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Scale-dependent merging of baroclinic vortices

Published online by Cambridge University Press:  26 April 2006

J. Verron  and
S. Valcke
J. Verron
Affiliation:
URA 1509 CNRS, Institut de Mécanique de Grenoble, BP 53X, 38041 Grenoble Cédex, France
S. Valcke
Affiliation:
URA 1509 CNRS, Institut de Mécanique de Grenoble, BP 53X, 38041 Grenoble Cédex, France
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Abstract

The influence of stratification on the merging of like-sign vortices of equal intensity and shape is investigated by numerical simulations in a quasi-geostrophic, two-layer stratified model. Two different types of vortices are considered: vortices defined as circular patches of uniform potential vorticity in the upper layer but no PV anomaly in the lower layer (referred to as PVI vortices), and vortices defined as circular patches of uniform relative vorticity in the upper layer but no motion in the lower layer (referred to as RVI vortices). In particular, it is found that, in the RVI case, the merging behaviour depends strongly on the magnitude of the stratification (i.e. the ratio of internal Rossby radius and vortex radius). The critical point here appears to be whether or not the initial eddies have a deep flow signature in terms of PV.

The specific phenomenon of scale-dependent merging observed is interpreted in terms of the competitive effects of hetonic interaction and vortex shape. In the case of weaker stratification, the baroclinic structure of the eddies can be seen as dominated by a mechanism of hetonic interaction in which bottom flow appears to counteract the tendency of surface eddies to merge. In the case of larger stratification, the eddy interaction mechanism is shown to be barotropically dominated, although interface deformation still determines the actual eddy vorticity profile during the initialization stage. Repulsion (hetonic) effect therefore oppose attraction (barotropic shape) effects in a competitive process dependent on the relationship between the original eddy lengthscale and the first internal Rossby radius.

A concluding discussion considers the implications of such analysis for real situations, in the ocean or in the laboratory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 264 , 10 April 1994 , pp. 81 - 106
Copyright
© 1994 Cambridge University Press

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References

Arhan, M. & Colin de Verdière, A. 1985 Dynamics of eddy motion in the eastern North-Atlantic. J. Phys. Oceanogr. 15, 153–170.Google Scholar
Basdevant, C., Legras, B., Sadourny, R. & Beland, M. 1981 A study of barotropic model flows: intermittency, waves and predictability. J. Atmos Sci. 38, 2305–2326.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structures in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Carnevale, G. F., Cavazza, P., Orlandi, P. & Purini, R. 1991 An explanation for anomalous vortex merger in rotating-tank experiments. Phys. Fluids A 3, 1411–1415.Google Scholar
Dritschel, D. G. & Waugh, D. W. 1992 Quantification of the inelastic interaction of unequal vortices in two-dimensional vortex dynamics. Phys. Fluids A 4, 1737–1744.Google Scholar
Gordon, A. L. & Haxby, W. F. 1990 Agulhas eddies invade the South Atlantic – evidence from Geosat altimeter and shipboard conductivity temperature depth survey, J. Geophys. Res. 95, 3117–3125.Google Scholar
Griffiths, R. W. & Hopfinger, E. J. 1987 Coalescing of geostrophic vortices. J. Fluid Mech. 178, 73–97.Google Scholar
Gryanik, V. M. 1983 Dynamics of singular geostrophic vortices in a two-level model of the atmosphere (or ocean). Izv. Akad. Nauk. SSSR Atmos. Oceanic Phys. 19, 171–179.Google Scholar
Hogg, N. & Stommel, H. 1985a 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
Hogg, N. & Stommel, H. 1985b Hetonic explosion: the breakup and spread of warm water pools as explained by baroclinic point vortices. J. Atmos Sci. 42, 1465–1479.Google Scholar
Holland, W. R. 1978 The role of mesoscale eddies in the general circulation of the ocean–Numerical experiment using a wind driven quasi-geostrophic model. J. Phys. Ocean 8, 363–392.Google Scholar
Hopfinger, E. J. & Heijst, G. J. F. van 1994 Vortices in rotating fluids. Ann. Rev. Fluid Mech. 25, 241–289.Google Scholar
Joyce, T. M. 1991 Review of US contributions to warm-core rings. Rev. Geophys. Suppl., 610–616.Google 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.Google Scholar
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.Google Scholar
McWilliams, J. C. 1989 Statistical properties of decaying geostrophic turbulence. J. Fluid Mech. 198, 199–230.Google Scholar
McWilliams, J. C. 1990 The vortices of geostrophic turbulence. J. Fluid Mech. 219, 387–404.Google 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.Google Scholar
Olson, D. B. 1991 Rings in the ocean. Ann. Rev. Earth Planet. Sci. 19, 283–311.Google Scholar
Overman, E. A. & Zabusky, N. J. 1982 Evolution and merger of isolated vortex structures. Phys. Fluids 25, 1297–1305.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Polvani, L. M. 1991 Two-layer geostrophic vortex dynamics. Part 2. Alignment and two-layer V-states. J. Fluid Mech. 225, 241–270.Google Scholar
Polvani, L. M., Zabusky, N. J. & Flierl, G. R. 1989 Two-layer geostrophic vortex dynamics. Part 1. Upper layer V-states and merger. J. Fluid Mech. 105, 215–242.Google Scholar
Valcke, S. & Verron, J, 1993 On interactions between two finite-core hetons. Phys. Fluids A 5, 2058–2060.Google Scholar
Verron, J. & Hopfinger, E. J. 1991 The enigmatic merging conditions of two-layer baroclinic vortices. C. R. Acad. Sci. Paris 313 (II), 737–742.Google Scholar
Verron, J., Hopfinger, E. J. & McWilliams, J. C. 1990 Sensitivity to initial conditions in the merging of two-layer baroclinic vortices. Phys. Fluids A 2, 886–889.Google Scholar
Waugh, D. W. 1992 The efficiency of symmetric vortex merger. Phys. Fluids A 4, 1745–1758.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google 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.Google Scholar