Carton, Xavier; Morvan, Mathieu; Reinaud, Jean N.; Sokolovskiy, Mikhail A.; L’Hegaret, Pierre; Vic, Clément Vortex merger near a topographic slope in a homogeneous rotating fluid. (English) Zbl 1387.86008 Regul. Chaotic Dyn. 22, No. 5, 455-478 (2017). Summary: The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two-dimensional, quasi-geostrophic, incompressible fluid.When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This alongshelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclones and near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times.For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process.Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones.Conclusions are drawn on possible improvements of the model configuration for an application to the ocean. Cited in 2 Documents MSC: 86A05 Hydrology, hydrography, oceanography 76B47 Vortex flows for incompressible inviscid fluids 76E30 Nonlinear effects in hydrodynamic stability 76B65 Rossby waves (MSC2010) Keywords:two-dimensional incompressible flow; vortex merger; critical merger distance; bottom slope; topographic wave and vortices; diffusion PDFBibTeX XMLCite \textit{X. Carton} et al., Regul. Chaotic Dyn. 22, No. 5, 455--478 (2017; Zbl 1387.86008) Full Text: DOI References: [1] Aguiar, A.C.B., Peliz, Á., and Carton, X., A Census of Meddies in a Long-Term High-Resolution Simulation, Prog. Oceanogr., 2013, vol. 116, pp. 80-94. [2] Angot, P., Bruneau, Ch.-H., and Fabrie, P., A Penalisation Method to Take into Account Obstacles in Viscous Flows, Numer. Math., 1999, vol. 81, no. 4, pp. 497-520. · Zbl 0921.76168 [3] Bambrey, R.R., Reinaud, J.N., and Dritschel, D.G., Strong Interactions between Two Corotating Quasi-Geostrophic Vortices, J. 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