Convective instability in a compressible atmosphere

Abstract

The degree of convective instability as expressed by the growth rate ω of linear modes, is calculated for a plane parallel polytropic atmosphere in the presence of radiative damping, without using Boussinesq approximation. A comparison with the results based on the Boussinesq approximation reveals that the use of the Boussinesq approximation leads to an overestimation of the radiative damping. The computation of ω as a function of the horizontal wave number yields a wavelength of maximal instability under a variety of conditions. For reasonable choices of physical parameters appropriate to the solar atmosphere, the fastest growing wavelengths turn out to be in the range 600-1200 km, and their e-folding times are in the range 200-2000 s.