

[48]  Darryl D. Holm,et al.  Inertial Range Scaling, Karman-Howarth Theorem and Intermittency for Forced and Decaying Lagrangian Averaged MHD in 2D , 2005, physics/0508173.

[49]  Maarten van Reeuwijk,et al.  Leray-α simulations of wall-bounded turbulent flows , 2009 .

[50]  G. Eyink,et al.  Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining , 2009, 0909.2386.

[51]  Hussein Aluie,et al.  Scale locality of magnetohydrodynamic turbulence. , 2009, Physical review letters.

[52]  P. S. Iroshnikov.  Turbulence of a conducting fluid in a strong magnetic field , 1963 .

[53]  Fabrice Debbasch,et al.  Effective dissipation and turbulence in spectrally truncated euler flows. , 2004, Physical review letters.

[54]  Darryl D. Holm,et al.  Regularization modeling for large-eddy simulation , 2002, nlin/0206026.

[55]  Pablo D. Mininni,et al.  Parallel Simulations in Turbulent MHD , 2005 .

[56]  Annick Pouquet,et al.  Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.