Abstract
We study the evolution of initially axisymmetric, large scale (Bu ≪ 1), geostrophic (Ro ≪ 1), barotropic vortices. In such a parameter regime, asymptotic expansion of rotating shallow water (RSW) leads to the frontal geostrophic (FG) model which is numerically implemented. Both in FG and in RSW, anticyclones travel westward faster than cyclones. In FG, vortices of both signs show initially a secondary meridional northward drift which we detail. However this last feature is not present in RSW numerical simulations. Vortices behave like quasi-geostrophic (QG) vortices i.e, showing an initial meridional drift that depends on vortex sign.
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References
Benilov E. S. Beta-induced translation of strong isolated eddies. J. Phys. Oceanogr., 26:2223–2229, 1996.
Ben Jelloul M. and V. Zeitlin. Remarks on the stability of the rotating shallow water vortices in the frontal dynamics regime. Nuouo Cim., 22:931–941, 1999.
Cushman-Roisin B., G. G. Sutyrin, and Benyang Tang. Two-layer geostrophic dynamics. part one: Governing equations. J. Phys. Oceanogr., 22:117–127, 1992.
Filatoff N., X. Carton, and S. Pous. Intermediate model based on geostrophic dynamics. Technical Report 006/97, S.H.O.M., Brest, 1997.
V. M. Kamenkovich. Theory of quasigeostrophic motions in a two-layer atmosphere with scale greater than rossby scale. Oceanology, 29(2):133–138, 1989.
Marcus P. S. Jupiter’s great red spot and other vortices. Annu. Rev. Astron. Astrophys., 31:523–573, 1993.
Nycander J. and G. G. Sutyrin Steadily translating anticyclones on the beta plane. Dyn. Atmos. Oceans, 16:473–498, 1992.
Olson D. B. Rings in the ocean. Annu. Rev. Earth Planet. Sci., 19:283–311, 1991.
Olson D. B. and R. H. Evans. Rings of the agulhas current. Deep-Sea Research, 33(1):27–42, 1986.
Pedlosky J. Geophysical fluid dynamics. Springer-Verlag, 2 edition, 1987.
Polvani L. M., J. C. McWilliams, M. A. Spall, and R. Ford. The coherent structures of shallow-water turbulence: Deformation-radius effects, cyclone/anticyclone asymmetry and gravity-wave generation. Chaos, 4(2):177–186, 1994.
Stegner A. and Zeitlin V. What can asymptotic expansions tell us about large-scale quasi-geostrophic anticyclonic vortices. Nonlin. Proc. Geophys., 2:186–193, 1995.
Swaters G. E. On the baroclinic dynamics, Hamiltonian formulation and general stability characteristics of density-driven surface currents and fronts over a sloping continental shelf. Phil. Trans. R. Soc. Lond. A, (345):295–325, 1993.
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© 2001 Springer Science+Business Media Dordrecht
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Jelloul, M.B., Carton, X.J. (2001). Asymptotic Models and Application to Vortex Dynamics. In: Hodnett, P.F. (eds) IUTAM Symposium on Advances in Mathematical Modelling of Atmosphere and Ocean Dynamics. Fluid Mechanics and Its Applications, vol 61. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0792-4_10
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DOI: https://doi.org/10.1007/978-94-010-0792-4_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-3853-9
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