## 2. Setup of the problemIn this section, we consider the
The lower layer () represents the convection zone and the overlaying photosphere. The upper layer represents the chromosphere and solar corona which occupy the half-space . The flow quantities below the interface (for ) are denoted by the subscript 1, while these quantities above the interface (for ) are distinguished by the subscript 2. The interface is taken to be located at . This model is a special case of the model which was considered by Vanlommel & Cadez (1998) and Vanlommel & Goossens (1999) (valid for the width of the chromosphere, ). Furthermore, we apply the Cowling approximation (Cowling 1941)
according to which perturbations to the gravity field are ignored. As
long as this is a valid assumption.
The solar curvature is negligible as long as
. Under these assumptions the Sun can
be modeled as plane-parallel with constant gravity It is assumed that the together with the boundary conditions at the interface, Here, is the mass density,
is the velocity, In what follows we assume two-dimensional motions with
and
and consider the case when the
transitional layer becomes a sharp
discontinuity of density and temperature. In particular, we take into
account the equilibrium state in which the flow
occurs in the lower medium only and
it depends both on Assuming that perturbations are small, we expand the fluid variables around this equilibrium and introduce the flux function such that © European Southern Observatory (ESO) 2000 Online publication: August 17, 2000 |