Linear convective instability in a radiating model atmosphere

Abstract

The convective instability of a model plane-parallel grey layer of radiating fluid which is heated from below and bounded above by a vacuum is investigated numerically. Both thermal conductivity and radiative transfer of energy are included. The equation governing the transfer of radiation through the steady, incompressible fluid can be simplified by using the Eddington approximation. The linearized equations of marginal stability are solved for a wide range of values of the optical depth of the layer and of the ratio of radiative conductivity to thermal conductivity. Limiting cases are observed for various parameter extremes and considered analytically. A radiative limit is found with a conventionally sized minimum Rayleigh number and horizontal wave number in a suitable scaling. The correct boundary conditions in this limit are found to be Dirichlet for the perturbation mean intensity or perturbation temperature fields.

Key Words:

• Radiative convection
• Eddington approximation