Novel developments in subgrid-scale modeling of space plasma: weakly compressible turbulence in the local interstellar medium

Abstract

A survey of various subgrid-scale (SGS) models for the study of compressible magnetohydrodynamic (MHD) turbulence of space plasma is given. A large eddy simulation (LES) method for the study of compressible MHD turbulence of polytropic fluid is developed. A theory of SGS turbulent flow for the new SGS terms, appearing after the Favre-filtering procedure in the system of MHD equations, is proposed. Modeling of decaying compressible MHD turbulence under various similarity numbers is carried out and the validity of the LES method for the modeling of a polytropic is shown. Numerical studies are performed for five different SGS closures: the Smagorinsky model, the Kolmogorov model, the cross-helicity model, the scale-similarity model and the mixed model. Suggested SGS parameterizations are studied and SGS models that demonstrate the most exact results for decaying compressible MHD turbulence, under various similarity numbers, are shown. Using the advantages of the LES method, a nontrivial space plasma compressible MHD turbulence regime is studied when initially supersonic fluctuations become weakly compressible. An as yet unexplained observation is that density fluctuations in the local interstellar medium exhibit a Kolmogorov-like spectrum over an extraordinary range of scales with a spectral index close to −5/3. In spite of the compressibility and the presence of a magnetic field in the local interstellar medium, density fluctuations nevertheless admit a Kolmogorov-like power law. Supersonic flows with high large-scale Mach numbers are characterized in the interstellar medium. Nevertheless, there are subsonic fluctuations of weakly compressible components of the interstellar medium. These weakly compressible subsonic fluctuations are responsible for the emergence of a Kolmogorov-type spectrum in the interstellar turbulence which is observed from experimental data. It is shown that density fluctuations are a passive scalar in a weakly compressible MHD turbulence velocity field and demonstrate a Kolmogorov-like spectrum.