Alfven wave propagation in the high solar corona
accepted by Astronomy and Astrophysics
R. Grappin, J. Léorat, A. Buttighoffer
Abstract
We consider monochromatic Alfv\'en 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 Alfv\'en wave
remains everywhere Alfv\'enic: the normalized cross-helicity is
$\sigma_c \simeq 1-10^{-3}$ 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 Alfv\'en speed and bulk velocity.
As a consequence, the Alfv\'en 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.
Source