Modeling anisotropic MHD turbulence in simulations of liquid metal flows

O. Widlund

Faxén Laboratory, Royal Institute of Technology SE-100 44, Stockholm, Sweden

Abstract
The dynamical properties of the MHD turbulence model proposed by Widlund etal. are examined for the case of homogeneous decaying turbulence. The model is a Reynolds stress closure, extended with a transport equation for a dimensional anisotropy variable, α, which carries information about length scale anisotropy. The analysis suggests that the model term originally proposed for the nonlinear energy transfer in the α equation should be modified. A unique set of model coefficients could be determined, which makes the model consistent with theory and experiments for interaction parameters N ranging from zero to infinity. The model coincides with the standard K-\eps model when there is no magnetic field. In the linear regime of large N, it produces the K ∼ t^−1/2 energy decay predicted by linear theory. When nonlinear effects are important, the model predicts K ∼ t^−1.7 and L_||  ∼ t^0.65, in agreement with the classical experiments by Alemany etal. Figs 5, Refs 11.