Phase-Mixing and Dissipation of Standing Shear Alfven waves

We study the phase mixing and dissipation of a packet of standing shear Alfv'en waves localized in a region with non-uniform Alfv'en background velocity. We investigate the validity of the exponential damping law in time, $\exp (-A{t}^3)$, presented by Heyvaerts & Priest (1983) for different ranges of Lundquist, $S$, and Reynolds, $R$, numbers. Our numerical results shows that it is valid for $(R,S)\ge {10}^7$.