Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-06-19T09:22:46.743Z Has data issue: false hasContentIssue false
  • English
  • Français

Destructive interactions between two counter-rotating quasi-geostrophic vortices

Published online by Cambridge University Press:  05 October 2009

JEAN N. REINAUD  and
DAVID G. DRITSCHEL
JEAN N. REINAUD*
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
DAVID G. DRITSCHEL
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
*
†Email address for correspondence: jean@mcs.st-and.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper illustrates the linear stability and the nonlinear evolution of two opposite-signed quasi-geostrophic vortices. We investigate the influence of the volume ratio between the two vortices as well as the influence of their vertical offset. Instability is always found for sufficiently close vortices. A convenient measure of the separation distance between the two vortices at their margin of stability is the horizontal gap between their two outermost edges. When the vortex volume ratio is very close to unity, the critical gap at the margin of stability tends to increase with the vertical offset. However, for volume ratios greater than 1.1, it decreases with the vertical offset. This is due to differences in the magnitude of the tilt angle of the vortices. The nonlinear evolution of unstable equilibria tends to be destructive, often breaking one vortex or both vortices into smaller vortices.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 639 , 25 November 2009 , pp. 195 - 211
Copyright
Copyright © Cambridge University Press 2009

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

Bambrey, R. R., Reinaud, J. N. & Dritschel, D. G. 2007 Strong interactions between two co-rotating quasi-geostrophic vortices. J. Fluid Mech. 592, 117–133.CrossRefGoogle Scholar
Dritschel, D. G. 1988 Contour surgery: a topological reconnection scheme for extended integrations using contour dynamics. J. Comput. Phys. 77, 240–266.Google Scholar
Dritschel, D. G. 1995 A general theory for two-dimensional vortex interactions. J. Fluid Mech. 293, 269–303.CrossRefGoogle Scholar
Dritschel, D. G. 2002 Vortex merger in rotating stratified flows. J. Fluid Mech. 455, 83–101.CrossRefGoogle Scholar
Dritschel, D. G. & Ambaum, M. H. P. 1997 A contour-advective semi-Lagrangian algorithm for the simulation of fine-scale conservative fields. Quart. J. R. Met. Soc. 123, 1097–1130.Google Scholar
Ebbesmeyer, C. C., Taft, B. A., McWilliams, J. C., Shen, C. Y., Riser, S. C., Rossby, H. T., Biscaye, P. E. & Östlund, H. G. 1986 Detection, structure and origin of extreme anomalies in a western atlantic oceanographic section. J. Phys. Oceanogr. 16, 591–612.Google Scholar
Garrett, C. 2000 The dynamic ocean, In Perspectives in Fluid Dynamics (ed. Batchelor, G. K., Moffatt, H. K. & Worster, M. G.), chap. 10, pp. 507–553. Cambridge University Press.Google Scholar
von Hardenberg, J., McWilliams, J. C., Provenzale, A., Shchpetkin, A. & Weiss, J. B. 2000 Vortex merging in quasi-geostrohic flows. J. Fluid Mech. 412, 331–353.CrossRefGoogle Scholar
Holton, J. R., Haynes, P. H., McIntyre, M. E., Douglass, A. R., Rood, R. B. & Pfister, L. 1995 Stratosphere–troposphere exchange. Rev. Geophys. 33 (4), 403–439.Google Scholar
Hua, B. L. & Haidvogel, D. B. 1986 Numerical simulations of the vertical structure of quasi-geostrophic turnulence. J. Atmos. Sci. 43 (23), 2923–2936.2.0.CO;2>CrossRefGoogle Scholar
McWilliams, J., Weiss, J. & Yavneh, I. 1999 The vortices of homogeneous geostrophic turbulence. J. Fluid Mech. 401, 1–26.CrossRefGoogle Scholar
Miyazaki, T., Yamamoto, M. & Fujishima, S. 2003 Counter-rotating quasigeostrophic ellipsoidal vortex pair. J. Phys. Soc Jpn 72 (8), 1942–1953.CrossRefGoogle Scholar
Ozugurlu, E., Reinaud, J. N. & Dritschel, D. G. 2008 Interaction between two quasi-geostrophic vortices of unequal potential-vorticity. J. Fluid Mech. 597, 395–414.CrossRefGoogle Scholar
Reinaud, J. N. & Dritschel, D. G. 2002 The merger of vertically offset quasi-geostrophic vortices. J. Fluid Mech. 469, 287–315.CrossRefGoogle Scholar
Reinaud, J. N. & Dritschel, D. G. 2005 The critical merger distance between two co-rotating quasi-geostrophic vortices. J. Fluid Mech. 522, 357–381.CrossRefGoogle Scholar
Reinaud, J. N., Dritschel, D. G. & Koudella, C. R. 2003 The shape of the vortices in quasi-geostrophic turbulence. J. Fluid Mech. 474, 175–192.CrossRefGoogle Scholar
Vallis, C. 2006 Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press.CrossRefGoogle Scholar