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Abstract
We study pairwise interactions of elliptical quasigeostrophic vortices as the limiting case of vanishingly thin uniform potential vorticity ellipsoids. In this limit, the product of the vertical extent of the ellipsoid and the potential vorticity within it is held fixed to a finite nonzero constant. Such elliptical 'lenses' inherit the property that, in isolation, they steadily rotate without changing shape. Here, we use this property to extend both standard moment models and Hamiltonian ellipsoidal models to approximate the dynamical interaction of such elliptical lenses. By neglecting nonelliptical deformations, the simplified models reduce the dynamics to just four degrees of freedom per vortex. For simplicity, we focus on pairwise interactions between identical elliptical vortices initially separated in both the horizontal and vertical directions. The dynamics of the simplified models are compared with the full quasigeostrophic (QG) dynamics of the system, and show good agreement as expected for sufficiently distant lenses. The results reveal the existence of families of steadily rotating equilibria in the initial horizontal and vertical separation parameter space. For sufficiently large vertical separations, equilibria with varying shape exist for all horizontal separations. Below a critical vertical separation (stretched by the constant ratio of buoyancy to Coriolis frequencies N/f), comparable to the mean radius of either vortex, a gap opens in horizontal separation where no equilibria are possible. Solutions near the edge of this gap are unstable. In the full QG system, equilibria at the edge of the gap exhibit corners (infinite curvature) along their boundaries. Comparisons of the model results with the full nonlinear QG evolution show that the early stages of the instability are captured by the Hamiltonian elliptical model but not by the moment model that inaccurately estimates shorterrange interactions.
Original language  English 

Pages (fromto)  491517 
Journal  Geophysical and Astrophysical Fluid Dynamics 
Volume  110 
Issue number  6 
Early online date  1 Nov 2016 
DOIs  
Publication status  Published  2016 
Keywords
 Vortex patches
 Surface quasigeostrophy
 Moment models
 Equilibrium states
 Stability
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Dive into the research topics of 'Models of interacting pairs of thin, quasigeostrophic vortices: steadystate solutions and nonlinear stability'. Together they form a unique fingerprint.Projects
 1 Finished

Geophysical Vortices: The Structure, stability and interaction of geophysical vortices
Reinaud, J. N., Dritschel, D. G. & Scott, R. K.
5/01/10 → 1/11/13
Project: Standard