Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-05-16T18:59:11.351Z Has data issue: false hasContentIssue false
  • English
  • Français

New stationary vortex solutions of the Hasegawa–Mima equation

Published online by Cambridge University Press:  13 March 2009

J. Nycander
J. Nycander
Affiliation:
Institute of Technology, Uppsala University, Box 534, S-752 21 Uppsala, Sweden
Get access Rights & Permissions [Opens in a new window]

Extract

Two different families of explicit stationary solutions of the Hasegawa–Mima equation are obtained. In the first case the well-known modon (dipole vortex) is used as the zeroth-order solution, and new solutions that are close to but distinctly different from it are found by perturbation analysis. In the second case the dispersive term of the equation is treated as a small parameter, and a radially symmetric solution (a monopole vortex) is used as the zeroth-order approximation. Both families of solutions are found to be infinite and to contain an arbitrary function. A recent general proof of the existence of infinitely many stationary solutions containing an arbitrary function is examined and found to be invalid.

Type
Research Article
Information
Journal of Plasma Physics , Volume 39 , Issue 3 , June 1988 , pp. 413 - 430
Copyright
Copyright © Cambridge University Press 1988

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

Aburdzhaniya, G. D., Ivanov, V. N., Kamenetz, F. F. & Pukhov, A. V. 1987 Physica Scripta, 35, 677.CrossRefGoogle Scholar
Filippov, D. V. & Yankov, V. V. 1986 Soviet J. Plasma Phys. 12, 548.Google Scholar
Flierl, G. R., Larichev, V. D., McWilliams, J. C. & Reznik, G. M. 1980 Dyn. Atmos. Oceans, 5, 1.CrossRefGoogle Scholar
Gordin, V. A. & Petviashvili, V. I. 1985 Dokl. Akad. Nauk SSSR, 285, 857.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
Horton, W., Liu, J., Meiss, J. D. & Sedlak, J. E. 1986 Phys. Fluids, 29, 1004.CrossRefGoogle Scholar
Laedke, E. W. & Spatschek, K. H. 1986 Phys. Fluids, 29, 133.CrossRefGoogle Scholar
Larichev, V. D. 1983 Izv. Akad. Nauk SSSR, Fiz. Atmosfery i Okeana, 19, 551.Google Scholar
Larichev, V. D. & Reznik, G. M. 1976 a, Dokl. Akad. Nauk SSSR, 231, 1077.Google Scholar
Larichev, V. D. & Reznik, G. M. 1976 b Oceanology, 16, 547.Google Scholar
Larichev, V. D. & Reznik, G. M. 1982 Dokl. Akad. Nauk SSSR, 264, 229.Google Scholar
McWilliams, J. C. & Zabusky, N. J. 1982 Geophys. Astrophys. Fluid Dyn. 19, 207.CrossRefGoogle Scholar
Makino, M., Kamimura, T. & Taniuti, T. 1981 J. Phys. Soc. Jpn, 50, 980.CrossRefGoogle Scholar
Meiss, J. D. & Horton, W. 1983 Phys. Fluids, 26, 990.CrossRefGoogle Scholar
Mikhailovskii, A. B., Lakhin, V. P., Mikhailovskaya, L. A. & Onishchenko, O. G. 1984 Soviet Phys. JETP, 59, 1198.Google Scholar
Nycander, J. 1987 Phys. Fluids, 30, 1585.CrossRefGoogle Scholar
Nycander, J., Pavlenko, V. P. & Stenflo, L. 1987 Phys. Fluids, 30, 1367.CrossRefGoogle Scholar
Overman, E. A. & Zabusky, N. J. 1982 Phys. Fluids, 25, 1297.CrossRefGoogle Scholar
Pavlenko, V. P. & Petviashvili, V. I. 1983 Soviet J. Plasma Phys. 9, 603.Google Scholar
Petviashvili, V. I. & Pokhotelov, O. A. 1985 JETP Lett. 42, 54.Google Scholar
Polvani, L. M. & Flierl, G. R. 1986 Phys. Fluids, 29, 2376.CrossRefGoogle Scholar
Shukla, P. K. 1987 Physica Scripta, 36, 500.CrossRefGoogle Scholar
Shukla, P. K. & Yu, M. Y. 1986 Phys. Fluids, 29, 1739.CrossRefGoogle Scholar
Swaters, G. E. 1986 Geophys. Astrophys. Fluid Dyn. 36, 85.CrossRefGoogle Scholar