Irradiated Atmosphere V: Effects of Vertical-Mixing induced Energy Transport on the Inhomogeneity

Abstract: Atmospheric variations over time and space boost planetary cooling, as outgoing internal flux responds to stellar radiation and opacity. Vertical mixing regulates this cooling. Our study examines how gravity waves or large-scale induced mixing interact with radiation transfer, affecting temperature inhomogeneity and internal flux. Through the radiative-convective-mixing equilibrium, mixing increases temperature inhomogeneity in the middle and lower atmospheres, redistributing internal flux. Stronger stellar radiation and mixing significantly reduce outgoing flux, slowing cooling. With constant infrared (IR) opacity, lower visible opacity and stronger mixing significantly reduce outgoing flux. Jensen's inequality implies that greater spatial disparities in stellar flux and opacity elevate the ratio of the average internal flux in inhomogeneous columns relative to that in homogeneous columns. This effect, particularly pronounced under high opacity contrasts, amplifies deep-layer temperature inhomogeneity and may enhance cooling. However, with mixing, overall cooling is weaker than without, as both the averaged internal flux of the inhomogeneous columns and that of the homogeneous column decline more sharply for the latter. Thus, while vertical mixing-induced inhomogeneity can enhance cooling, the overall cooling effect remains weaker than in the non-mixing case. Therefore, vertical mixing, by regulating atmospheric structure and flux, is key to understanding planetary cooling.