Weakly nonlinear analysis of mean flow generation for tidally locked exoplanets

We study a model developed by Showman and Polvani [Equatorial superrotation on tidally locked exoplanets. Astrophys. J. 2011, 738, 71–94] to study the behaviour of a thin, upper atmospheric layer of a tidally locked exoplanet; in particular, the behaviour of the atmospheres of “hot Jupiters”, gas giants orbiting close to their stars and tidally locked to them, having a dayside and a nightside. We are interested in trying to elucidate the mechanism found by Showman and Polvani for the generation on such planets of an equatorial superrotation, ie. a rapid easterly current in the region about the equator. We extend their analysis of the two simple linear cases studied in the appendices of their paper by including the (small) nonlinear terms which then interact to generate mean flows. In the first of these cases, we expand about the small radiative time scale and find that the mean flow at the equator is eastward, This case may be particularly relevant for the hottest of tidally locked exoplanets. In the other case, we use a multiple parameter asymptotic expansion where the drag time scale is very large but much less than the reciprocal of the small amplitude scale of the expansion. In this case, we again find that the nonlinear terms generate a mean flow that is eastward at the equator. These results may help to provide a possible explanation for the equatorial superrotation.