Solitary Rossby waves with baroclinic modes

A class of exact solutions of the equation of conservation of the quasi-geostrophic vorticity in a continuously stratified ocean on the β-plane is studied. These are stationary solitary waves traveling east and having horizontal scale comparable with the Rossby deformation radius, which exist due to the balance between the nonlinearity and β-effect. The solutions look like a sum of a barotropic modon and a number of axially symmetric baroclinic components. The baroclinicity, represented in the form of vertical normal modes, introduces an extra “degree of freedom” into the problem (as compared with the barotropic model) and allows for the construction of solutions with continuous pressure, density, velocity, vorticity and acceleration. As an example, the procedures of building solutions with one and two baroclinic modes are described in detail, and the properties of the resulting solitary waves are discussed. It is shown that by inserting real ambient density distributions into such solutions, it is possible to model synoptic eddies in the ocean

Emergence of modons from collapsing vortex structures on the β-plane

The evolution of unstable barotropic vortices is studied numerically. Exact solutions to the equation of potential vorticity conservation under the rigid lid condition, as well as nonsteady-state configurations, are set as initial states in the evolutionary experiments. The examined shielded modon structures usually collapse within one to several synoptic periods and radiate vortex pairs propagating westward and eastward. The latter are shown to be modons of Larichev and Reznik. The westward dipoles are identified as nonlocal modons, that is, vortical cores of stationary nonlinear Rossby waves. In the case of standing Stern modons, some small initial perturbations induce slow westward drift and subsequent collapse of the vortex structure due to the Rossby wave radiation, others lead to their transformation into Larichev and Reznik\u27s modons. This conclusion is supported by the results of a numerical integration of the linear stability problem

Contraction of westward-travelling nonlocal modons due to the vorticity filament emission

International audienceLong-term evolution of westward-travelling non-local modons on the ?-plane, i.e. dipolar vortices imbedded in slowly damping Rossby wave fields, is studied numerically. In the framework of the nondivergent (barotropic) model, two stages of the evolution are observed. At the first stage (for about 30 synoptic periods), the parameters and the form of the vortex practically remain constant, whereas at the second stage, vorticity filaments are emitted. Due to the filamentation, the vortex core contracts, the potential vorticity peaks of the vortex pair get closer, and the modon speeds up. In the divergent (equivalent-barotropic) model, nonlocal modons and the Lamb modon (that has no wave field outside the dipolar core) evolve much more slowly, essentially preserving the initial shape and propagation speed until about 100 synoptic periods

Instabilities of the flow around a cylinder and emission of vortex dipoles

Instabilities and long-term evolution of two-dimensional circular flows around a rigid circular cylinder (island) are studied analytically and numerically. For that we consider a base flow consisting of two concentric neighbouring rings of uniform but different vorticity, with the inner ring touching the cylinder. We first study the inviscid linear stability of such flows to perturbations of the free edges of the rings. For a given ratio of the vorticity in the rings, the governing parameters of the problem are the radii of the inner and outer rings scaled on the cylinder radius. In this two-dimensional parameter space, we determine analytically the regions of linear stability/instability of each azimuthal mode m=1, 2, .... In the physically most meaningful case of zero net circulation, for each mode m > 1, two regions are identified: a regular instability region where mode m is unstable along with some other modes, and a unique instability region where only mode m is unstable. After the conditions of linear instability are established, inviscid contour-dynamics and high-Reynolds-number finite-element simulations are conducted. In the regular instability regions, simulations of both kinds typically result in the formation of vortical dipoles or multipoles. In the unique instability regions, where the inner vorticity ring is much thinner than the outer ring, the inviscid contour-dynamics simulations do not reveal dipole emission. In the viscous simulation, because viscosity has time to widen the inner ring, the instability develops in the same manner as in the regular instability regions

Instability of a shear flow around a circular island and emission of vortex dipoles

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Instability of a shear flow around a circular island and emission of vortex dipoles

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Laboratory experiments on multipolar vortices in a rotating fluid

The instability properties of isolated monopolar vortices have been investigated experimentally and the corresponding multipolar quasisteady states have been compared with semianalytical vorticity-distributed solutions to the Euler equations in two dimensions. A novel experimental technique was introduced to generate unstable monopolar vortices whose nonlinear evolution resulted in the formation of multipolar vortices. Dye-visualization and particle imaging techniques revealed the existence of tripolar, quadrupolar, and pentapolar vortices. Also evidence was found of the onset of hexapolar and heptapolar vortices. The observed multipolar vortices were found to be unstable and generally broke up into multipolar vortices of lesser complexity. The characteristic flow properties of the quadrupolar vortex were in close agreement with the semianalytical model solutions. Higher-order multipolar vortices were observed to be susceptible to strong inertial oscillations. © 2010 American Institute of Physic

Geostrophic tripolar vortices in a two-layer fluid : linear stability and nonlinear evolution of equilibria

We investigate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii. The two branches of equilibria can co-exist and intersect for small deformation radii. Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabouts do, thus inducing stronger vortex interactions. However, for larger deformation radii, eccentric roundabouts can also be unstable. Then, the two branches of equilibria do not cross. The branch of eccentric roundabouts only exists for large separations. Near the end of the branch of eccentric roundabouts (at the smallest separation), one of the like-signed vortices exhibits a sharp inner corner where instabilities can be triggered. Finally, we investigate the nonlinear evolution of a few selected cases of tripoles.PostprintPeer reviewe