|dc.contributor.author||Polvani, Lorenzo M.||
|dc.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||en_US||
|dc.description.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
|dc.publisher||Massachusetts Institute of Technology and Woods Hole Oceanographic Institution||en_US||
|dc.title||Geostrophic vortex dynamics||en_US||