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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: m.s.ruderman@sheffield.ac.uk
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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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