Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation

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The stability of steady magnetohydrodynamic flows of an inviscid incompressible fluid is studied using the energy method. It is shown that certain symmetry transformations of steady solutions of the equations of ideal magnetohydrodynamics have an important property: if a given steady magnetohydrodynamic flow is stable by the energy method, then certain infinite-dimensional families of steady flows obtained from the given flow by these transformations are also stable. This result is used to obtain new sufficient conditions for linear stability. In particular, it is shown that certain classes of steady magnetohydrodynamic flows in which both the magnetic field and the velocity depend on all three spatial coordinates are stable.
Original languageEnglish
Pages (from-to)3586-3594
Number of pages8
JournalPhysics of Plasmas
Issue number7
Publication statusPublished - Jul 2004


  • plasma magnetohydrodynamics,
  • plasma instability

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