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Negative energy standing wave instability in the presence of flow

  • Michael S. Ruderman (a1) (a2)

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.

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Corresponding author

Email address for correspondence: m.s.ruderman@sheffield.ac.uk

References

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Andries, J. & Goossens, M. 2001 Kelvin–Helmholtz instabilities and resonant flow instabilities for a coronal plume model with plasma pressure. Astron. Astrophys. 368, 10831094.
Benjamin, T. B. 1963 The threefold classification of unstable disturbances in flexible surfaces bounding inviscid flows. J. Fluid Mech. 16, 436450.
Cairns, R. A. 1979 The role of negative energy waves in some instabilities of parallel flow. J. Fluid Mech. 92, 114.
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.
Joarder, P. S., Nakariakov, V. M. & Roberts, B. 1997 A manifestation of negative energy waves in the solar atmosphere. Solar Phys. 176, 285297.
Kadomtsev, B. B., Mikhailovskii, A. V. & Timofeev, A. V. 1965 Negative energy waves in dispersive media. Sov. Phys. JETP 20, 15171526.
Mikhailovskii, A. V. 1974 Theory of Plasma Instabilities. Consultants Bureau.
Nezlin, M. V. 1976 Negative energy waves and anomalous Dopler effect. Sov. Phys. Uspekhi 19, 481495.
Ostrovskii, L. A., Rybak, S. A. & Tsimring, L. Sh. 1986 Negative energy waves in hydrodynamics. Sov. Phys. Uspekhi 29, 10401052.
Pierce, J. 1974 Almost All About Waves. The MIT Press.
Ruderman, M. S. 2010 The effect of flows on transverse oscillations of coronal loops. Solar Phys. 267, 377391.
Ruderman, M. S. & Belov, N. A. 2010 Stability of MHD shear flows: application to space physics. J. Phys. Conf. Ser. 216, 012016.
Ruderman, M. S. & Goossens, M. 1995 Surface Alfvén waves of negative energy. J. Plasma Phys. 54, 149155.
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, 2657326584.
Ryutova, M. P. 1988 Negative-energy waves in a plasma with structured magnetic fields. Sov. Phys. JETP 67, 15941601.
Stepanyants, Yu. A. & Fabrikant, A. L. 1989 Propagation of waves in hydrodynamic shear flows. Sov. Phys. Uspekhi 32, 783805.
Taroyan, Y. & Ruderman, M. S. 2011 MHD waves and instabilities in space plasma flows. Space Sci. Rev. 158, 505523.
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Negative energy standing wave instability in the presence of flow

  • Michael S. Ruderman (a1) (a2)

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