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An experimental study of unstable barotropic vortices in a rotating fluid

Published online by Cambridge University Press:  26 April 2006

R. C. Kloosterziel  and
G. J. F. van Heijst
R. C. Kloosterziel
Affiliation:
Institute of Meteorology and Oceanography, University of Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands Present affiliation: Institute for Nonlinear Science, La Jolla, CA 92093, USA.
G. J. F. van Heijst
Affiliation:
Institute of Meteorology and Oceanography, University of Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands
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Abstract

Laboratory experiments on barotropic vortices in a rotating fluid revealed that the instability behaviour of cyclonic and anticyclonic vortices is remarkably different. Depending on its initial vorticity distribution, the cyclonic vortex has in a number of experiments been observed to be unstable to wavenumber-2 perturbations, leading to the gradual formation of a stable tripolar vortex structure. This tripole consists of an elongated cyclonic core vortex adjoined by two anticyclonic satellite vortices.

In contrast, the anticyclonic vortex shows a rather explosive instability behaviour, in the sense that it is observed to immediately split up into two dipoles. Under somewhat different circumstances the higher-order mode-3 instability is observed, in which the anticyclonic core has a triangular shape, with three smaller cyclonic satellite vortices at its sides.

A modified version of Rayleigh's instability criterion offers a qualitative explanation for this apparent difference between unstable cyclonic and anticyclonic vortices.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 1 - 24
Copyright
© 1991 Cambridge University Press

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References

Bayly, B. J.: 1988 Three-dimensional centrifugal-type instabilities in inviscid two-dimensional flows. Phys. Fluids 31, 56–64.Google Scholar
Carnevale, G. F., Kloosterziel, R. C. & Van Heijst, G. J. F.: 1990 Propagation of barotropic vortices over topography in a rotating tank. J. Fluid Mech. (submitted).Google Scholar
Carnevale, G. F., Vallis, G. K., Purini, R. & Briscolini, M., 1988 Propagation of barotropic modons over topography. Geophys. Astrophys. Fluid Dyn. 41, 45–101.Google Scholar
Carton, X. J., Flierl, G. R. & Polvani, L. M., 1989 The generation of tripoles from unstable axisymmetric isolated vortex structures. Europhys. Lett. 9, 339–344.Google Scholar
Carton, X. J. & Mcwilliams, J. C., 1989 Barotropic and baroclinic instabilities of axisymmetric vortices in a quasi-geostrophic model. In Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. J. C. J. Nihoul & B. M. Jamart), pp. 225–244. Elsevier.
Chandrasekhar, S.: 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Cushman-Roisin, B., Heil, W. H. & Nof, D., 1985 Oscillations and rotations of elliptical warm-core vortices. J. Geophys. Res. 90, 11756–11764.Google Scholar
Drazin, P. G. & Reid, W. H., 1981 Hydrodynamic Stability. Cambridge University Press.
Flierl, G. R.: 1985 Instability of vortices. Woods Hole Oceanogr. Inst., Tech. Rep. WHOI-85–36, pp. 119–121.Google Scholar
Flierl, G. R.: 1988 On the instability of geostrophic vortices. J. Fluid Mech. 197, 349–388.Google Scholar
Gent, P. R. & McWilliams, J. C., 1986 The instability of circular vortices. Geophys. Astrophys. Fluid Dyn. 35, 209–233.Google Scholar
Ginsburg, A. I., Kostianoy, A. G., Pavlov, A. M. & Fedorov, K. N., 1987 Laboratory reproduction of mushroom-like currents (vortex dipoles) under rotation and stratification conditions. Izv. Akad. Nauk. 8SSR Atmos. Ocean. Phys. 23, 170–178.Google Scholar
Griffiths, R. W. & Hopfinger, E. J., 1987 Coalescing of geostrophic vortices. J. Fluid Mech. 178, 73–97.Google Scholar
Griffiths, R. W. & Linden, P. F., 1981 The stability of vortices in a rotating, stratified fluid. J. Fluid Mech. 105, 283–316.Google Scholar
van Heijst, G. J. F. & Kloosterziel, R. C. 1989 Tripolar vortices in a rotating fluid. Nature 338, 569–571.Google Scholar
van Heijst, G. J. F., Kloosterziel, R. C. & Williams, C. W. M. 1991 Laboratory experiments on the tripolar vortex in a rotating fluid. J. Fluid Mech. (to appear).Google Scholar
Holton, J. R.: 1979 An Introduction to Dynamic Meteorology (2nd edn). Academic.
Ikeda, M.: 1981 Instability and splitting of mesoscale rings using a two-layer quasi-geostrophic model on an f-plane. J. Phys. Oceanogr 11, 987–998.Google Scholar
Kloosterziel, R. C.: 1990 Barotropic vortices in a rotating fluid. Ph.D. thesis, University of Utrecht, The Netherlands.
Kloosterziel, R. C. & van Heijst, G. J. F.: 1989 On tripolar vortices. In Mesoscale /Synoptic Coherent Structures in Geophysical Turbulence (ed. J. C. J. Nihoul & B. M. Jamart), pp. 609–625. Elsevier.
Kloosterziel, R. O. & van Heijst, G. J. F.: 1990 The evolution of stable barotropic vortices in a rotating free-surface fluid. J. Fluid Mech. (submitted).Google Scholar
Legras, B., Santangelo, P. & Benzi, R., 1988 High-resolution numerical experiments for forced two-dimensional turbulence. Europhys. Lett. 5, 37–42.Google Scholar
Leith, C. E.: 1984 Minimum enstrophy vortices. Phys. Fluids 27, 1388–1395.Google Scholar
Mcwilliams, J. C. & Gent, P. R., 1986 The evolution of sub-mesoscale, coherent vortices on the β-plane. Geophys. Astrophys. Fluid Dyn. 35, 235–255.Google Scholar
Mory, M., Stern, M. E. & Griffiths, R. W., 1987 Coherent baroclinic eddies on a sloping bottom. J. Fluid Mech. 183, 45–62.Google Scholar
Polvani, L. M. & Carton, X. J., 1990 The tripole: a new coherent vortex structure of incompressible two-dimensional flows. Geophys. Astrophys. Fluid Dyn. 52, 87–102.Google Scholar
Rayleigh, Lord: 1916 On the dynamics of revolving fluids. Proc. R. Soc. Lond. A 93, 148–154.Google Scholar
Robinson, A. R. (ed.) 1983 Eddies in Marine Science. Springer.
Saunders, P. M.: 1973 The instability of a baroclinic vortex. J. Phys. Oceanogr. 3, 61–65.Google Scholar
Stern, M. E.: 1987 Horizontal entrainment and detrainment in large-scale eddies. J. Phys. Oceanogr. 17, 1688–1695.Google Scholar
Swenson, M.: 1987 Instability of equivalent barotropic riders. J. Phys. Oceanogr. 17, 492–506.Google Scholar