Book Description

The elementary theory of hydromagnetic waves in an inviscid incompressible, perfectly conducting fluid of infinite extent, embedded in a uniform magnetic field, indicates their propagation is purely one-dimensional, along the magnetic lines of force, and hence without attenuation. The object is to investigate how t is property is modified by the effects of compressibility, finite electric l con uctivity, viscosity, and the combined effects of finite electrical conductivity and viscosity. Complexities are introduced one by one. The disturbance is specified in terms of vorticity and current density. It appears that the compressibility of a medium acts as a wave filter discriminating between components of vorticity and passing only those directed along the magnetic field. Dissip tive effects introduce great mathematical difficulties. The partial differential equations governing these phenomena are of mixed type: hyperbolic-parabolic, and this indicates that the disturbances diffuse outward as they travel along magnetic lines of force. Th symmetrical role played in these equations by the coefficients of kinematic viscosity and magnetic viscosity is outlined. Some mathematical analogi s between magnetohydrodynamics and ordinary hydrodynamics are studied. Weber's transformation is extended to he potential vector of electrodynamics and the equation for the magnetic field is integrated in terms of Lagrangian variables of hydrodynamics. (Author).