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Point-vortex application to vortex stability, evolution, and statistical equilibrium




Persing, John, author
Montgomery, Michael T., author

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The nonlinear evolution of an isolated, barotropic vortex in an infinite, frictionless domain is examined with a cloud of like-signed point-vortices. The stability of systems of point­ vortices is reviewed as well as the stability of continuous systems possessing a sign reversal in the radial vorticity gradient like that observed in the inner core of hurricanes. The new result is the application of point-vortices to examine the evolution of a hurricane­ like vortex system. Using a three-region approximation to the radial vorticity profile, the nondimensional problem can be reduced to two parameters. These are the inner radius of the vorticity maximum 8 and the tangential wind speed at this radius Vtan(8). The relaxation time scale is on the order of five circuit times, and the relaxed vorticity profile ranges from near solid-body rotation to highly monopolar profiles. The relaxation time-scale and the monopolicity of the relaxed vorticity profile show some correlation to the strength of the linear instability in the initial system, although a more thorough examination of the parameter space is proposed to obtain a complete understanding of the processes involved in the relaxation.


June 1995.
Also issued as John Persing's thesis (M.S.) -- Colorado State University, 1995.

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Hurricanes -- Mathematical models
Vortex-motion -- Mathematical models


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