Linear stability theory of zonal shear flows with a free surface

    Authors

    B. K. Shivamoggi;D. K. Rollins

    Abbreviated Journal Title

    Geophys. Astrophys. Fluid Dyn.

    Keywords

    zonal flow stability; Rossby waves; ocean free surface effect; BAROTROPIC INSTABILITY; Astronomy & Astrophysics; Geochemistry & Geophysics; Mechanics

    Abstract

    We investigate the linear stability of zonal shear flows with a free surface (like the flow in oceans) taking into account the buoyancy effects at the deformed free surface. The necessary and sufficient conditions for the existence of neutral and unstable modes are established, and a semicircle theorem for unstable modes is deduced. An upper bound on the growth rate of an unstable mode is established. We have given a sufficient condition for stability that has a close resemblance with Miles' criterion for stability of a continuously stratified shear flow. The number of distinct unstable modes is shown not to exceed the number of neutral modes. The stability characteristics of smoothly-varying unbounded shear-layer flow profiles for long-wave disturbances are investigated. Finally, stability of a linear zonal flow velocity profile and a zonal Bickley jet-flow profile are investigated. Some of these results are new even in the special barotropic case (with no free-surface effect).

    Journal Title

    Geophysical and Astrophysical Fluid Dynamics

    Volume

    95

    Issue/Number

    1-2

    Publication Date

    1-1-2001

    Document Type

    Article

    Language

    English

    First Page

    31

    Last Page

    53

    WOS Identifier

    WOS:000180157900002

    ISSN

    0309-1929

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