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Finite Rossby radius effects on vortex motion near a gap

Nilawar, RS; Johnson, ER; McDonald, NR; (2012) Finite Rossby radius effects on vortex motion near a gap. Physics of Fluids , 24 (6) , Article 066601. 10.1063/1.4721432. Green open access

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Abstract

This work investigates the effect of the Rossby radius of deformation on the motion of a vortex near a gap in an infinitely long barrier. A key parameter determining the behaviour of the vortex is a, the ratio of the Rossby radius of deformation to the width of the gap. Assuming quasi-geostrophic dynamics for a single-layer, reduced-gravity fluid, an integral equation is derived whose solution gives the velocity at any point in the fluid. The integral equation is solved numerically and the velocity field is integrated to give the trajectories of point vortices. Combined with the method of contour dynamics, the method can be used to compute the evolution of finite area patches of constant vorticity. The trajectories of point vortices and vortex patches are compared. The patches are initially circular and the centroids of those vortex patches that remain close to circular follow the trajectory and speed of their equivalent point vortices when appropriately normalised. The critical point vortex trajectory (the separatrix) which divides vortices that leap across the gap and those that pass through, is computed for various a. Decreasing the Rossby radius of deformation increases the tendency of vortices to pass through the gap. The effect of various background flows on both point vortex and vortex patch motion is also described.

Type: Article
Title: Finite Rossby radius effects on vortex motion near a gap
Open access status: An open access version is available from UCL Discovery
DOI: 10.1063/1.4721432
Publisher version: http://dx.doi.org/10.1063/1.4721432
Language: English
Additional information: Reprinted with permission from Nilawar, RS; Johnson, ER; McDonald, NR; (2012) Finite Rossby radius effects on vortex motion near a gap. Physics of Fluids, 24 (6), Article 066601, 10.1063/1.4721432. Copyright 2012, American Institute of Physics.
Keywords: confined flow, critical points, integral equations, numerical analysis, vortices
UCL classification: UCL > School of BEAMS > Faculty of Maths and Physical Sciences
UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Mathematics
URI: http://discovery.ucl.ac.uk/id/eprint/1349057
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