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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)