Radiative transfer in a static model atmosphere

Radiative transfer through a model plane-parallel grey atmosphere is invest igated. For the purposes of this study the atmosphere is considered to cons ist of a stationary, inviscid and incompressible fluid. A definitive descri ption of this state is essential for an analysis of the convective instabil ity of such an atmosphere, which will be considered in later papers. The fl uid is assumed to be in local thermodynamic equilibrium (LTE) and the treat ment of the radiation field is simplified through the use of the Eddington approximation. This results in a pair of simultaneous equations for the tem perature and mean radiative intensity. It is shown that the structure of th e atmosphere, under the assumption of convective stability, depends on two dimensionless parameters which can be related to the ratio of radiative to conductive heat transfer and the ratio of layer depth to photon mean free p ath. Analysis reveals that when the bulk of the atmosphere is in radiative equilibrium boundary layers are required at the upper and lower surfaces in order to satisfy the appropriate boundary conditions. The structure of the se boundary layers is analyzed through the method of asymptotic matching. T hese results predict structure of the temperature and mean intensity at the parameter extremes appropriate for both planetary and stellar applications .