Development of a Reynolds stress closure for modeling of homogeneous MHD turbulence

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Abstract
A Reynolds stress closure is developed for homogeneous shear-free turbulence subjected to a strong magnetic field at low magnetic Reynolds numbers. A scalar dimensionality anisotropy parameter is introduced to carry information about the distribution of energy in spectral space. This information is vital in modeling MHD turbulence, as it determines both magnitude and anisotropy of the Joule dissipation tensor. The Joule dissipation tensor is modeled by a tensor function, which is bilinear in the Reynolds stress anisotropy and the unit direction vector of the magnetic field. The tensor function coefficients are second-order in the scalar dimensionality parameter. A phenomenological transport equation for the dimensionality parameter is proposed. The model is closed using the pressure–strain model of Sarkar, Speziale and Gatski and a magnetic destruction term in the standard dissipation equation. The purely magnetic linear problem contains no undetermined constants, while the complete model contains two constants. Model predictions for the case of decaying turbulence show very good agreement with direct numerical simulations.