Statistical theory for magnetohydrodynamic turbulent shear flows

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Abstract
A statistical theory is developed for magnetohydrodynamic turbulent shear flows in the presence of both mean velocity and magnetic gradients. In the case of magnetic Prandtl number unity, the correlations between fluctuating velocity and magnetic fields, which play a crucially important role in the equations for the mean velocity and magnetic fields, are calculated with the aid of the two‐scale, direct‐interaction approximation. The electromotive force expressing the effect of turbulent fields in the equation for mean magnetic field is found from the results. Particularly, the electromotive force related linearly to the mean magnetic field is shown to originate from the statistical inhomogeneity of fluctuating fields, which is sustained by the mean field gradients.