Alfven wave propagation in the high solar corona

We consider monochromatic Alfven perturbations propagating upward in the high corona, in the distance range between 2 and 9 solar radii. The corona is made of a closed loop region and of an open flow region, with or without structured streams generated by stationary temperature inhomogeneities in the corona. The wave period is 36 min., the plasma beta varies between 0.25 at the poles and 1.2 at the equator. We integrate the time-dependent, three-dimensional axisymmetric polytropic MHD equations. Filters are used to damp energy at the grid scale. The mean flow and waves are dealt with self-consistently, by using transparent boundary conditions, which prevent spurious reflections at the inner coronal boundary. We find that the mother Alfven wave remains everywhere Alfvenic: the normalized cross-helicity is sigma (c) - 1-10(-3) except within a thin layer around the heliospheric current sheet. The radial evolution depends on the latitude. In a large domain around the heliospheric current sheet, the wave is very strongly damped, whatever its amplitude, by the phase mixing, i.e., the shear of the wave front due to transverse gradients of the Alfven speed and bulk velocity. As a consequence, the Alfven wave nowhere reaches the heliospheric current sheet. At higher latitudes, and outside structured streams, the amplitude varies in agreement with the WKB prediction, albeit with some dissipation due to nonlinear steepening (depending on the wave amplitude); as a rule, the propagation angle varies, i.e., the propagation is alternatively oblique and quasi-parallel. On the other hand, streams show specific properties: the amplitude does not follow the WKB law, but the propagation angle remains constantly oblique. As a consequence, the streams show a strong minimum in the amplitude of the compressive fluctuations.