ABSTRACT
This chapter deals with two single-layer Rayleigh-Bénard convection models, the nonlinear stability of the relevant exact solutions of which are investigated by means of a longituduinal-planform analysis. The first involves an aerosol model employing a Boussinesq particle-gas system retaining both the particle and collision pressures and considering particle to particle radiative effects, while relaxing the usual assumption of thermal equilibrium between those particles and the gas and neglecting the adiabatic gradient term in both its energy equations. Then, an analysis of the criteria governing the occurrence of supercritically re-equilibrated stationary rolls yields a minimum Rayleigh number and a critical wavelength, which are completely compatible in their layer-depth behavior with normal convective and columnar instabilities observed in mixtures of smoke with air or carbon dioxide. The second involves a similar model for convection in planetary atmospheres where due to the relatively large value of the depth of the convection layer, the adiabatic gradient term had to be retained in its Boussinesq compressible gas Rayleigh number, which now was a measure of this so-called superadiabaticity. Then this nonlinear stability analysis determined that a linear radiative cooling term of temperature was the best choice for describing the high-aspect ratios observed in the upper planetary atmospheric layers of Venus.
