M.A. Sokolovskiy, J. Verron, X.J. Carton. The formation of new quasi-stationary vortex patterns from the interaction of two identical vortices in a rotating fluid. Ocean Dynamics, 2018, v. 68, N 6, pp. 723-733.
Within the framework of the quasi-geostrophic approximation, the interactions of two identical initially circular vortex patches are studied using the contour dynamics/surgery method. The cases of barotropic vortices and of vortices in the upper layer of a two-layer fluid are considered. Diagrams showing the end states of vortex interactions and, in particular, the new regime of vortex triplet formation are constructed for a wide range of external parameters. This paper shows that, in the nonlinear evolution of two such (like-signed) vortices, the filaments and vorticity fragments surrounding the merged vortex often collapse into satellite vortices. Therefore, the conditions for the formation and the quasi-steady motions of a new type of triplet-shaped vortex structure are obtained.
2020M.A. Sokolovskiy, X.J. Carton, B.N. Filyushkin. Mathematical modeling of vortex interaction using a three-layer quasigeostrophic model. Part 2: Finite-core-vortex approach and oceanographic application. Mathematics, 2020, v. 8, N 8, 1267
2020M.A. Sokolovskiy, X.J. Carton, B.N. Filyushkin. Mathematical modeling of vortex interaction using a three-layer quasigeostrophic model. Part 1: Point-vortex approach. Mathematics, 2020, v. 8, N 8, 1228, doi:10.3390/math8081228