Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-19T01:28:13.644Z Has data issue: false hasContentIssue false
  • English
  • Français

Coalescing of geostrophic vortices

Published online by Cambridge University Press:  21 April 2006

R. W. Griffiths  and
E. J. Hopfinger
R. W. Griffiths
Affiliation:
Research School of Earth Sciences, Australian National University, GPO Box 4, Canberra, A.C.T. 2601, Australia.
E. J. Hopfinger
Affiliation:
Institut de Mecanique, Laboratoire Associé au C.N.R.S., Université de Grenoble, B.P. 68, 38402 St. Martin d'Heres, France.
Get access Rights & Permissions [Opens in a new window]

Abstract

Close interactions between pairs of two-dimensional vortices of like sign were investigated in experiments with barotropic vortices and baroclinic vortices. The vortices were generated by sources or sinks in a rotating fluid which, respectively, was homogeneous or contained a two-layer density stratification. For two identical anticyclonic, unstratified vortices there was a critical separation distance beyond which the vortices coalesced to form a single larger anticyclone. The critical distance d*, scaled by the radius R of a core having non-zero relative vorticity, was d*/R = 3.3 ± 0.2. This value is in agreement with results of previous numerical simulations for finite-area vortices in non-rotating flows. The effects on vortex structure of Ekman pumping due to the presence of a rigid boundary caused cyclonic vortices to coalesee from larger distances. Baroclinic vortices in a two-layer stratification were also found to coalesce despite a potential-energy barrier. However, the critical separation distance depended on the internal Rossby radius. When the Rossby radius was large compared with the core radius, vortices coalesced from distances much greater than the critical distance for barotropic vortices. Coalescing of two vortices of equal size and strength led to two symmetric entwined spirals of water, while close interaction of unequal vortices caused the weaker vortex to be wrapped around the outer edge of the stronger. Implications of these results are discussed for ocean eddies and intense atmospheric cyclones.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 73 - 97
Copyright
© 1987 Cambridge University Press

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

Andrews, J. C. & Scully Power, P. 1976 The structure of an East Australian Current anticyclonic eddy. J. Phys. Oceanogr. 27, 405–415.Google Scholar
Aref, H. 1983 Integrable, chaotic, and turbulent vortex motion in two-dimensional flows. Ann. Rev. Fluid Mech. 15, 345–389.Google Scholar
Brand, S. 1970 Interaction of binary tropical cyclones of the western North Pacific Ocean. J. Appl. Met. 9, 433–441.Google Scholar
Brown, A. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Christiansen, J. P. 1973 Numerical simulations of hydrodynamics by the method of point vortices. J. Comput. Phys. 13, 363–379.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
Cresswell, G. R. 1982 The coalescence of two East Australia Current warm-core eddies. Science 215, 161–164.Google Scholar
Cresswell, G. R. & Legeckis, R. 1986 Eddies off southeastern Australia, 1980/81. Deep-Sea Res. 33, 1527.Google Scholar
Dritschel, D. G. 1985 The stability and energetics of corotating uniform vortices. J. Fluid Mech. 157, 95–134.Google Scholar
Flierl, G. R. 1979 A simple model for the structure of warm and cold core rings. J. Geophys. Res. 84, 781–785.Google Scholar
Fujiwhara, S. 1913 Short note on the behaviour of two vortices. Proc. Physico-Math. Soc. Japan, Third Series 13, 106–110.Google Scholar
Fujiwhara, S. 1923 On the growth and decay of vortical systems. Q. J. R. Met. Soc. 49, 75–104.Google Scholar
Gill, A. E. & Griffiths, R. W. 1981 Why should two anticyclonic eddies merge? In Ocean Modelling, 41. Unpublished manuscript.
Griffiths, R. W. & Hopfinger, E. J. 1986 Experiments with baroclinic vortex pairs in a rotating fluid. J. Fluid Mech. 173, 501–518.Google Scholar
Griffiths, R. W. & Linden, P. F. 1981 The instability of vortices in a rotating, stratified fluid. J. Fluid Mech. 105, 283–316.Google Scholar
Griffiths, R. W. & Linden, P. F. 1985 Intermittent baroclinic instability and fluctuations in geophysical circulations. Nature 316, 801–803.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. 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
Hoover, E. W. 1961 Relative motion of hurricane pairs. Mon. Weath. Rev. 89, 251–255.Google Scholar
Nilsson, C. S. & Cresswell, G. R. 1980 The formation and evolution of East Australia Current warm-core eddies. Prog. Oceanogr. 9, 133–183.Google Scholar
Nof, D. 1986 The coalescence of isolated eddies. J. Phys. Oceanogr. (submitted).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.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. 624 pp.
Pierrehumbert, R. T. & Widnall, S. E. 1981 The structure of organized vortices in a free shear layer. J. Fluid Mech. 102, 301–313.Google Scholar
Rossow, V. J. 1977 Convective merging of vortex cores in lift-generated wakes. J. Aircraft 14, 283–290.Google Scholar
Saffman, P. G. & Szeto, R. 1980 Equilibrium shapes of a pair of equal uniform vortices. Phys. Fluids 23, 2339–2342.Google Scholar
Thorpe, S. A. 1973 Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech. 61, 731–751.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: a mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google Scholar