  The variational principle of V. I. Arnold [J. Appl. Math. Mech. Vol. 29, P.
1002 (1965)] is extended to the general conservative inhomogeneous,
compressible, and conducting fluid. The concept of iso-vortical flows is
generalized to an "invariant foliation" of the phase space. The foliation,
which may or may not correspond to explicit conservation laws, is derived from
the equations of motion and used for Lyapunov stability. A nonlinear
three-dimensional (magneto-) hydrodynamic stability criterion is formulated.
