Behavior Modes of a Quasi-Geostrophic Ellipsoidal Vortex in a Horizontal Flow With Vertical Shear

The paper addresses the problem of the behaviour modes of baroclinic geostrophic vortices with ellipsoidal-shaped cores in horizontal flows with a vertical shift. In such flows, the vortex core is confined between two stationary horizontal planes, which the vortex touches at its upper and lower points. Under the influence of the background flow, the lengths of all the axes of the ellipsoid can change, and the angles of orientation of the vortex in space also change. The authors identify three modes of vortex behaviour. The first mode is the survival mode of the vortex in a shear flow, where the vortex undergoes finite oscillations of the semi-axes for an indefinite period of time and may exhibit complex behaviour in terms of its orientation angles. This mode corresponds to strong vortices. In the second mode, the vortex is stretched along the flow from the very beginning, remaining with finite horizontal dimensions perpendicular to the flow and compressed vertically. This is the destruction mode of the vortex by the flow, where the final result is the formation of a thin vertical structure of the ocean from the vortex. Weak vortices undergo this type of evolution. This mode is referred to as the “unlimited stretching mode.” Finally, there is a third mode, called the “finite lifetime mode,” in which, for a finite period of time, the vortex behaves similarly to the survival mode (its shape is finitely deformed, and the vortex rotates or oscillates in space), but eventually, the vortex stretches indefinitely in a manner similar to the destruction mode. The authors have delineated the regions of existence for each mode on a dimensionless parameter plane of the problem and determined the boundaries separating the above-mentioned modes of vortex behaviour.