Abstract:
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.
Citation:
Xavier Carton, Mathieu Morvan, Jean N. Reinaud, Mikhail A. Sokolovskiy, Pierre L'Hegaret, Clément Vic, “Vortex Merger near a Topographic Slope in a Homogeneous Rotating Fluid”, Regul. Chaotic Dyn., 22:5 (2017), 455–478
\Bibitem{CarMorRei17}
\by Xavier Carton, Mathieu Morvan, Jean N. Reinaud, Mikhail A. Sokolovskiy, Pierre L'Hegaret, Cl\'ement Vic
\paper Vortex Merger near a Topographic Slope in a Homogeneous Rotating Fluid
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 5
\pages 455--478
\mathnet{http://mi.mathnet.ru/rcd270}
\crossref{https://doi.org/10.1134/S156035471705001X}
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https://www.mathnet.ru/eng/rcd270
https://www.mathnet.ru/eng/rcd/v22/i5/p455
This publication is cited in the following 5 articles:
Erwan Oulhen, Jean N. Reinaud, Xavier Carton, “Formation of small-scale vortices in the core of a large merged vortex”, Geophysical & Astrophysical Fluid Dynamics, 116:5-6 (2022), 411
Armand Vic, Xavier Carton, Jonathan Gula, “The Interaction of Two Unsteady Point Vortex Sources
in a Deformation Field in 2D Incompressible Flows”, Regul. Chaotic Dyn., 26:6 (2021), 618–646
L. Xu, “Numerical study of the material transport in the viscous vortex dipole flow”, Phys. Fluids, 31:5 (2019), 053602
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 Dyn., 68:6 (2018), 723–733
de Marez Ch., Carton X., Morvan M., Reinaud J.N., “The Interaction of Two Surface Vortices Near a Topographic Slope in a Stratified Ocean”, Fluids, 2:4 (2017), 57
Citation in format AMSBIB
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