Abstract
A new approach is proposed to solve linear theory of conditionally unstable convection. In the traditional methods (Haque, 1952; Lilly, 1960; Kuo, 1961) the relationship among growth rate, width of the unstable region and static stability parameter is determined by first finding functional forms in unstably and stably stratified regions independently, and then imposing the continuity conditions for pressure and normal velocity at the boundaries between the two regions. In this study, the problem is considered to be a linear steady response of a stably stratified atmosphere to localized heating, where the growth rate is regarded as a Rayleigh damping/Newtonian cooling-type damping rate. This problem of forced motion is linked to the convection problem when the horizontal distribution of the heating rate is required to be proportional to that of the upward motion. Thus linear theory of conditionally unstable convection is reduced to a special case of the general problem of forced motion in a stably stratified atmosphere. From the standpoint of the forcing problem, the formation of the downward motion outside the unstable region is explained by the internal gravity waves propagating succesively in the stably stratified atmosphere.
