On the Stretching of Mesoscale Vortices into Filaments and their Distribution over the Ocean Surface

We consider various aspects of interaction of vortices with a barotropic flow. When a vortex interacts with a flow, there exist three variants of the flow-core behavior: rotation, nutational oscillations, and unlimited stretching. In the first two cases, the vortex remains a localized formation, such that the ellipse semiaxes undergo oscillations near certain average values. In the third case, the shape of the vortex varies as follows: one horizontal axis increases indefinitely and the second horizontal axis tends to zero so that the vertical size of the vortex does not change and the vortex itself stretches into a filament in top view, remaining ellipsoidal. As a result, vortex formations, which are called filaments, emerge in the ocean. They emerge from the vortices which are initially almost circular in the horizontal plane and represent structures stretched in one direction and having nonzero vorticity. In this work, an analytical and graphical method for determining the regimes of behavior of three-dimensional ellipsoidal vortices is proposed for the first time for an inhomogeneous horizontal current which is linear with respect to the horizontal coordinates. Conditions for inevitable stretching of the vortices into filaments are studied. It is established that the vortex stretching is manifested in spots (domains) on 60–67% of the world ocean surface and the characteristic dimensions of these spots amount to about 200 km. The vortex stretching into filaments ensures energy pumping from mesoscale processes to submesoscale ones. According to the global oceanic reanalysis GLORYS12V1, the domain distributions in the World Ocean are plotted. It is shown that irrespective of the spatial-averaging scales, the integral area of regions in which the mesoscale vortices can stretch into filaments is dominant.