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.