Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T05:50:36.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear MHD waves on an interface of finite thickness with compressibility and resonant damping

Published online by Cambridge University Press:  13 March 2009

A. V. Khrabrov  and
B.U.Ö. Sonnerup
A. V. Khrabrov
Affiliation:
Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755-8000, U.S.A.
B.U.Ö. Sonnerup
Affiliation:
Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755-8000, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

Weakly nonlinear surface waves rippling an MHD tangential discontinuity (TD) of finite thickness are studied. The waves are two-dimensional and evanescent in the direction normal to the inhomogeneous layer. A novel approach is utilized to treat weakly nonlinear evanescent wave fields in physical space. The evolution equation obtained, which governs the interface displacement as a function of time and position, extends previous results of Ruderman and Goossens, valid for propagation along a unidirectional magnetic field in a stationary incompressible plasma, to a TD of general field geometry in a compressible plasma in the presence of stable velocity shear. Certain conservation properties of the evolution equation are presented, including the Hamiltonian formulation. Exploratory numerical results are reported. The model is of potential use in the analysis of observed quasi-stationary perturbations at the earth's magnetopause.

Type
Research Article
Information
Journal of Plasma Physics , Volume 55 , Issue 2 , April 1996 , pp. 145 - 172
Copyright
Copyright © Cambridge University Press 1996

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

Buti, B. 1985 Nonlinear surface phenomena in plasmas. Advances in Space Physics: Invited Reviews, 1985 Plasma Physics Colloquium, International Centre for Theoretical Physics, Trieste, pp. 167–209. World Scientific, Singapore.Google Scholar
Chen, L. & Hasegawa, A. 1974 A theory of long-period magnetic pulsations 1. Steady state excitation of field line resonance. J. Geophys. Res. 79, 1024–1032.CrossRefGoogle Scholar
Fejer, J. A. 1964 Hydromagnetic stability at a fluid velocity discontinuity between compressible fluids. Phys. Fluids 7, 499–503.CrossRefGoogle Scholar
Harvey, A. P. & Tupholme, G. E. 1992 Propagation of anisotropic elastic and piezoelectric nonlinear surface acoustic waves. Wave Motion 16, 125–136.CrossRefGoogle Scholar
Khrabrov, A. V. 1994 Asymptotic methods for nonlinear magnetospheric boundary waves. Ph.D. thesis, Dartmouth College.Google Scholar
Khrabrov, A. V. & Sonnerup, B. U. Ö. 1992 Nonlinear waves on a three-layer MHD tangential discontinuity. Physics of Space Plasmas: Proceedings of the 1992 Cambridge workshop in Geoplasma Physics, MIT (ed. Chang, T. & Jasperse, J. R.), pp. 541–550. SPI Conference Proceedings and Reprint Series, 12, Scientific Publishers, Cambridge, MA.Google Scholar
Landau, L. D. & Ltfshitz, E. M. 1984 Electrodynamics of Continuous Media, 2nd edn.Pergamon Press, Oxford.Google Scholar
Rankin, R., Harrold, B. G., Samson, J. C. & Frycz, P. 1993 The nonlinear evolution of field line resonance in the Earth's magnetosphere. J. Geophys. Res. 98, 5839–5853.CrossRefGoogle Scholar
Roberts, B. 1981 Wave propagation in a magnetically structured atmosphere, 1, Surface waves at a magnetic interface. Solar Phys. 69, 27–38.CrossRefGoogle Scholar
Ruderman, M. S. 1985 Nonlinear surface waves in incompressible plasma Soviet Phys., Fluid Dyn. 20, 85–97.CrossRefGoogle Scholar
Ruderman, M. S. 1988 Nonlinear surface waves at magnetic interface in compressible plasma. Plasma. Phys. Conir. Fusion 30, 1117–1125.CrossRefGoogle Scholar
Ruderman, M. S. & Goossens, M. 1993 Nonlinearity effect on resonant absorption of surface Alfvén waves in incompressible plasmas. Solar Phys. 143, 69–88.CrossRefGoogle Scholar
Sonnerup, B. U. Ö., Hau, L.-N. & Walthour, D. W. 1992 On steady field-aligned double- adiabatic flow. J. Geophys. Res. 97, 12015–12028.CrossRefGoogle Scholar
Southwood, D. J. 1968 The hydromagnetic stability of the magnetospheric boundary. Planet. Space Sci. 16, 587–605.CrossRefGoogle Scholar
Southwood, D. J. 1974 Some features of the field-line resonances in the magnetosphere. Planet. Space Sci. 22, 483–491.CrossRefGoogle Scholar
Walthour, D. W., Sonnerup, B. U. O., Pashmann, G., Luhr, H., Klumpar, D. & Potemra, T. 1993 Remote sensing of two-dimensional magnetopause structures. J. Geophys. Res. 98, 1489–1504.CrossRefGoogle Scholar
Yang, G. & Hollweg, J. V. 1991 The effects of velocity shear on the resonance absorption of MHD waves: cold plasma. J. Geophys. Res. 96, 13807–13813.CrossRefGoogle Scholar