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The formation of new quasi-stationary vortex patterns from the interaction of two identical vortices in a rotating fluid

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Abstract

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.

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References

  • Assassi C, Morel Y, Vandermeirsch F, Chaigneau A, Pegliasco C, Morrow RM, Colas F, Fleury S, Carton X, Klein P, Cambra R (2016) An index to distinguish surface and subsurface intensified vortices from surface observations. J Phys Oceanogr 46(8):2529–2552

    Article  Google Scholar 

  • Bambrey RR, Reinaud JN, Dritschel DG (2007) Strong interactions between two co-rotating quasi-geostrophic vortices. J Fluid Mech 592:117–133

    Article  Google Scholar 

  • Bertrand C, Carton XJ (1993) Vortex merger on the beta-plane. C R Acad Sci Paris 316:1201–1206

    Google Scholar 

  • Capéran P, Verron J (1988) Numerical simulation of a physical experiment on two-dimensional vortex merger. Fluid Dyn Res 3(1–4):87–92

    Article  Google Scholar 

  • Capuano TA, Speich S, Carton X, Blanke B (2018) Mesoscale and submesoscale processes in the Southeast Atlantic and their impact on the regional thermohaline structure. J Geophys Res Oceans 123:1961. https://doi.org/10.1002/2017JC013396 to appear (online 12 March 2018)

    Article  Google Scholar 

  • Carnevale GF, Cavazza P, Orlandi P, Purini R (1991) An explanation for anomalous vortex merger in rotating tank experiments. Phys Fluids A 3:1411–1415

    Article  Google Scholar 

  • Carton XJ (1992) On the merger of shielded vortices. Europhys Lett 18:697–703

    Article  Google Scholar 

  • Carton XJ (2001) Hydrodynamical modelling of oceanic vortices. Surv Geophys 22(3):179–263

    Article  Google Scholar 

  • Carton X, Maze G, Legras B (2002) A two-dimensional vortex merger in an external strain field. J Turbul 3:045

    Article  Google Scholar 

  • Carton X, Ciani D, Verron J, Reinaud J, Sokolovskiy M (2016) Vortex merger in surface quasi-geostrophy. Geophys Astrophys Fluid Dyn 110(1):1–22

    Article  Google Scholar 

  • Carton X, Morvan M, Reinaud JN, Sokolovskiy MA, L’Hegaret P, Vic C (2017) Vortex merger near topographic slope in a homogeneous rotating fluid. Regular Chaotic Dyn 22(5):455–478

    Article  Google Scholar 

  • Cerretelli C, Williamson CHK (2003) The physical mechanism for vortex merging. J Fluid Mech 475:41–77

    Article  Google Scholar 

  • Chelton DB, Schlax MG, Samelson RM (2011) Global observations of nonlinear mesoscale eddies. Prog Oceanogr 91(2):167–216

    Article  Google Scholar 

  • Christiansen JP, Zabusky NJ (1973) Instability, coalescence and fission of finite-area vortex structures. J Fluid Mech 61(part2):219–243

    Article  Google Scholar 

  • Ciani D, Carton X, Verron J (2016) On the merger of subsurface isolated vortices. Geophys Astrophys Fluid Dyn 110(1):23–49

    Article  Google Scholar 

  • Ciani D, Carton X, Barbosa Aguiar AC, Peliz A, Bashmachnikov I, Ienna F, Chapron B, Santolieri R (2017) Surface signature of Mediterranean water eddies in a long-term high-resolution numerical model. Deep Sea Res Part I Oceanogr Res Pap 130:12–29

    Article  Google Scholar 

  • Delbende I, Piton B, Rossi M (2015) Merging of two helical vortices. Eur J Mech B Fluid 49(Part B):363–372

    Article  Google Scholar 

  • Dritschel DG (1986) The nonlinear evolution of rotating configurations of uniform vorticity. J Fluid Mech 172:157–182

    Article  Google Scholar 

  • Dritschel DG, Waugh DW (1992) Quantification of the inelastic interaction of inequal vortices in two-dimensional vortex dynamics. Phys Fluids A 4(8):1737–1744

    Article  Google Scholar 

  • Dritschel DG, Zabusky NJ (1996) On the nature of vortex interactions and models in unforced nearly-inviscid two-dimensional turbulence. Phys Fluids 8(5):1252–1256

    Article  Google Scholar 

  • Filyushkin BN, Sokolovskiy MA (2011) Modeling the evolution of intrathermocline lenses in the Atlantic Ocean. J Mar Res 69(2–3):191–220

    Article  Google Scholar 

  • Freymuth P, Bank W, Palmer M (1984) First experimental evidence of vortex splitting. Phys Fluids 27(5):1045–1046

    Article  Google Scholar 

  • Freymuth P, Bank W, Palmer M (1985) Futher experimental evidence of vortex splitting. J Fluid Mech 152:289–299

    Article  Google Scholar 

  • Hopfinger EJ, van Heijst GJF (1993) Vortices in rotating fluids. Ann Rev Fluid Mech 25:241–289

    Article  Google Scholar 

  • Katsumata K (2016) Eddies observed by Argo floats. Part I. Eddy transport in the upper 1000 dbar. J Phys Oceanogr 46(11):3471–3486

    Article  Google Scholar 

  • Kirchhoff G (1876) Vorlesungen űber mathematische Physik: Mechanik. Taubner, Leipzig

    Google Scholar 

  • Kozlov VF, Makarov VG (1984) Evolution modeling of unstable geostrophic eddies in a barotropic ocean. Oceanology 24(5):556–560

    Google Scholar 

  • Lamb H (1932) Hydrodynamics, 6th edn. Cambridge University Press, Cambridge

    Google Scholar 

  • Love AEH (1893) On the stability of certain vortex motion. Proc Lond Math Soc s1–25:18–43

    Article  Google Scholar 

  • Melander MV, Zabusky NJ, McWilliams JC (1988) Symmetric vortex merger in two dimensions: causes and conditions. J Fluid Mech 195:303–340

    Article  Google Scholar 

  • Meunier P, Leweke T (2001) Three-dimensional instability during vortex merging. Phys Fluids 13(10):2747–2751

    Article  Google Scholar 

  • Meunier P, Ehrenstein U, Leweke T, Rossi M (2002) A merger criterion for two-dimensional co-rotating vortices. Phys Fluids 14(8):2757–2766

    Article  Google Scholar 

  • Overman EA, Zabusky NJ (1982) Evolution and merger of isolated vortex structures. Phys Fluids 25:1297–1305

    Article  Google Scholar 

  • Polvani LM, Zabusky NJ, Flierl GR (1989) Two-layer geostrophic vortex dynamics: 1. Upper-layer V-states and merger. J Fluid Mech 205:215–242

    Article  Google Scholar 

  • Reinaud JN, Dritschel DG (2002) The merger of vertically offset quasi-geostrophic vortices. J Fluid Mech 469:287–315

    Article  Google Scholar 

  • Reinaud JN, Dritschel DG (2005) The critical merger distance between two co-rotating quasi-geostrophic vortices. J Fluid Mech 522:357–381

    Article  Google Scholar 

  • Roberts KV, Christiansen JP (1972) Topics in computational fluid mechanics. Comput Phys Commun 3(Suppl 1):14–32

    Article  Google Scholar 

  • Roshko A (1976) Structure of turbulent shear flows: a new look. AIAA Journal 14th Aerospace Sciences Meeting Paper No 76–78

  • Rousselet L, Doglioli A, Maes C, Blanke B, Petrenko A (2016) Impacts of mesoscale activity on the water masses and circulation in the Coral Sea. J Geophys Res Oceans 121:7277–7289

    Article  Google Scholar 

  • Saffman PG, Szeto R (1980) Equilibrium shape of a pair of equal vortices. Phys Fluids 23(12):2339–2342

    Article  Google Scholar 

  • Sokolovskiy MA, Verron J (2000) Finite-core hetons: stability and interactions. J Fluid Mech 423:127–154

    Article  Google Scholar 

  • Sokolovskiy MA, Verron J (2014) Dynamics of vortex structures in a stratified rotating fluid. Series atmospheric and oceanographic sciences library, vol 47. Springer, Switzerland

    Google Scholar 

  • Valcke S, Verron J (1993) On interactions between two finite-core hetons. Phys Fluids A 5(8):2058–2060

    Article  Google Scholar 

  • Verron J, Hopfinger E (1991) The enigmatic merging conditions of two-layer baroclinic vortices. C R Acad Sci Paris Ser II 313(7):737–742

    Google Scholar 

  • Verron J, Valcke S (1994) Scale-dependent merging of baroclinic vortices. J Fluid Mech 264:81–106

    Article  Google Scholar 

  • Verron J, Hopfinger E, McWilliams JC (1990) Sensitivity to initial conditions in the merging of two-layer baroclinic vortices. Phys Fluids A 2(6):886–889

    Article  Google Scholar 

  • von Hardenberg J, McWilliams JC, Provenzale A, Shchepetkin A, Weiss JB (2000) Vortex merging in quasi-geostrophic flows. J Fluid Mech 412:331–353

    Article  Google Scholar 

  • Waugh DW (1992) The efficiency of symmetric vortex merger. Phys Fluids A 4(8):1745–1758

    Article  Google Scholar 

  • Winant CD, Browand FK (1974) Vortex pairing: the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J Fluid Mech 63(2):237–255

    Article  Google Scholar 

  • Zabusky NJ, Hughes MH, Roberts KV (1979) Contour dynamics for the Euler equations in two dimensions. J Comput Phys 30(1):96–106

    Article  Google Scholar 

  • Zhang Z, Zhong Y, Tian J, Yang Q, Zhao W (2014) Estimation of eddy heat transport in the global ocean from Argo data. Acta Oceanol Sin 33(1):42–47

    Article  Google Scholar 

Download references

Funding

This is a contribution to PRC CNRS/RFBR 1069/16-55-150001. From the side of the MAS work was carried out within the framework of the state task no. 0149-2018-0001. This study receive support from Russian Foundation for Basic Research (Project No 16-05-00121), Russian Scientific Foundation (Project No. 14-50-00095), Ministry of Education and Science of Russian Federation (Project No. 14.W.03.31.0006).

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Authors and Affiliations

  1. Institute of Water Problems of Russian Academy of Sciences, 3 Gubkina Str., Moscow, Russia, 119333

    Mikhail A. Sokolovskiy

  2. Shirshov Institute of Oceanology of Russian Academy of Sciences, 36 Nahimovskiy Pr., Moscow, Russia, 117997

    Mikhail A. Sokolovskiy

  3. Institut des Géosciences de l’Environnement (IGE), CS 40 700, 38058, Grenoble Cedex 9, France

    Jacques Verron

  4. Laboratoire d’Océanographie Physique et Spatiale, IUEM/UBO, Rue Dumont D’Urville, 29280, Plouzané, France

    Xavier J. Carton

Authors
  1. Mikhail A. Sokolovskiy
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  2. Jacques Verron
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  3. Xavier J. Carton
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Corresponding author

Correspondence to Mikhail A. Sokolovskiy.

Additional information

Responsible Editor: Sergey Prants

This article is part of the Topical Collection on the International Conference “Vortices and coherent structures: from ocean to microfluids,” Vladivostok, Russia, 28–31 August 2017

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Sokolovskiy, M.A., Verron, J. & Carton, X.J. The formation of new quasi-stationary vortex patterns from the interaction of two identical vortices in a rotating fluid. Ocean Dynamics 68, 723–733 (2018). https://doi.org/10.1007/s10236-018-1163-7

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  • DOI: https://doi.org/10.1007/s10236-018-1163-7

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