The damping of slow MHD waves in solar coronal magnetic fields

III. The effect of mode coupling

School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, Scotland e-mail: ineke@mcs.st-and.ac.uk

Received: 5 March 2004
Accepted: 22 June 2004

Abstract

The properties of slow MHD waves in a two dimensional model are investigated, in a low-beta plasma. Including a horizontal density variation causes “phase mixing” and coupling between slow and fast MHD waves. The effects of different density profiles, different driving frequencies, different values for the viscosity coefficient and plasma beta (<1) are studied. Using numerical simulations, it was found that the behaviour of the perturbed velocity was strongly dependent on the values of the parameters. From analytical approximations, a strong interaction with the fundamental, normal modes of the system was found to play an important role. The coupling to the fast wave proved to be an inefficient way to extract energy from the driven slow wave and is unlikely to be responsible for the rapid damping of propagating slow MHD waves, observed by TRACE. The “phase mixing” of the slow waves due to the (horizontal) density inhomogeneity does cause a significant amount of damping, but is again unlikely to be sufficiently strong to explain the rapid observed damping.