Nonlinear Hydrodynamic Stability

The variational principle of V.I. Arnold [J.Appl.Math.Mech.{bold 29}, 1002 (1965)] is extended to general ideal magnetohydrodynamics (MHD). This is done using the trick of ``superdynamics,`` or the replacement of certain terms in the equations of motion by arbitrary functions. The variational constraint thus introduced leads to a sufficient, and likely necessary, Lyapunov stability criterion. All ideal MHD equilibria with fluid flow, except those with parallel sub-Alfvenic flow, are unstable according to this criterion. The method of superdynamics is extensible to other Hamiltonian systems. {copyright} {ital 1998} {ital The American Physical Society}