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On general transformations and variational principles for the magnetohydrodynamics of ideal fluids. Part 1. Fundamental principles

Published online by Cambridge University Press:  26 April 2006

V. A. Vladimirov  and
H. K. Moffatt
V. A. Vladimirov
Affiliation:
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
H. K. Moffatt
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
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Abstract

A new frozen-in field w (generalizing vorticity) is constructed for ideal magnetohydrodynamic flow. In conjunction with the frozen-in magnetic field 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 Φ of Lagrangian coordinates. It is shown that the first variation δ1R vanishes if Φ is suitably chosen (as minus a generalized Bernoulli integral). Expressions for the second variation δ2R are presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 283 , 25 January 1995 , pp. 125 - 139
Copyright
© 1995 Cambridge University Press

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