Rotating modons over isolated topography in a two-layer ocean
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The nonlinear quasigeostrophic equations for two layers with finite scale topography in the lower layer are reduced to steady form by focusing on solutions that rotate at a constant rate and also decay monotonically outside the topography. The solutions, here called rotating baroclinic modons, are a composition of one radially dependent azimuthal component and a basic axisymmetric component. Smoothness conditions (global continuity of the streamfunction and its first derivatives), when applied to the azimuthal mode, result in a complicated eigenvalue problem. The consequence of this is a single azimuthal mode with arbitrary amplitude. When applied to the axisymmetric solution component, the smoothness conditions allow for a vortex of arbitrary amplitude, a rider, in each layer. These riders determine the rotation rate, which may be cyclonic or anticyclonic, as well as other modon parameters. Two special cases of the theory are discussed and numerical examples of the general solutions are given. The solutions exhibit a rich variety of behavior with a countable infinity of exact solution multipoles. The paper concludes with a comparison of the properties of rotating and rectilinear baroclinic modons and some speculations on applications of the theory.
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