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Radiating Vortices in Geophysical Fluid Dynamics

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Abstract

The dynamics of a single vortex on a beta-plane is discussed in this paper. A barotropic, an equivalent barotropic, one-and-a half and two-layer models are considered. The momentum and energy balances are used to describe the evolution of a vortex. A quasi-stationary balance of the Rossby, Zhukovsky-Kutta forces and the force induced by Rossby-wave radiation, describes the dynamics of the barotropic vortex. A net Coriolis force occurs if the fluid is stratified. The difference between the dynamics of cyclones and anticyclones results directly from the Coriolis force acting on a single vortex in a stratified fluid.

All vortices radiate Rossby waves in the quasigeostrophic approximation but intense anticyclones propagate steadily in a one-and-a half layer model. A critical amplitude that bounds radiating and steadily propagating anticyclones is found. Steady propagation of anticyclones in general is impossible in a two-layer fluid due to the radiation of a barotropic Rossby-wave. Some solutions of solitary wave type which are known for a two-layer model, survive owing to wave interference.

A single vortex can extract energy from a Rossby wave if synchronism conditions are satisfied. The wave interference again plays a crucial role in this case. The wave interference also determines the energy exchange of vortices located at larger distances. If the distance between the vortices is shorter than the length of the radiated waves, modon may be formed due to a small energy loss.

The unbounded monotonic variation of the planetary vorticity is a characteristic feature of a beta-plane approximation. As a result, a single vortex propagates up to a ''rest latitude'' where it disappears. The evolution of a single barotropic vortex over bottom topography provides another example of a background vorticity distribution with a local extremum above hills (valleys) or ridges (troughs). Physics of its movement differs from a beta-plane case, but if a vortex lies over broad topography, equations are similar and the evolution of a vortex manifests the same typical features. Particularly, a cyclonic vortex tends to drift to the top of a hill or a ridge. An anticyclonic vortex, on the contrary, slides to the bottom of a valley or a trough.

An interaction of a barotropic vortex with a broad mean flow is tractable qualitatively on the basis of previous results. Numerical examples illustrating absorption of a small vortex by a larger one and a vortex movement across the flow, are direct analogies of the vortex evolution over a hill and a ridge, respectively. At the same time, strong influence of strain drastically changes the vortex structure.

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References

  • Adem, J.: 1956, 'A series solution for the barotropic vorticity equation and its application in the study of atmospheric vortices', Tellus 8, 364–372.

    Google Scholar 

  • Armi, L., Hebert, D., Oakey, N., Price, J. F., Richardson, P. L., Rossby, H. T., and Ruddick, B.: 1989, 'Two years in the life of a mediterranean salt lens', J.Phys.Oceanogr. 19, 354–370.

    Google Scholar 

  • Batchelor, G. K.: 1967, An Introduction to Fluid Dynamics, Cambridge University Press.

  • Booker, J. R. and Bretherton, F. P.: 1967, 'The critical layer for internal gravity waves in a shear flow', J.Fluid Mech. 27, 513–539.

    Google Scholar 

  • Bretherton, F. P. and Karweit, M.: 1975, 'Mid-ocean mesoscale modelling', in R. O. Reid, A. R. Robinson, and K. Bryan (eds. ), Numerical Models of Ocean Circulation, U. S. Nat. Acad. Sci., pp. 237–249.

  • Carnevale, G. F., Kloosterziel, R. C., and van Heijst, G. J. F.: 1991, 'Propagation of barotropic vorticesover topography in a rotating tank', J.Fluid Mech. 223, 119–139.

    Google Scholar 

  • Charney, J. C. and Flierl, G. R.: 1981, 'Oceanic analogous of large scale atmospheric motion', in: B. Warren and C. Wunch (eds. ), Evolution of Physical Oceanography, MIT Press, pp. 504–548.

  • Dritschel, D. G.: 1990, 'The stability of elliptical vortices in an external straining flow', J.Fluid Mech. 210, 223–261.

    Google Scholar 

  • Ferell, W.: 1859, 'The motion of fluids and solids relative to the Earth's surface', Math.Mon. 1, 300–307.

    Google Scholar 

  • Fiorino, M. and Elsberry, R. L.: 1989, 'Some aspects of vortex structure related to tropical cyclonemotion', J.Atmos.Sci. 46, 975–990.

    Google Scholar 

  • Flierl, G. R.: 1984, 'Rossby wave radiation from a strongly nonlinear warm eddy', J.Phys.Oceanogr. 14, 47–58.

    Google Scholar 

  • Flierl, G. R.: 1987, 'Isolated eddy models in geophysics', Ann.Rev.Fluid Mech. 19, 493–530.

    Google Scholar 

  • Flierl, G. R., Larichev, V. D., McWilliams, J. C., and Reznik, G. M.: 1980, 'The dynamics of baroclinicand barotropic solitary eddies', Dyn.Atmos.Oceans. 5, 1–41.

    Google Scholar 

  • Flierl, G. R., Stern, M. E., and Whitehead, J. A.: 1983, 'The physical significance of modons: Laboratoryexperiments and general integral constraints', Dyn.Atmos.Oceans. 7, 233–263.

    Google Scholar 

  • Flierl, G. R. and Haines, K.: 1994, 'The decay of modons due to Rossby wave radiation', Phys.of Fluid 6, 3, 487–3,497.

    Google Scholar 

  • Gill, A. E.: 1982, Atmosphere-Ocean Dynamics, Academic Press.

  • Gill, A. E., Green, J. S., and Simmons, A. J.: 1974, 'Energy partition on the large-scale ocean circulation and the production of mid-ocean eddies', Deep-Sea Res. 7, 499–528.

    Google Scholar 

  • Hopfinger, E. J. and van Heijst, G. J. F.: 1993, 'Vortices in rotating fluids', Ann.Rev.Fluid Mech. 25, 241–289.

    Google Scholar 

  • Kida, S.: 1981, 'Motion of an elliptic vortex in a uniform shear flow', J.Phys.Soc.Japan 50, 3517–3520.

    Google Scholar 

  • Korotaev, G. K.: 1980a, Asymptotical Regime of Isolated Barotropic Eddy Dynamics, in: Marine Hydrophysical Investigations, 1, Marine Hydrophys. Inst., Sevastopol, pp. 5–18 (in Russian).

  • Korotaev, G. K.: 1980b, Structure, Dynamics and Energetic of Synoptic Variability of the Ocean, Preprint, Marine Hydrophys. Inst., Sevastopol, 64 pp (in Russian).

  • Korotaev, G. K.: 1988, Theoretical Modelling of Synoptical Variability of the Ocean, Naukova Dumka, Kiev, 160 pp (in Russian).

  • Korotaev, G. K.: 1993, Interaction between the Synoptic Eddy and the Rossby wave, Marine Hydrophysical Journal, 1, Sevastopol, pp. 3–12 (in Russian).

    Google Scholar 

  • Korotaev, G. K.: 1994, 'Geostrophic Vortices on a Plane. Their Dynamics and Interaction', Atmos.and Ocean.Phys. 29(6), 727–734.

    Google Scholar 

  • Korotaev, G. K. and Fedotov, A. B.: 1994, 'Dynamics of an Isolated Barotropic Eddy on a Beta-Plane', J.Fluid Mech. 264, 277–301.

    Google Scholar 

  • Legras, B. and Dritschel, D. G.: 1993, 'Vortex Stripping and the Generation of High Vorticity Gradientsin Two-Dimensional Flow', App.Sci.Res. 51, 445–455.

    Google Scholar 

  • Li, X. and Wang, B.: 1994, 'Barotropic Dynamics of Beta Gyre and Beta Drift', J.Atmos.Sci. 51, 746–756.

    Google Scholar 

  • McCartney, M. S.: 1975, 'Inertial Taylor Columns on a Beta-Plane', J.Fluid Mech. 68, 71–96.

    Google Scholar 

  • McWilliams, J. C.: 1983, 'Interaction of Isolated Vortices. II. Modon Generation by Monopole Colli-sion', Geophys.Astrophys Fluid Dynamics 24, 1–22.

    Google Scholar 

  • McWilliams, J. C.: 1984, 'The Emergence of Isolated Coherent Vortices in Turbulent Flow', J.FluidMech. 146, 21–43.

    Google Scholar 

  • McWilliams, J. C.: 1990, 'The Vortices of Two-Dimensional Turbulence', J.Fluid Mech. 219, 361–385.

    Google Scholar 

  • McWilliams, J. C. and Flierl, G. R.: 1979, 'On the Evolution of Isolated, Nonlinear Vortices', J.Phys.Oceanogr. 9, 1155–1182.

    Google Scholar 

  • Meacham, S. P., Flierl, G. R., and Send, U.: 1990, 'Vortices in Shear', Dyn.Atmos.Ocean. 14, 333–386.

    Google Scholar 

  • Melander, M. V., Zabusky, N. J., and Styczek, A. S.: 1986, 'A Moment Model for Vortex Interactions ofthe Two-Dimensional Euler Equations: 1. Computational Validation of a Hamiltonian EllipticalRepresentation', J.Fluid Mech. 167, 95–115.

    Google Scholar 

  • Mied, R. and Lindemann, G. J.: 1979, 'The propagation and evolution of cyclonic gulf stream rings', J.Phys.Oceanogr. 7, 670–683.

    Google Scholar 

  • Nycander, J. and Sutyrin, G. G.: 1992, 'Steadily translating anticyclones on the beta-plane', Dyn.Atmos.Oceans 16, 473–498.

    Google Scholar 

  • Pedlosky, J.: 1987, Geophysical Fluid Dynamics, Springer-Verlag, 710 pp.

  • Reznik, G. M.: 1992, 'Dynamics of Singular Vortices on the Beta-Plane', J.Fluid Mech. 240, 405–432.

    Google Scholar 

  • Reznik, G. M. and Dewar, W. K.: 1994, 'An Analytical Theory of Distributed Axisymmetric BarotropicVortices on the Beta-Plane', J.Fluid Mech. 269, 301–321.

    Google Scholar 

  • Richardson, P. L., Cheny, R. E., and Mantini, L. A.: 1977, 'Tracking a Gulf Stream Ring with FreeDrifting Surface Buoy', J.Phys.Oceanogr. 7, 580–590.

    Google Scholar 

  • Richardson, P. L., Walsh, D., Armi, L., Schroder, M., and Price, J. F.: 1989, 'Tracking Three Meddieswith SOFAR Floats', J.Phys.Oceanogr. 19, 371–383.

    Google Scholar 

  • Rossby, C. G.: 1948, 'On the Displacement and Intensity Change of Atmospheric Vortices', J.Mar.Res. 7, 175–187.

    Google Scholar 

  • Shapiro, L. G. and Ooyama, K. V.: 1990, 'Barotropic Vortex Evolution on a Beta Plane', J.Atmos.Sci. 47, 170–187.

    Google Scholar 

  • Smith, R. K., Ulrich, W., and Dietachmayer, G.: 1990, 'A Numerical Study of Tropical CycloneMotion Using a Barotropic Model. Part1: The Role of Vortex Asymmetries', Quart.J.Roy.Meteor.Soc. 116, 337–362.

    Google Scholar 

  • Stepanyants, Yu. A. and Fabrikant, A. L.: 1992, 'Features of the Cherenkov's Emission of Drift Wavesin Hydrodynamics and in a Plasma', Sov.Phys.JETF 75(5), 818–824.

    Google Scholar 

  • Stern, M. E.: 1991, 'Entrainment of an Eddy at the Edge of a Jet', J.Fluid Mech. 228, 343–360.

    Google Scholar 

  • Stern, M. E. and Flierl, G. R.: 1987, 'On the Interaction of a Vortex with a Shear Flow', J.Geophys.Res. 92(C10), 1,0733–1,0744.

    Google Scholar 

  • Sutyrin, G. G.: 1987, 'The Beta-Effect and the Evolution of a Localised Vortex', Sov.Phys.Dokl. 32, 791–793.

    Google Scholar 

  • Sutyrin, G. G.: 1988, 'Motion of an Intense Vortex on a Rotating Globe', Fluid Dyn. 23, 215–223.

    Google Scholar 

  • Sutyrin, G. G. and Dewar, W. K.: 1992, 'Almost Symmetric Solitary Eddies in a Two-Layer Ocean', J.Fluid Mech. 238, 633–656.

    Google Scholar 

  • Sutyrin, G. G. and Flierl, G. R.: 1994, 'Intense Vortex Motion on the Beta Plane: Development of the Beta Gyre', J.Atmos.Sci. 51, 773–790.

    Google Scholar 

  • Sutyrin, G. G., Hesthaven, J. S., Lynov, J. P., and Rasmussen, J. J.: 1994, 'Dynamical Properties ofVortical Structures on the Beta-Plane', J.Fluid Mech. 268, 103–131.

    Google Scholar 

  • Timofeev, A. V.: 1970, 'Nonhomogeneous Current Oscillations in Plasma and Fluid', Progr.Phys.Sci. 102(2), 185–210 (in Russian).

    Google Scholar 

  • Van Dyke, M.: 1964, Perturbation Method in Fluid Mechanics, Academic Press.

  • Wang, Y. and Holland, G. J.: 1996, 'The Beta Drift of Baroclinic Vortices. Pt. I: Adiabatic Vortices', J.Atmos.Sci. 53, 411–427.

    Google Scholar 

Download references

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  1. Marine Hydrophysical Institute, Sevastopol, 335000, Crimea, Ukraine

    G.K. Korotaev

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Korotaev, G. Radiating Vortices in Geophysical Fluid Dynamics. Surveys in Geophysics 18, 567–618 (1997). https://doi.org/10.1023/A:1006583017505

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