The power of structural modeling of subgrid scales  application to astrophysical plasmas
Abstract
In numerous astrophysical phenomena the dynamical range can span 10s of orders of magnitude. This implies more than billions of degreesoffreedom and precludes direct numerical simulations from ever being a realistic possibility. A physical model is necessary to capture the unresolved physics occurring at the subgrid scales (SGS).Structural modeling is a powerful concept which renders itself applicable to various physical systems. It stems from the idea of capturing the structure of the SGS terms in the evolution equations based on the scaleseparation mechanism and independently of the underlying physics. It originates in the hydrodynamics field of largeeddy simulations. We apply it to the study of astrophysical MHD.Here, we present a nonlinear SGS model for compressible MHD turbulence. The model is validated a priori at the tensorial, vectorial and scalar levels against of set of highresolution simulations of stochastically forced homogeneous isotropic turbulence in a periodic box. The parameter space spans 2 decades in sonic Mach numbers (0.2  20) and approximately one decade in magnetic Mach number ~(18). This covers the superAlfvenic sub, trans, and hypersonic regimes, with a range of plasma beta from 0.05 to 25. The Reynolds number is of the order of 10^{3}.At the tensor level, the model components correlate well with the turbulence ones, at the level of 0.8 and above. Vectorially, the alignment with the true SGS terms is encouraging with more than 50% of the model within 30° of the data. At the scalar level we look at the dynamics of the SGS energy and crosshelicity. The corresponding SGS flux terms have median correlations of ~0.8. Physically, the model represents well the two directions of the energy cascade.In comparison, traditional functional models exhibit poor local correlations with the data already at the scalar level. Vectorially, they are indifferent to the anisotropy of the SGS terms. They often struggle to represent the energy backscatter from small to large scales as well as the turbulent dynamo mechanism.Overall, the new model surpasses the traditional ones in all tests by a large margin.
 Publication:

IAU General Assembly
 Pub Date:
 August 2015
 Bibcode:
 2015IAUGA..2255556G