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Vortex Rossby waves on smooth circular vortices Part I. Theory

By Gilbert Brunet A and Michael T. Montgomery B


A complete theory of the linear initial-value problem for Rossby waves on a class of smooth circular vortices in both f-plane and polar-region geometries is presented in the limit of small and large Rossby deformation radius. Although restricted to the interior region of barotropically stable circular vortices possessing a single extrema in tangential wind, the theory covers all azimuthal wavenumbers. The non-dimensional evolution equation for perturbation potential vorticity is shown to depend on only one parameter, G, involving the azimuthal wavenumber, the basic state radial potential vorticity gradient, the interior deformation radius, and the interior Rossby number. In Hankel transform space the problem admits a Schrödinger’s equation formulation which permits a qualitative and quantitative discussion of the interaction between vortex Rossby wave disturbances and the mean vortex. New conservation laws are developed which give exact time-evolving bounds for disturbance kinetic energy. Using results from the theory of Lie groups a nontrivial separation of variables can be achieved to obtain an exact solution for asymmetric balanced disturbances covering a wide range of geophysical vortex applications including tropical cyclone, polar vortex, and cyclone/anticyclone interiors in barotropic dynamics. The expansion for square summable potentia

Topics: Continuous-spectrum, Cyli
Year: 2001
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