Three Studies in Hydromagnetics.

Abstract

This thesis consists of an introduction to the field of hydromagnetics, followed by three separate studies in this subject. The first is a study of the small-amplitude hydromagnetic radiation from a localized disturbing source in an unbounded dissipationless fluid permeated by a constant uniform magnetic field. The relevant linearized vector wave equation is treated by Fourier transform methods, utilizing the stationary-phase approximation. Asymptotic solutions are obtained for the wave-zone amplitude in the three modes emitted, and these are discussed in some detail; analytically, geometrically, and physically. Expressions are obtained for the angular distribution of the power radiated into these modes by a distributed source. The second study concerns itself with some special two-dimensional hydromagnetic steady flows. Various general properties of these flows are discussed. Ten exact solutions of the exact nonlinear equations of flow are derived and some of their features noted. The third study is an investigation of whether, for the case of a deep 'lake' of dissipationless incompressible conducting fluid in a constant uniform magnetic field, there exist characteristic small-amplitude gravity surface-waves different from those known in hydrodynamics. It is concluded that no surface waves exist at all if the magnetic field has a component normal to the undisturbed surface, and that if the field is tangential to the surface, there are no new wave types with a characteristic dispersion law.