## Resonant flow instability of MHD surface waves
^{1} Centre for Plasma-Astrophysics, K.U. Leuven,
Celestijnenlaan 200 B, B-3001 Heverlee, Belgium^{2} School of Mathematical and Computational Sciences, Univ.
St. Andrews, St. Andrews, KY16 9SS, Scotland, UK
We study the effect of velocity shear on the spectrum of MHD surface waves. A nonuniform intermediate region is taken into account, so that the surface wave can be subject to resonant absorption. In order to deal in a mathematically and also physically consistent manner with the resonant wave excitation, we analytically derive the dissipative solution around the resonant surface in resistive MHD. Using these analytical solutions in our eigenvalue code, the effect of the velocity shear on the damping rate of the surface wave can easily be investigated with limited numerical effort. The presence of the flow can both increase and decrease the efficiency of resonant absorption. We also show how the resonance can lead to instability of the global surface mode for a certain range of values for the velocity shear. The resonant flow instabilities, which are physically distinct from the nonresonant Kelvin-Helmholz instabilities can occur for velocity shears significantly below the Kelvin-Helmholz threshold. Although resonant absorption as dissipation mechanism is present, the amplitude of the surface mode grows in time. The resonant flow instability can be explained in terms of negative energy waves : to get an unstable negative energy wave, some dissipative process is required to ensure energy dissipation.
* Research Assistant of the F.W.O.-Vlaanderen
## Contents- 1. Introduction
- 2. The steady equilibrium state
- 3. The linearized MHD equations
- 4. The analytical solution around the resonance
- 5. The numerical procedure
- 6. Results
- 7. Negative energy waves
- 8. Summary and discussion
- Acknowledgements
- References
© European Southern Observatory (ESO) 1998 Online publication: March 23, 1998 |