A Simplified Radiative-Dynamical Model for the Static Stability of Rotating Atmospheres

Abstract In order to obtain estimates of the static stability in rotating atmospheres without performing numerical integrations of the equations of motion, a simple model is developed in which the radiative flux of heat is assumed to be balanced by the fluxes of sensible beat and potential energy due to large-scale eddies. The radiative flux divergence is modeled by a linearization about the radiative equilibrium state and the dynamical fluxes are modeled by calculating correlations from stability theory and by assuming that the amplitudes are limited by nonlinear effects. From the energy equation a single algebraic equation is derived for the mean equilibrium value of the Richardson number, Ri, in the troposphere. The radiative equilibrium state is assumed to be known. Once the solution for RI is found, the mean vertical and meridional gradients of potential temperature, 〈∂θ/∂z〉 and 〈∂θ/∂y〉, and the main properties of the mean zonal wind and eddies can be easily calculated. Even though many important flu...