  In this paper we show that the Craik-Leibovich (CL) equation in hydrodynamics
is the Euler equation on the dual of a certain central extension of the Lie
algebra of divergence-free vector fields. From this geometric viewpoint, one
can give a generalization of CL equation on any Riemannian manifold with
boundary. We also prove a stability theorem for 2-dimensional steady flows of
the Craik-Leibovich equation.
