  A necessary and sufficient condition for linear stability of inviscid
parallel shear flow is formulated by developing a novel variational principle,
where the velocity profile is assumed to be monotonic and analytic. It is shown
that unstable eigenvalues of Rayleigh's equation (which is a non-selfadjoint
eigenvalue problem) can be associated with positive eigenvalues of a certain
selfadjoint operator. The stability is therefore determined by maximizing a
quadratic form, which is theoretically and numerically more tractable than
directly solving Rayleigh's equation. This variational stability criterion is
based on the understandings of Krein signature for continuous spectrum and is
applicable to other stability problems of infinite-dimensional Hamiltonian
systems.
