  General theoretical results via a Hamiltonian formulation are developed for
zonal shear flows with the inclusion of the vortex stretching effect of the
deformed free surface. These results include a generalization of the
Flierl-Stern-Whitehead zero angular momentum theorem} for localized nonlinear
structures on or off the beta-plane, and sufficient conditions for linear and
nonlinear stability in the Liapunov sense - the latter are derived via bounds
on the equilibrium potential vorticity gradient.
