Phase mixing of Alfven waves in a stratified and open atmosphere

Phase mixing was introduced by Heyvaerts and Priest (1983) as a mechanism f or heating the plasma in the open magnetic field regions of coronal holes. Here the basic process is modified to include a stratified atmosphere in wh ich the density decreases with height. We present an analytical solution in the case of zero dissipation and use a numerical code in the non-zero diss ipation case to describe the effect of strati fication on phase mixing. The exponential damping behaviour derived by Heyvaerts and Priest is largely c onfirmed in the non stratified limit. However, it is shown that the decreas e in density lengthens the oscillation wavelengths and thereby reduces the generation of transverse gradients. Furthermore we found that in a stratifi ed atmosphere the perturbed magnetic field and velocity behave quite differ ently depending on whether we consider resistivity or viscosity. Ohmic heat ing is spread out over a greater height range in a stratified medium wherea s viscous heating is not strongly influenced by the stratification.