About the magnetohydrodynamics of rotatory nonhomogeneous fluid in the stationary case (Q2755196)

The magnetohydrodynamic model of conducting rotatory stratified inviscid fluid is investigated in stationary case with the assumption that magnetic field vector and velocity vector are parallel. Three types of magnetic field stratification are registered: sub-Alfvénic, Alfvénic and super-Alfvénic. Two possibilities to reduce the three parametric problem to solving linear equations are established. In the first case the modified velocity vector is expressed in terms of potential satisfying Laplace equation, while in the second case this vector is expressed in terms of extended potential satisfying Helmholtz equation. Two-parametric problem based on symmetry integrals is reduced to nonlinear second-order partial differential equation for determination of the modified stream function. This relation is the generalization of Yih's equation, well-known in the usual dynamics of nonhomogeneous fluids. Some cases are established when the equation for modified stream function is reduced to linear one. Magnetohydrodynamic generalization of the spherical Hill vortex well-known in classical hydrodynamics is obtained. Exact solutions are obtained for internal waves of finite amplitude for plane and circular layers of magnetized nonhomogeneous fluid. The influence of magnetic field on dispersion relationships is analysed.