About the magnetohydrodynamics of rotatory nonhomogeneous fluid in the stationary case
type: Item
instance of: scholarly article
zbMATH Open document ID: 1072.76690
author: N. V. Saltanov
author: V. N. Saltanov
publication date: 2001-11-08T00:00:00Z
Mathematics Subject Classification ID: 76W05
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 76B70
Mathematics Subject Classification ID: 76B47
zbMATH DE Number: 1669702
zbMATH Keywords: magnetohydrodynamics
zbMATH Keywords: rotatory nonhomogeneous fluid
zbMATH Keywords: stationary motion
zbMATH Keywords: Hill vortex
MaRDI profile type: Publication
title: About the magnetohydrodynamics of rotatory nonhomogeneous fluid in the stationary case
published in: Prykladna Gidromekhanika
review text: 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.
description: scientific article; zbMATH DE number 1669702