Zonal shear flows with a free surface: Hamiltonian formulation and linear and nonlinear stability

    Authors

    B. K. Shivamoggi;G. J. F. van Heijst

    Comments

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    Abstract

    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.

    Journal Title

    Geophysical and Astrophysical Fluid Dynamics

    Volume

    103

    Issue/Number

    4

    Publication Date

    1-1-2009

    Document Type

    Article

    First Page

    293

    Last Page

    301

    WOS Identifier

    WOS:000269450300002

    ISSN

    0309-1929

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