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Three-scale expansion of the solution of the magnetohydrodynamic equations and the Reynolds equation for a tokamak. (English. Russian original) Zbl 0818.76093
Theor. Math. Phys. 98, No. 2, 202-211 (1994); translation from Teor. Mat. Fiz. 98, No. 2, 297-311 (1994).
Summary: An asymptotic solution of the equations of magnetohydrodynamics (MHD) at large Reynolds numbers is constructed. The three-scale asymptotic solution describes the evolution of small rapidly varying perturbations of the equilibrium state with allowance for nonlinear interaction. It is shown that in the linearly unstable situation there arises an anisotropic coherent structure whose evolution leads to energy exchange between the high- and low-frequency waves. A closed system of MHD Reynolds equations for the anisotropic structure that permits calculation of the Reynolds stresses is derived.
MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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