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Negative energy standing wave instability in the presence of flow

Published online by Cambridge University Press:  08 January 2018

Michael S. Ruderman
Michael S. Ruderman*
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK Space Research Institute (IKI), Russian Academy of Sciences, 117997 Moscow, Russia
*
†Email address for correspondence: [email protected]
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Abstract

We study standing waves on the surface of a tangential discontinuity in an incompressible plasma. The plasma is moving with constant velocity at one side of the discontinuity, while it is at rest at the other side. The moving plasma is ideal and the plasma at rest is viscous. We only consider the long wavelength limit where the viscous Reynolds number is large. A standing wave is a superposition of a forward and a backward wave. When the flow speed is between the critical speed and the Kelvin–Helmholtz threshold the backward wave is a negative energy wave, while the forward wave is always a positive energy wave. We show that viscosity causes the standing wave to grow. Its increment is equal to the difference between the negative energy wave increment and the positive energy wave decrement.

Keywords

plasma flowsplasma instabilitiesplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 1 , February 2018 , 905840101
Copyright
© Cambridge University Press 2018 

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References

Andries, J. & Goossens, M. 2001 Kelvin–Helmholtz instabilities and resonant flow instabilities for a coronal plume model with plasma pressure. Astron. Astrophys. 368, 1083–1094.Google Scholar
Benjamin, T. B. 1963 The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows. J. Fluid Mech. 16, 436–450.Google Scholar
Cairns, R. A. 1979 The role of negative energy waves in some instabilities of parallel flow. J. Fluid Mech. 92, 1–14.Google Scholar
Fabrikant, A. L. & Stepanyants, Yu. A. 1998 Propagation of Waves in Shear Flows, World Scientific Series on Nonlinear Science Series A: vol. 18. World Scientific.Google Scholar
Joarder, P. S., Nakariakov, V. M. & Roberts, B. 1997 A manifestation of negative energy waves in the solar atmosphere. Solar Phys. 176, 285–297.CrossRefGoogle Scholar
Kadomtsev, B. B., Mikhailovskii, A. V. & Timofeev, A. V. 1965 Negative energy waves in dispersive media. Sov. Phys. JETP 20, 1517–1526.Google Scholar
Mikhailovskii, A. V. 1974 Theory of Plasma Instabilities. Consultants Bureau.Google Scholar
Nezlin, M. V. 1976 Negative energy waves and anomalous Dopler effect. Sov. Phys. Uspekhi 19, 481–495.Google Scholar
Ostrovskii, L. A., Rybak, S. A. & Tsimring, L. Sh. 1986 Negative energy waves in hydrodynamics. Sov. Phys. Uspekhi 29, 1040–1052.Google Scholar
Pierce, J. 1974 Almost All About Waves. The MIT Press.Google Scholar
Ruderman, M. S. 2010 The effect of flows on transverse oscillations of coronal loops. Solar Phys. 267, 377–391.Google Scholar
Ruderman, M. S. & Belov, N. A. 2010 Stability of MHD shear flows: application to space physics. J. Phys. Conf. Ser. 216, 012016.Google Scholar
Ruderman, M. S. & Goossens, M. 1995 Surface Alfvén waves of negative energy. J. Plasma Phys. 54, 149–155.Google Scholar
Ruderman, M. S. & Wright, A. N. 1998 Excitation of resonant Alfvén waves in the magnetosphere by negative energy surface waves on the magnetopause. J. Geophys. Res. 103, 26573–26584.Google Scholar
Ryutova, M. P. 1988 Negative-energy waves in a plasma with structured magnetic fields. Sov. Phys. JETP 67, 1594–1601.Google Scholar
Stepanyants, Yu. A. & Fabrikant, A. L. 1989 Propagation of waves in hydrodynamic shear flows. Sov. Phys. Uspekhi 32, 783–805.Google Scholar
Taroyan, Y. & Ruderman, M. S. 2011 MHD waves and instabilities in space plasma flows. Space Sci. Rev. 158, 505–523.Google Scholar