  We give a sufficient condition for the nonlinear stability of steady flows of
a two-dimensional ideal fluid in a bounded multiply-connected domain, which
generalizes a stability criterion proved by Arnold in the 1960s. The most
important ingredient of the proof is to establish a variational
characterization for the steady flow under consideration, which is achieved
based on the energy-Casimir method proposed by Arnold, and the supporting
functional method introduced by Wolansky and Ghil. Nonlinear stability then
follows from a compactness argument related to the variational characterization
and proper use of conserved quantities of the two-dimensional Euler equations.
