Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T09:09:47.942Z Has data issue: false hasContentIssue false
  • English
  • Français

Long-range interaction and elastic collisions of isolated vortices

Published online by Cambridge University Press:  08 August 2008

TIMOUR RADKO
TIMOUR RADKO*
Affiliation:
Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This study explores the interaction of two nearly axisymmetric two-dimensional vortices using a combination of numerical simulations and analytical arguments. We consider isolated or ‘shielded’ eddies, characterized by zero net vorticity. The ability of such vortices to propagate and interact is associated with the small dipolar component that is introduced initially. Numerical contour dynamics experiments indicate that the interaction of shielded eddies takes one of two forms, depending on their initial separation and on the relative orientation of their dipolar components. Eddies can influence each other by remotely modifying the dipolar moments of partner vortices, an effect manifested in a gentle deflection of their trajectories from a straight course. Strong interactions occur when eddies collide and rebound. The remote interaction is explained by weakly nonlinear theory in which the basic state consists of identical circularly symmetric eddies and the perturbation is assumed to be small. It is argued that the elastic rebounds observed during direct collisions are induced by the exchange of fluid between colliding vortices.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 610 , 10 September 2008 , pp. 285 - 310
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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.CrossRefGoogle Scholar
Beckers, M., Clercx, H. J. H., van Heijst, G. J. F. & Verzicco, R. 2002 Dipole formation by two interacting shielded monopoles in a stratified fluid. Phys. Fluids 14, 704–720.CrossRefGoogle Scholar
Beckers, M., Verzicco, R., Clercx, H. J. H. & van Heijst, G. J. F. 2001 ‘Dynamics of pancake-like vortices in a stratified fluid: experiments, model and numerical simulations. J. Fluid Mech. 433, 1–27.CrossRefGoogle Scholar
Carton, X. J. 1992 On the merger of shielded vortices. Europhys. Lett. 18, 697–703.Google Scholar
Carton, X. J. 2001 Hydrodynamical modeling of oceanic vortices. Surveys Geophys. 22, 179–263.CrossRefGoogle Scholar
Chassignet, E. P., Olson, D. B. & Boudra, D. B. 1990 Motion and evolution of oceanic rings in a numerical model and in observations. J. Geophys. Res. 95, 22121–22140.Google Scholar
Christiansen, J. P. & Zabusky, N. J. 1973 Instability, coalescence and fission of finite-area vortex structures. J. Fluid Mech. 61, 219–243.Google Scholar
Cornillon, P. & Park, K. A. 2001 Warm core ring velocities inferred from NSCAT. Geophys. Res. Lett. 28, 575–578.Google Scholar
Cresswell, G. R. 1982 The coalescence of two East Australia Current warm-core rings. Science 215, 161–164.CrossRefGoogle Scholar
Dritschel, G. 1986 The non-linear evolution of rotating configurations of uniform vorticity. J. Fluid Mech. 172, 157–182.CrossRefGoogle Scholar
Flament, P., Lumpkin, R. Tournadre, J. & Armi, L. 2001 Vortex pairing in an unstable anticyclonic shear flow: Discrete subharmonics of one pendulum day. J. Fluid Mech. 440, 401–409.CrossRefGoogle Scholar
Flierl, G. R. 1988 On the instability of geostrophic vortices. J. Fluid Mech. 197, 349–388.Google Scholar
Griffiths, R. W. & Hopfinger, E. J. 1986 Experiments with baroclinic vortex pairs in a rotating fluid. J. Fluid Mech. 173, 501–518.CrossRefGoogle Scholar
Griffiths, R. W. & Hopfinger, E. J. 1987 Coalescing of geostrophic vortices. J. Fluid Mech. 178, 73–97.CrossRefGoogle Scholar
Hogg, N. G. & Stommel, H. M. 1985 The heton, an elementary interaction between discrete baroclinic geostrophic vortices and its implications concerning eddy heat-flow. Proc. R. Soc. Lond. A 397, 1–20.Google Scholar
Joyce, T. M. & McDougall, T. J. 1992 Physical structure and temporal evolution of Gulf Stream warm-core ring 82B. Deep-Sea Res. A 39, S19–S44.CrossRefGoogle Scholar
Killworth, P. D. 1986 On the propagation of isolated multilayer and continuously stratified eddies. J. Phys. Oceanogr. 16, 709–716.2.0.CO;2>CrossRefGoogle Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.CrossRefGoogle Scholar
McWilliams, J. C. & Flierl, G. R. 1979 On the evolution of isolated, nonlinear vortices. J. Phys. Oceanogr. 9, 1155–1182.2.0.CO;2>CrossRefGoogle Scholar
Melander, M. V., Zabusky, N. J. & McWilliams, J. C. 1988 Symmetric vortex merger in two dimensions: Causes and conditions. J. Fluid Mech. 195, 303–340.CrossRefGoogle Scholar
Michalke, A. & Timme, A. 1967 On the inviscid stability of certain two-dimensional vortex-type flows. J. Fluid Mech. 29, 647–666.CrossRefGoogle Scholar
Nof, D. 1981 On the beta-induced movement of isolated baroclinic eddies. J. Phys. Oceanogr. 11, 1662–1672.2.0.CO;2>CrossRefGoogle Scholar
Nof, D. 1983 On the migration of isolated eddies with application to Gulf Stream rings. J. Mar. Res. 41, 399–425.CrossRefGoogle Scholar
Olson, D. B. 1980 The physical oceanography of two rings observed by the cyclonic ring experiment. Part II: Dynamics. J. Phys. Oceanogr. 10, 514–528.2.0.CO;2>CrossRefGoogle Scholar
Olson, D. B. 1991 Rings in the ocean. Annu. Rev. Earth Planet. Sci. 19, 283–311.Google Scholar
Olson, D. B., Schmitt, R. W., Kennelly, M. & Joyce, T. M. 1985 A two-layer diagnostic model of the long-term physical evolution of warm-core ring 82B. J. Geophys. Res. 90, 8813–8822.CrossRefGoogle Scholar
Radko, T. & Stern, M. E. 1999 On the propagation of oceanic mesoscale vortices. J. Fluid Mech. 380, 39–57.CrossRefGoogle Scholar
Radko, T. & Stern, M. E. 2000 Self-propagating eddies on the stratifed f-plane. J. Phys. Oceanogr. 30, 3134–3144.2.0.CO;2>CrossRefGoogle Scholar
Robinson, A. R. (Ed.) 1983 Eddies in Marine Science. Springer.CrossRefGoogle Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.Google Scholar
Stern, M. E. 1987 Horizontal entrainment and detrainment in large-scale eddies. J. Phys. Oceanogr. 17, 1688–1695.Google Scholar
Stern, M. E. 2000 Scattering of an eddy advected by a current towards a topographic obstacle. J. Fluid Mech. 402, 211–223.Google Scholar
Stern, M. E. & Pratt, L. J. 1985 Dynamics of vorticity fronts. J. Fluid Mech. 161, 513–532.Google Scholar
Stern, M. E. & Radko, T. 1998 The self propagating quasi-monopolar vortex. J. Phys. Oceanogr. 28, 22–39.2.0.CO;2>CrossRefGoogle Scholar
Sutyrin, G. G. & Flierl, G. R. 1994 Intense vortex motion on the beta plane: development of the beta gyres. J. Atmos. Sci. 51, 773–790.2.0.CO;2>CrossRefGoogle Scholar
Trieling, R. R. & van Heijst, G. J. F. 1998 Decay of monopolar vortices in a stratified fluid. Fluid Dyn. Res. 23, 27–43.CrossRefGoogle Scholar
Yasuda, I. & Flierl, G. R. 1995 Two-dimensional asymmetric vortex merger: contour dynamics experiment. J. Oceanogr. 51, 145–170.CrossRefGoogle Scholar
Yasuda, I., Okuda, K. & Hirai, M. 1992 Evolution of a Kuroshi warm-core ring: Variability of the hydrographic structure. Deep-Sea Res. 39 (Suppl.), 5131–5161.CrossRefGoogle Scholar
Zabusky, N. J., Hughes, M. H. & Roberts, K. V. 1979 Contour dynamics for the Euler equations in two dimensions. J. Comput. Phys. 30, 96–106.CrossRefGoogle Scholar