Ideal magnetohydrodynamics and passive scalar motion as geodesics on semidirect product groups

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Abstract

Three-dimensional ideal magnetohydrodynamic (3d-iMHD) equations are shown to be a geodesic equation on an infinite-dimensional Lie group. The group is the semidirect product of a group of volume-preserving diffeomorphisms (particle motion) and a linear space of divergenceless vector fields (current density). The present theory includes the work of Zeitlin and Kambe (1993) for two-dimensional iMHD flow as a special case. Passive scalar motion in N-dimensional ideal hydrodynamic flow is also generally shown to be described by a geodesic equation.

Original languageEnglish
Article number004
JournalJournal of Physics A: Mathematical and General
Volume27
Issue number2
DOIs
Publication statusPublished - 1994 Dec 1
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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