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Dynamics of an isolated barotropic eddy on a beta-plane

Published online by Cambridge University Press:  26 April 2006

Gennady K. Korotaev  and
Alexander B. Fedotov
Gennady K. Korotaev
Affiliation:
Marine Hydrophysical Institute, Sevastopol 335000 Ukraine
Alexander B. Fedotov
Affiliation:
Marine Hydrophysical Institute, Sevastopol 335000 Ukraine
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Abstract

The dynamics of a Gaussian isolated barotropic eddy on a β-plane is considered. The analytical solution of the evolution of an isolated vortex is constructed by analogy to the theory of a point vortex. The results of a numerical experiment are compared with the conclusions of the theory for the case of the Gaussian vortex. Characteristics of the vortex such as its radius, trajectory of movement, kinetic energy, residual vorticity, and the structure of the vortex are discussed. The analysis of the numerical results shows that the experimentally determined radius of the vortex, its energy, and residual vorticity are in good agreement with the theory. On the other hand there is a difference between analytical and experimental values of velocity components, and hence in the trajectory of the centre of the vortex. The location of the separatrix of the streak function and its saddle point are considered as important characteristics of the structure of the vortex. We consider the phenomenon of the generation of the vortex sheet connected with the separatrix location as a cause of the difference between the experimental and analytical estimates of the velocity of the vortex.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 264 , 10 April 1994 , pp. 277 - 301
Copyright
© 1994 Cambridge University Press

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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
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Bretherton, F. P. & Karweit, M. 1975 Mid-ocean mesoscale modeling. In Numerical Models of Ocean Circulation (ed. R. O. Reid, A. R. Robinson & K. Bryan), pp. 237–249. National Academy of Sciences.
Cushman-Roisin, B., Chassignet, E. P. & Tang, B. 1990 On the westward motion of mesoscale eddies. J. Phys. Oceanogr. 20, 758–768.Google Scholar
Flierl, G. R. 1984 Rossby wave radiation from a strongly nonlinear warm eddy. J. Phys. Oceanogr. 14, 47–58.Google Scholar
Korotaev, G. K. 1980a Asymptotical regime of isolated barotropic synoptical eddy dynamics. In Marine Hydrophysical Investigations N1, pp. 5–18. Sevastopol: Marine Hydrophys. Inst. (in Russian).
Korotaev, G. K. 1980b Structure, dynamics and energetics of synoptical variability of the ocean. Sevastopol: Marine Hydrophys. Inst. Preprint, 64 pp. (in Russian).
Korotaev, G. K. 1988 Theoretical Modeling of Synoptical Variability of the Ocean. Kiev: Naukova Dumka (in Russian).
McWilliams, J. C. & Flierl, G. R. 1979 On the evolution of isolated, nonlinear vortices. J. Phys. Oceanogr. 9, 1155–1182.Google Scholar
McWilliams, J. C., Flierl, G. R., Larichev, V. D. & Reznik, G. M. 1981 Numerical studies of barotropic modons. Dyn. Atmos. Oceans. 5, 219–238.Google Scholar
Orszag, S. 1971 Numerical simulation of incompressible flows within simple boundaries. I. Galerkin (spectral) representation. Stud. Appl. Maths 50, 293–328.Google Scholar
Rossby, C. G. 1948 On displacements and intensity changes of atmospheric vortices. J. Mar. Res. 7, 175–187.Google Scholar
Shapiro, L. J. & Ooyama, K. V. 1980 Barotropic vortex on a beta plane. J. Atmos. Sci. 47, 170–187.Google Scholar
Smith, R. K. & Ulrich, W. 1990 An analytical theory of tropical cyclone motion using a barotropic model. J. Atmos. Sci. 47, 1973–1986.Google Scholar
Smith, R. K., Ulrich, W. & Dietachmayer, G. 1990 A numerical study of tropical cyclone motion using a barotropic model. I: The role of vortex asymmetries. Q.J.R. Met. Soc. 116, 337–362.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic.