Showing papers by "Lorenzo M. Polvani published in 1988"

Geostrophic Vortex Dynamics

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.

The Effect of Dissipation on Spatially Growing Nonlinear Baroclinic Waves

Abstract: The question of convective (i.e., spatial) instability of baroclinic waves on an f-plane is studied in the context of the two-layer model. The viscous and inviscid marginal curves for linear convective instability are obtained. The finite-amplitude problem shows that when dissipation is O(1) it acts to stabilize the waves that are of Eady type. For very small dissipation the weakly nonlinear analysis reveals that at low frequencies, contrary to what is known to occur in the temporal problem, in addition to the baroclinic component a barotropic correction to the “mean” flow is generated by the nonlinearities, and spatial equilibration occurs provided the ratio of shear to mean flow does not exceed some critical value. In the same limit, the slightly dissipative nonlinear dynamics reveals the presence of large spatial vacillations immediately downstream of the source, even if asymptotically (i.e., very far away from the source) the amplitudes are found to reach steady values. No case of period doub...