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Laboratory experiments on the tripolar vortex in a rotating fluid

  • G. J. F. van Heijst (a1), R. C. Kloosterziel (a1) and C. W. M. Williams (a1)


Within the framework of the study of coherent vortex structures as emerging in rotating, quasi-two-dimensional flows, the tripolar vortex is a relatively novel feature. It consists of a symmetric, linear arrangement of three patches of distributed vorticity of alternate signs, and the axis of this configuration rotates about the centre of the core vortex. This paper describes an experimental study of the formation of a tripole from an unstable axisymmetric vortex in a solidly rotating, homogeneous fluid. The flow is visualized by addition of dye, and is measured by streak photography of tracer particles. After digitization, the spatial distributions of the vorticity ω and the stream function ψ are calculated numerically, and 'scatter plots’ of ω versus ψ are presented for the various stages in the tripole formation process. Owing to viscous effects (spin-down by the bottom Ekman layer and lateral entrainment of ambient fluid) the tripole shows an exponential decay, both in its rotation speed and its internal, relative flow. The comparison of the observed flow characteristics with a simple point-vortex model shows reasonable quantitative agreement.



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Aref, H.: 1979 Motion of three vortices. Phys. Fluids 22, 393400.
Batchelor, G. K.: 1967 An Introduction to Fluid Dynamics. Cambridge University Press, 615 pp.
Benzi, R., Patarnello, S. & Santangelo, P., 1987 On the statistical properties of two-dimensional decaying turbulence. Europhys. Lett. 3, 811818.
Benzi, R., Patarnello, S. & Santangelo, P., 1988 Self-similar coherent structures in two-dimensional decaying turbulence. J. Phys. A: Math. Gen. 21, 12211237.
Carnevale, G. F., Kloosterziel, R. C. & Van Heijst, G. J. F.: 1991 Propagation of barotropic vortices over topography in a rotating tank. J. Fluid Mech. (submitted).
Carton, X. J., Fliebl, G. R. & Polvani, L. M., 1989 The generation of tripoles from unstable axisymmetric isolated vortex structures. Europhys. Lett. 9, 339344.
Chandbasekhar, S.: 1961 Hydrodynamic and Hydromagnetic Stability. Oxford University Press, 654 pp.
Drazin, P. G. & Reid, W. H., 1981 Hydrodynamic Stability. Cambridge University Press, 527 pp.
Fliebl, G. R.: 1988 On the instability of geostrophic vortices. J. Fluid Mech. 197, 349388.
Greenspan, H. P. & Howard, L. N., 1963 On a time-dependent motion of a rotating fluid. J. Fluid Mech. 17, 385404.
Hasegawa, A.: 1985 Self-organization processes in continuous media. Adv. Phys. 34, 142.
Van Heijst, G. J. F. & Flór, J. B. 1989 Dipole formation and collisions in a stratified fluid. Nature 340, 212215.
Van Heijst, G. J. F. & Kloostebziel, R. C. 1989 Tripolar vortices in a rotating fluid. Nature 338, 569571.
Holton, J. R.: 1979 An Introduction to Dynamic Meteorology (2nd edn.). Academic, 391 pp.
Ikeda, M.: 1981 Instability and splitting of mesoscale rings using a two-layer quasi-geostrophic model on an f-plane. J. Phys. Oceanogr. 11, 987998.
Kloostebziel, R. C.: 1990 Barotropic vortices in a rotating fluid. Ph.D. thesis, University of Utrecht, The Netherlands.
Kloostebziel, 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. 609625. Elsevier.
Kloostebziel, R. C. & Van Heijst, G. J. F.: 1991a An experimental study of unstable barotropic vortices in a rotating fluid. J. Fluid Mech. 223, 124.
Kloostebziel, R. C. & Van Heijst, G. J. F.: 1991b The evolution of stable barotropic vortices in a rotating free-surface fluid. J. Fluid Mech. (submitted).
Lamb, H.: 1936 Hydrodynamics (6th edn.) Cambridge University Press, 738 pp.
Legras, B., Santangelo, P. & Benzi, R., 1988 High-resolution numerical experiments for forced two-dimensional turbulence. Europhys. Lett. 5, 3742.
Leith, C. E.: 1984 Minimum enstrophy vortices. Phys. Fluids 27, 13881395.
McWllllams, J. C.: 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 2143.
Mobikawa, G. K. & Swenson, E. V., 1971 Interacting motion of rectilinear geostrophic vortices. Phys. Fluids 14, 10581073.
Duc, J. M. Nguyen & Sommeria, J. 1988 Experimental characterization of steady two-dimensional vortex couples. J. Fluid Mech. 192, 175192.
Polvani, L. M. & Carton, X. J., 1990 The tripole: a new coherent vortex structure of incompressible two-dimensional flows. Geophys. Astrophys. Fluid Dyn. 51, 87102.
Sadoubny, S.: 1985 Quasi-geostrophic turbulence: an introduction. In Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics (ed. M. Ghill), pp. 133158. North-Holland.
Stern, M. E.: 1987 Horizontal entrainment and detrainment in large-scale eddies. J. Phys. Oceanogr. 17, 16881695.
Swenson, M.: 1987 Instability of equivalent barotropic riders. J. Phys. Oceanogr. 17, 492506.
Taylor, J. B.: 1974 Relaxation of toroidal plasma and generation of reverse magnetic fields. Phys. Rev. Lett. 33, 11391141.
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Laboratory experiments on the tripolar vortex in a rotating fluid

  • G. J. F. van Heijst (a1), R. C. Kloosterziel (a1) and C. W. M. Williams (a1)


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