Journal Title
Title of Journal: Theor Comput Fluid Dyn
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Abbravation: Theoretical and Computational Fluid Dynamics
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Publisher
Springer-Verlag
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Authors: Paul K Newton
Publish Date: 2009/06/07
Volume: 24, Issue: 1-4, Pages: 137-149
Abstract
We describe the dynamical system governing the evolution of a system of point vortices on a rotating spherical shell highlighting features which break what would otherwise be an integrable problem The importance of the misalignment of the centerofvorticity vector associated with a cluster of point vortices with the axis of rotation is emphasized as a crucial factor in the interpretation of dynamical features for many flow configurations We then describe two important physical mechanisms which break what would otherwise be an integrable problem—the interactions between the local centerofvorticity vectors of more than one region of concentrated vorticity and the coupling between the centerofvorticity vector and the background vorticity field which supports Rossby waves Focusing on the Polar vortex splitting event of September 2002 we describe simple ie low dimensional mechanisms that can trigger instabilities whose subsequent development cause the onset of chaotic advection and global particle transport At the linear level eigenvalues that oscillate between elliptic and hyperbolic configurations initiate the pinchoff process of a passive patch representing the Polar vortex At the nonlinear level the evolution and topological bifurcations of the streamline patterns are responsible for its further splitting stretching and subsequent transport over the sphere We finish by briefly describing how to incorporate conservation of potential vorticity and the development of a model governing the probability density function associated with the point vortex system
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