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Unsteady behaviour of a topography-modulated tripole

Published online by Cambridge University Press:  26 April 2006

O. U. Velasco Fuentes ,
G. J. F. van Heijst  and
N. P. M. van Lipzig
O. U. Velasco Fuentes
Affiliation:
Fluid Dynamics Laboratory, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands Present affiliation: CICESE, Departamento de Oceanografía Física, 22800 Ensenada, B.C., México.
G. J. F. van Heijst
Affiliation:
Fluid Dynamics Laboratory, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
N. P. M. van Lipzig
Affiliation:
Fluid Dynamics Laboratory, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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Abstract

The evolution of a tripolar vortex under the influence of a parabolic topography – like the free surface of a rotating fluid – is studied experimentally and with a point-vortex model. Laboratory experiments reveal that tripoles generated off-axis become asymmetric and the whole structure travels towards the centre of the tank along an anticyclonic spiral. During this translation the structure rotates quasi-periodically with the core pairing alternately with one of the satellites. An asymmetric point-vortex tripole (with the central vortex located at a distance ε from the middle point of the configuration) displays a periodic motion which is qualitatively similar to the motion of the laboratory tripoles. The exchange of fluid between the three vortices as a function of the perturbation parameter ε is studied using the lobe-dynamics technique. A point-vortex tripole modulated on the basis of conservation of potential vorticity reproduces quantitatively the trajectories of the individual vortices measured in the laboratory. As in the experiments, the model shows that fluid is strongly stirred in the region surrounding the vortex cores and that the tripole carries a finite amount of fluid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 307 , 25 January 1996 , pp. 11 - 41
Copyright
© 1996 Cambridge University Press

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References

Aref, H. 1979 Motion of three vortices. Phys. Fluids 22, 393–400.Google Scholar
Aref, H. 1984 Stirring by chaotic advection. J. Fluid Mech. 143, 1–21.Google Scholar
Aref, H. 1989 Three-vortex motion with zero total circulation: Addendum. Z. Angew. Math. Phys. 40, 495–500.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Carnevale, G. F., Kloosterziel, R. C. & HEIJST, G. J. F. VAN 1991 Propagation of barotropic vortices over topography in a rotating tank. J. Fluid Mech. 233, 119–139.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. & Legras, B. 1994 The life-cycle of tripoles in two-dimensional incompressible flow. J. Fluid Mech. 267, 53–82.Google Scholar
Flor, J. B., Govers, W. S. S., Heijst, G. J. F. VAN & Sluis, R. VAN 1993 Formation of a tripolar vortex in a stratified fluid. Appl. Sci. Res. 51, 405–409.Google Scholar
Gröbli, W. 1877 Specielle Probleme über die Bewegung geradliniger paralleler Wirbelfäden. Zürcher und Furrer, Zürich.
Heijst, G. J. F. VAN & Kloosterziel, R. C. 1989 Tripolar vortices in a rotating fluid. Nature 338, 369–371.Google Scholar
Heijst, G. J. F. VAN, Kloosterziel, R. C. & Williams, C. W. M. 1991 Laboratory experiments on the tripolar vortex in a rotating fluid. J. Fluid Mech. 225, 301–331.Google Scholar
Heijst, G. J. F. VAN & Velasco Fuentes, O. U. 1994 Unsteady behaviour of a tripolar vortex on a γ-plane. In Modelling of Oceanic Vortices (ed. G. J. F. van Heijst). Verhandelingen Koninklijke Nederlandse Akademie van Wetenschappen. North-Holland.
Kono, J. & Yamagata, T. 1977 The behaviour of a vortex pair on the beta plane. Proc. Oceanogr. Soc. Japan 36, 83–84 (in Japanese).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
Nof, D. 1990 Modons and monopoles on a γ-plane. Geophys. Astrophys. Fluid Dyn. 52, 71–87.Google Scholar
Novikov, E. A. 1976 Dynamics and statistics of a system of point vortices. Sov. Phys. JETP 41, 937–943.Google Scholar
Orlandi, P. & Heijst, G. J. F. VAN 1992 Numerical simulation of tripolar vortices in 2D flow. Fluid Dyn. Res. 9, 179–206.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Pingree, R. D. & LeCann, B. 1992 Three anticyclonic slope water oceanic eddies (swoddies) in the southern Bay of Biscay in 1990. Deep-Sea Res. 39, 1147–1175.Google Scholar
Poincaré, H. 1893 Théorie des Tourbillons. Leçons Professees Pendant le Deuxième Semestre 1891–1892 (ed. G. Carré). Paris.
Polvani, L. M. & Wisdom, J. 1990 On chaotic flow around the Kida vortex. In Topological Aspects of Fluid Mechanics (ed. H. K. Moffatt & A. Tsinober). Cambridge University Press.
Rom-Kedar, V., Leonard, A. & Wiggins, S. 1990 An analytical study of transport, mixing and chaos in an unsteady vortical flow. J. Fluid Mech. 214, 347–394.Google Scholar
Rott, N. 1989 Three-vortex motion with zero total circulation. Z. Angew. Math. Phys. 40, 473–494.Google Scholar
Sutyrin, G. G., Hesthaven, J. S., Lynov, J. P. & Rasmussen, J. J. 1994 Dynamical properties of vortical structures on the beta-plane. J. Fluid Mech. 268, 103–131.Google Scholar
Synge, J. L. 1949 On the motion of three vortices. Can. J. Maths 1, 257–270.Google Scholar
Velasco Fuentes, O. U. 1994 Propagation and transport properties of dipolar vortices on a γ plane. Phys. Fluids 6, 3341–3352.Google Scholar
Velasco Fuentes, O. U. & Heijst, G. J. F. VAN 1994 Experimental study of dipolar vortices on a topographic β-plane. J. Fluid Mech. 259, 79–106.Google Scholar
Velasco Fuentes, O. U., Heijst, G. J. F. VAN & Cremers, B. E. 1995 Chaotic advection by dipolar vortices on a β-plane. J. Fluid Mech. 291, 139–161.Google Scholar
Wiggins, S. 1992 Chaotic Transport in Dynamical Systems. Springer.
Zabusky, N. J. & Mcwilliams, J. C. 1982 A modulated point-vortex model for geostrophic, β-plane dynamics. Phys. Fluids 25, 2175–2182.Google Scholar