Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-02T21:38:57.606Z Has data issue: false hasContentIssue false
  • English
  • Français

A perturbation theory for the solitary-drift-vortex solutions of the Hasegawa-Mima equation

Published online by Cambridge University Press:  13 March 2009

Gordon E. Swaters
Gordon E. Swaters
Affiliation:
Applied Mathematics Institute, Department of Mathematics, University of Alberta, Edmonton, Alberta, CanadaT6G 2G1
Get access Rights & Permissions [Opens in a new window]

Abstract

A multiple-scales adiabatic perturbation theory is presented describing the adiabatic dissipation of the solitary vortex-pair solutions of the Hasegawa-Mima equation. The vortex parameter transport equations are derived as solvability conditions for the asymptotic expansion and are identical with the transport equations previously derived by Aburdzhaniya et al. (1987) using an energy- and enstrophy-conservation balance procedure. The theoretical results are compared with high-resolution numerical simulations. Global properties such as the decay in the enstrophy and energy are accurately reproduced. Local properties such as the position of the centre of the vortex pair, decay of the extrema in the vorticity and stream-function fields, and the dilation of the vortex dipole are also in good agreement. In addition, time series of vorticity–stream-function scatter diagrams for the numerical simulations are presented to verify the adiabatic ansatz.

Type
Research Article
Information
Journal of Plasma Physics , Volume 41 , Issue 3 , June 1989 , pp. 523 - 539
Copyright
Copyright © Cambridge University Press 1989

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

Ablowitz, M. J. & Segur, H. 1981 Solitons and the Inverse Scattering Transform. SIAM Studies in Applied Mathematics no. 425.CrossRefGoogle Scholar
Aburdzhaniya, G. D., Ivanov, V. N., Kamenetz, F. F. & Pukhov, A. V. 1987 Physica Scripta, 35, 677.CrossRefGoogle Scholar
Arakawa, A. 1966 J. Comp. Phys. 1, 119.CrossRefGoogle Scholar
Flierl, G. R. 1987 Ann. Rev. Fluid Mech. 19, 493.CrossRefGoogle Scholar
Grimshaw, R. H. J. 1979 a Proc. R. Soc. Lond. A 368, 359.Google Scholar
Grimshaw, R. H. J. 1979 b Proc. R. Soc. Lond. A 368, 377.Google Scholar
Grimshaw, R. H. J. 1981 Proc. R. Soc. Lond. A 376, 319.Google Scholar
Hasegawa, A., Maclennan, C. G. & Kodama, Y. 1979 Phys. Fluids, 22, 2122.CrossRefGoogle Scholar
Hasegawa, A. & Mima, K. 1978 Phys. Fluids, 21, 87.CrossRefGoogle Scholar
Holm, D. D., Marsden, J. E., Ratiu, T. & Weinstein, A. 1985 Phys. Rep. 123, 1.CrossRefGoogle Scholar
Horton, W., Liu, J., Meiss, J. D. & Sedlak, J. E. 1986 Phys. Fluids, 29, 1004.CrossRefGoogle Scholar
Karpman, V. I. 1977 Phys. Lett. 60A, 307.CrossRefGoogle Scholar
Karpman, V. I. & Maslov, E. M. 1978 Soviet Phys. JETP, 48, 252.Google Scholar
Kaup, D. J. & Newell, A. C. 1978 Proc. R. Soc. Lond. A 361, 413.Google Scholar
Knickerbocker, C. J. & Newell, A. C. 1980 J. Fluid Mech. 98, 803.CrossRefGoogle Scholar
Kodama, Y. & Ablowitz, M. J. 1981 Stud. Appl. Maths, 64, 225.CrossRefGoogle Scholar
Laedke, E. W. & Spatschek, K. H. 1986 Phys. Fluids, 29, 133.CrossRefGoogle Scholar
Larichev, V. D. & Reznik, G. M. 1976 Rep. USSR Acad. Sci. 231, 1077.Google Scholar
McWilliams, J. C., Flierl, G. R., Larichev, V. D. & Reznik, G. M. 1981 Dyn. Atmos. Oceans, 5, 219.CrossRefGoogle Scholar
Meiss, J. D. & Horton, W. 1983 Phys. Fluids, 26, 990.CrossRefGoogle Scholar
Nycander, J. 1988 J. Plasma Phys. 39, 413.CrossRefGoogle Scholar
Nycander, J., Pavlenko, V. P. & Stenflo, L. 1987 Phys. Fluids, 30, 1367.CrossRefGoogle Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics, 2nd edition. Springer.CrossRefGoogle Scholar
Seliger, R. L. & Whitham, G. B. 1968 Proc. R. Soc. Lond. A 305, 1.Google Scholar
Shukla, P. K. 1985 Phys. Rev. A 32, 1858.CrossRefGoogle Scholar
Stern, M. 1975 J. Mar. Res. 33, 1.Google Scholar
Swaters, G. E. 1985 J. Phys. Oceanogr. 15, 1212.2.0.CO;2>CrossRefGoogle Scholar
Swaters, G. E. 1986 a Phys. Fluids, 29, 1419.CrossRefGoogle Scholar
Swaters, G. E. 1986 b Geophys. Astrophys. Fluid Dyn. 36, 85.CrossRefGoogle Scholar
Swaters, G. E. & Flierl, G. R. 1989 Mesoscale/Synoptic Coherent Structures in Geophysical Turbulence (ed. Nihoul, J. C. J.). Elsevier.Google Scholar
Virasoro, M. A. 1981 Phys. Rev. Lett. 47, 1181.CrossRefGoogle Scholar
Weinstein, A. 1983 Phys. Fluids, 26, 388.CrossRefGoogle Scholar
Yu, M. Y., Shukla, P. K. & Varma, R. K. 1985 Phys. Fluids, 28, 2925.CrossRefGoogle Scholar