NDLI: The N-vortex problem on a sphere: geophysical mechanisms that break integrability

Content Provider	Springer Nature Link
Author	Newton, Paul K.
Copyright Year	2009
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 center-of-vorticity 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 center-of-vorticity vectors of more than one region of concentrated vorticity, and the coupling between the center-of-vorticity vector and the background vorticity field which supports Rossby waves. Focusing on the Polar vortex splitting event of September 2002, we describe simple (i.e., 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 pinch-off 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.
Ending Page	149
Page Count	13
Starting Page	137
File Format	PDF
ISSN	09354964
e-ISSN	14322250
Journal	Theoretical and Computational Fluid Dynamics
Issue Number	1-4
Volume Number	24
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-06-07
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Antarctic polar vortex Engineering Fluid Dynamics N-vortex problem on sphere Nonintegrable Hamiltonian systems Computational Science and Engineering Classical Continuum Physics
Content Type	Text
Resource Type	Article
Subject	Fluid Flow and Transfer Processes Condensed Matter Physics Computational Mechanics

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