ON GENERAL TRANSFORMATIONS AND VARIATIONAL PRINCIPLES FOR THE MAGNETOHYDRODYNAMICS OF IDEAL FLUIDS .1. FUNDAMENTAL PRINCIPLES

摘要

A new frozen-in field w (generalizing vorticity) is constructed for ideal magnetohydrodynamic flow. In conjunction with the frozen-in magnetic held h, this is used to obtain a generalized Weber transformation of the MHD equations, expressing the velocity as a bilinear form in generalized Weber variables. This expression is also obtained from Hamilton's principle of least action, and the canonically conjugate Hamiltonian variables for MHD flow are identified. Two alternative energy-type variational principles for three-dimensional steady MHD flow are established. Both involve a functional R which is the sum of the total energy and another conserved functional, the volume integral of a function Phi of Lagrangian coordinates. It is shown that the first variation delta(1)R vanishes if Phi is suitably chosen (as minus a generalized Bernoulli integral). Expressions for the second variation delta(2)R are presented. [References: 21]