Hamiltonian description of monopoles on a rotating sphere

The Poisson bracket for 2D hydrodynamics on a Riemann manifold is considered. For a special class of vorticities a general method is suggested for reducing this bracket to Gardner-Zakharov-Faddeev bracket by changing the functional variable. When applying to a rotating sphere, new Hamiltonian equations are obtained for Rossby monopoles in terms of the vorticity extremum coordinates and the distance from it to the vorticity lines. The equations have clear physical meaning and may be used as a split-up scheme for numerical solution.