Finite Rossby radius effects on vortex motion near a gap

Abstract

The continuous spectrum of time-harmonic shear layers Phys. Fluids 24, 034101 (2012) The interaction of a vortex ring with a sloped sediment layer: Critical criteria for incipient grain motion Phys. Fluids 24, 026604 (2012) Numerical study of flow characteristics behind a stationary circular cylinder with a flapping plate Phys. 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, reducedgravity 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.

A point vortex model for the formation of ocean eddies by flow separation

“…Therefore, the trajectory of the vortex is a straight line, parallel to the wall until the end of the wall is reached and then a semi-circular arc around the tip until it can again move off parallel to the wall. This can be shown asymptotically by reformulating problem (14) and (15) as an integral equation using the infinite domain Green's function for (14),…”

Parametric resonance in the dynamics of an elliptic vortex in a periodically strained environment

“…Such models are usually highly nonlinear, making it possible to gain insight into many phenomena that are difficult to predict within a geophysical setting (Provenzale, 1999;Balasuriya and Jones, 2001;Koshel and Prants, 2006;Samelson, 2013;Ryzhov and Koshel, 2013;Kostrykin et al, 2006;Koshel et al, 2008Koshel et al, , 2013Koshel et al, , 2014Haller, 2015). For instance, such vortex models can shed some light on the dynamics of interacting coherent mesoscale vortices (Reznik and Dewar, 1994;Gryanik et al, 2000;Reznik and Kizner, 2010;Carton et al, 2010Carton et al, , 2013Reinaud and Carton, 2015), sustainability of such vortices against external flows (McKiver and Dritschel, 2003;Liu and Roebber, 2008;Perrot and Carton, 2010), or topographic influence (Kozlov et al, 2005;Johnson and McDonald, 2005;Ryzhov et al, 2010;Sutyrin et al, 2011;Nilawar et al, 2012), and so on.…”