Turbulent fluctuations in magnetohydrodynamic (MHD) flows can become strongly anisotropic or even quasi-2D under the action of an applied magnetic field. We investigate this phenomenon in the case of low magnetic Reynolds numbers. It has been found in earlier DNS and LES of homogeneous turbulence that the degree of anisotropy is predominantly determined by the value of the magnetic interaction parameter and only slightly depends on the Reynolds number, type of large-scale dynamics, and the length scale. Furthermore, it has been demonstrated that the dynamic Smagorinsky model is capable of self-adjustment to the effects of anisotropy. In this paper, we capitalize on these results and propose a simple and effective generalization of the traditional non-dynamic Smagorinsky model to the case of anisotropic MHD turbulence
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