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

Zonal Shear Flows with a Free Surface: Hamiltonian Formulation and Linear and Nonlinear Stability