Stability properties of and scaling laws for a dry radiative‐convective atmosphere

Abstract

AbstractThis work is a theoretical and numerical study of the stability properties and scaling laws associated with an idealized radiative‐convective model. We find that the linear‐stability threshold in the model can be described by a radiative Rayleigh number, a parameter that incorporates radiative effects but otherwise resembles the classical Rayleigh number. The energy method is used to find a nonlinear‐stability threshold below which all perturbations, whether infinitesimal or finite‐amplitude, decay. The model behaviour when weakly nonlinear convection occurs is studied via the mean‐field equations. We find that changing the values of viscosity, thermal diffusivity, and radiative damping has only weak effects on the vertical convective heat flux, in contrast to the case for weakly nonlinear Rayleigh‐Bénard convection. Finally, we propose scaling laws for the vertical convective heat flux, vertical velocity, and temperature perturbations.