Simple model of the wave pattern in the atmosphere of a slow rotating planet due to surface irregularities

Abstract

Recent observations show a persistent pattern on Venus surface, interpreted as a stationary wave due to the interaction of the prevailing winds with the orography of the planet. In this work we use an idealized model of the phenomenon that allows for a fully analytical solution applied to a slow rotating planet with idealized obstacles. We use Venus as a testing case. Taking advantage of the high Rossby number of the atmospheric flow in Venus we model the velocity as potential and solve the stationary shallow-water equations on a sphere, in which a base flow is perturbed by the orography. The corresponding Green function is derived and the atmosphere thickness perturbation obtained as a convolution with the terrain height distribution. Delta-like terrain distributions give thus explicit expressions of the atmosphere height pattern, that can be translated into temperature variations to be compared with observations in the case of Venus. In particular, it is found that the height perturbation due to a localized obstacle has a longitudinal extension related to the latitudinal extension of the base flow, and quantified in terms of a latitudinal variable related to latitude in a non-linear way.