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    Geostrophic vortex dynamics

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    Polvani_thesis.pdf (5.033Mb)
    Date
    1988-08
    Author
    Polvani, Lorenzo M.  Concept link
    Metadata
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    Citable URI
    https://hdl.handle.net/1912/4961
    DOI
    10.1575/1912/4961
    Keyword
    Vortex-motion
    Abstract
    By generalizing the method of contour dynamics to the quasigeostrophic two layer model, we have proposed and solved a number of fundamental problems in the dynamics of rotating and stratified vorticity fields. A variety of rotating and translating potential vorticity equilibria (V-states) in one and two layers have been obtained, shedding new light on potential vorticity dynamics in the geostrophic context. In particular,the equivalent barotropic model is shown to be a singular limit of the two-layer model for scales large compared to the radius of deformation. The question of coalescence of two vortices in the same layer (merger) and· in different layers (alignment) is studied in detail. Critical initial separation distances for coalescence are numerically established as functions of the radius of deformation and the relative thickness of the layers at rest. The connection between coalescence and the existence of stable rotating doubly-connected V-states is shown to be an illuminating generalization of the Euler results. The question of filamentation of two-dimensional vorticity interfaces is addressed from a new geometrical perspective. The analysis of the topology of the streamfunction in a frame of reference rotating with the instantaneous angular velocity of the vorticity distribution (the corotating frame) is shown to yield new powerful insights on the nonlinear evolution of the vorticity field. In particular, the presence of hyperbolic (critical) points of the corotating streamfunction that come in contact with the vorticity interface is found to be directly responsible for the generation of filaments. The importance ofthe position of the critical points of the comoving streamfunction is found to generalize to the two-layer quasigeostrophic context. They are shown to play the crucial role in determining the limits, in parameter space, on the existence of a number of two-layer rotating and translating potential vorticity equilibria.
    Description
    Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution August 1988
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    • Physical Oceanography (PO)
    • WHOI Theses
    Suggested Citation
    Thesis: Polvani, Lorenzo M., "Geostrophic vortex dynamics", 1988-08, DOI:10.1575/1912/4961, https://hdl.handle.net/1912/4961
     

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