Zonal shear flows with a free surface: Hamiltonian formulation and linear and nonlinear stability
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 (equivalent barotropic model). These results include a generalization of the Flierl-Stern-Whitehead zero angular momentum theorem for localized nonlinear structures (whether or not on a beta-plane), and sufficient conditions for linear and nonlinear stability in the Liapunov sense - the latter are given as estimates in terms of an L(2)-type perturbation norm which are global in time and are derived via bounds on the equilibrium potential vorticity gradient.
Geophysical and Astrophysical Fluid Dynamics
"Zonal shear flows with a free surface: Hamiltonian formulation and linear and nonlinear stability" (2009). Faculty Bibliography 2000s. 2136.