Astron. Astrophys. 330, 726-738 (1998)

Numerical simulations of impulsively generated MHD waves
in a potential coronal arcade

R. Oliver , K. Murawski ^* and J.L. Ballester

Departament de Fsica, Universitat de les Illes Balears, E-07071 Palma de Mallorca, Spain

Received 1 October 1996 / Accepted 12 September 1997

Abstract

Impulsively generated waves in coronal arcades are simulated numerically by an application of nonlinear ideal magnetohydrodynamic (MHD) equations. The simulations are performed in the -plane on a non-uniform Cartesian mesh. In this geometry the magnetic field can be expressed in terms of the vector potential. The governing equations, which are applied in the limit of low plasma- , are solved by a flux corrected transport method. The model excludes the Alfvén waves and, since the slow mode is absent in the cold plasma limit, the excited disturbances are fast magnetosonic waves.

Numerical results show that for short times after the impulse is launched (i. e., in the linear regime), only motions normal to the equilibrium magnetic field get propagated away from the position of the initial displacement and that any velocity parallel to the unperturbed magnetic field lines remains essentially unchanged in time. In the nonlinear regime there is conversion between normal and parallel flow and the two velocity components propagate from the site of the initial impulse. In addition, nonlinearities that are built in the MHD equations modify the shape and speed of the propagating wavefront, an effect that becomes most noticeable where the wave amplitude is larger. The effect of nonlinearity on down-going perturbations is to speed up positive wave amplitudes and to slow down negative wave amplitudes (positive and negative refers to the sign of the normal velocity component). On the contrary, up-going positive and negative waves are slowed down and speeded up, respectively. Impulsively generated waves exhibit temporal signatures with characteristic time scales of the order of 10 s. Similar scales have been recently reported in radio observations, microwaves, and hard X-rays.

Key words: Sun: corona Sun: magnetic fields MHD

* Permanent address: Division of Environmental Studies, Technical University of Lublin, ul. Nadbystrzycka 40, 20-618 Lublin, Poland

Send offprint requests to: J.L. Ballester

Contents

• 1. Introduction
• 2. Physical model
• 3. Equilibrium configuration
• 4. Linear wave equation
• 5. Numerical simulations of MHD equations
• 6. Numerical model
• 7. Results and discussion
  • 7.1. Linear waves in a uniform density medium
  • 7.2. Linear waves for various profiles of and
  • 7.3. Comparison with analytical results ()
  • 7.4. Nonlinear waves
• 8. Summary and conclusions
• Acknowledgements
• Appendix A: model equation for fast waves propagating vertically in a cold coronal arcade
• References

© European Southern Observatory (ESO) 1998

Online publication: January 16, 1998
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