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Evolution of wave packets in magnetohydrodynamics

Published online by Cambridge University Press:  13 March 2009

Anju Pusri  and
S. K. Malik
Anju Pusri
Affiliation:
Department of Mathematics, Panjab University, Chandigarh-160014, India
S. K. Malik
Affiliation:
Department of Mathematics, Panjab University, Chandigarh-160014, India
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Abstract

The propagation of wave packets on the surface of an electrically conducting fluid of uniform depth in the presence of a tangential magnetic field is investigated in (2 + 1) dimensions. The evolution of wave envelope is governed by two coupled partial differential equations with cubic nonlinearity. The stability analysis reveals the existence of different regions of instability. The effect of the applied magnetic field is not only significant but also different for different regions of stability. ‘Envelope soliton’ and ‘waveguide’ solutions of the amplitude equation are also discussed. The self-focusing phenomenon that arises when the amplitude of the wave becomes infinite in finite time is also examined. It is found that in a certain region of the stability diagram it may be easier to observe this phenomenon in the presence of a magnetic field. The Rayleigh-Taylor problem is also studied and various criteria for the existence of instability are obtained.

Type
Research Article
Information
Journal of Plasma Physics , Volume 53 , Issue 2 , April 1995 , pp. 145 - 167
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

Ablowitz, J. & Segur, H. 1979 J. Fluid Mech. 92, 691.CrossRefGoogle Scholar
Benney, D. J. 1977 Stud. Appl. Maths 56, 81.CrossRefGoogle Scholar
Berkshire, F. H. & Gibbon, J. D. 1983 Stud. Appl. Maths 69, 229.CrossRefGoogle Scholar
Davey, A. & Stewartson, K. 1974 Proc. R. Soc. Lond. A 338, 101.Google Scholar
Djordjevic, V. D. & Redekopp, L. G. 1977 J. Fluid Mech. 74, 703.CrossRefGoogle Scholar
Gibbon, J. P. & Mcguinness, M. J. 1980 Phys. Lett. 77A, 118.CrossRefGoogle Scholar
Hasimoto, H. & Ono, H. 1972 J. Phys. Soc. Japan 33, 805.CrossRefGoogle Scholar
Kant, R. & Malik, S. K. 1987 J. Magn. Magn. Mat.). 65, 347.CrossRefGoogle Scholar
Kawahara, T. 1975 J. Phys. Soc. Japan 38, 265.CrossRefGoogle Scholar
Malik, S. K. & Singh, M. 1989 Continuum Mechanics and its Applications (ed. Graham, G. C. A. & Malik, S. K.). Hemisphere, N.Y., 679.Google Scholar
Nayfeh, A. H. 1973 Perturbation Methods. Wiley.Google Scholar
Nayfeh, A. H. 1976 J. Appl. Mech. 43, 584.CrossRefGoogle Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.Google Scholar
Zakharov, V. E. 1972 Soviet Phys. JETP 72, 908.Google Scholar