On General Transformations and Variational Principles for the Magnetohydrodynamics of Ideal Fluids. Part 1. Fundamental Principles

Research output: Contribution to journalArticle

45 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)125-139
Number of pages15
JournalJournal of Fluid Mechanics
Volume283
DOIs
Publication statusPublished - 1995

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Fingerprint Dive into the research topics of 'On General Transformations and Variational Principles for the Magnetohydrodynamics of Ideal Fluids. Part 1. Fundamental Principles'. Together they form a unique fingerprint.

  • Cite this