E.A. Ryzhov, M.A. Sokolovskiy. Interaction of two-layer vortex pair with a submerged cylindrical obstacle in a two-layer rotating fluid. Physics of Fluids, 2016, v. 28, 056602 (18 pp).
We consider the dynamics of a two-layer compensated vortex pair (heton) interacting with a submerged cylindrical obstacle of small height located in the lower layer of a two-layer fluid in the f-plane. The pair consists of two counter-rotating vortices of equal strengths each located in different layers of the two-layer rotating fluid. We make use of two approaches.The first one considers a model of point vortices, and the second one assumes the vortices as finite-core vorticity patches analyzed by means of contour dynamics techniques. The point vortex model features two regimes of the pair’s motion: an unbounded motion as the pair advances to infinity after being deflected by the cylindrical obstacle and an oscillatory motion inside a bounded region near the cylindrical obstacle. The oscillations, in turn, are of two types. The first corresponds to a finite yet unpredictable number of vortex revolutions near the cylinder, and the second results in an infinite number of revolutions. By exploiting contour dynamics techniques, we obtain very similar unbounded dynamics of a distributed vorticity heton given relatively strong stratification. An important feature of this dynamics is that the contours associated with the pair hold almost unperturbed signifying sufficient stability. By decreasing stratification, we observe complicated dynamics involving vorticity redistribution and vortex splitting.
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