Two-layer geostrophic vortex dynamics. Part 2. Alignment and two-layer V-states

Abstract

We generalize the methods of two-dimensional contour dynamics to study a twolayer rotating fluid that obeys the quasi-geostrophic equations. We consider here only the case of a constant-potential-vorticity lower layer. We derive equilibrium solutions for monopolar (rotating) and dipolar (translating) geostrophic vortices in the upper layer, and compare them with the Euler case. We show that the equivalent barotropic (infinite lower layer) case is a singular limit of the two-layer system. We also investigate the effect of a finite lower layer on the merger of two regions of equalsign potential vorticity in the upper layer. We discuss our results in the light of the recent laboratory experiments of Griffiths & Hopfinger (1986). The process of filamentation is found to be greatly suppressed for equivalent barotropic dynamics on scales larger than the radius of deformation. We show that the variation of the critical initial distance for merger as a function of the radius of deformation and the ratio of the layers at rest is closely related to the existence of vortex-pair equilibria and their geometrical properties.

Surface signature of Mediterranean water eddies in the Northeastern Atlantic: effect of the upper ocean stratification

“…4).H is typically 200 m less than H , the depth of the centre of meddy core (Hebert, 1988;Paillet et al, 2002;Carton et al, 2002). Further vortex-vortex interaction may lead to alignment of the two vortices or co-rotation of the structures around a common centre (Polvani, 1991). When the radii of the vortices are smaller than or equal to the first Rossby deformation radius and when the initial separation of the centres is about half the meddy radius, the second evolution is the most probable one.…”

Transformation of an Agulhas eddy near the continental slope

“…This investigation differs from that of Matano and Beier (2003) and Wang (1992), who used point vortices based on the work by Hogg and Stommel (1985). We use two closed regions of constant vorticity based on the work by Polvani (1991), and the dipole-like heton propagates perpendicular to the line of centers, rather than along the line of centers as in the work by Matano and Beier (2003).…”

“…For the case of counter-rotating vortices, with motion of each vortex residing in a separate layer, we use a "heton" pair (Hogg and Stommel, 1985;Polvani, 1991, except the layer depths are unequal) to illustrate the dipole behavior. However, the vortices do not overlap completely, so that there is a dipole moment propelling them westward.…”

Baroclinic vortices over a sloping bottom

“…When AR ~ 1 the mean area again increases, and the asymptotic limit is the 1.5 layer case. Here, filamentation is suppressed as in Polvani et al (1991) and the vortices are ceasing to interact with vortices far away from themselves. As before, it is the defeat of the barotropic mode which is responsible for the shift.…”

“…The study of mergers between surface vortices of Polvani et al (1991) is again of relevance. One aspect they considered is the effect on mergers of increasing the lower layer depth, and in particular mergers in one and a half layers.…”