Dissipation of Alfven waves in compressible inhomogeneous media

In weakly dissipative media governed by the magnetohydrodynamics (MHD) equations, any efficient mechanism of energy dissipation requires the formation of small scales. Using numerical simulations, we study the propel ties of Alfven wanes propagating in a compressible inhomegeneous medium, with an inhomogeneity transverse to the direction of wave propagation. Two dynamical effects, energy pinching and phase mixing, are responsible for the small-scales formation, similarly to the incompressible case. Moreover compressive perturbations, slow waves and a static entropy wave are generated; the former are subject to steepening and form shock waves, which efficiently dissipate their energy, regardless of the Reynolds number. Rough estimates show that the dissipation times are consistent with those required to dissipate Alfven waves of photospheric origin inside the solar corona.