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.

我们研究了由 Showman 和 Polvani 开发的模型 [潮汐锁定系外行星上的赤道超旋转。天体物理学。J. 2011, 738, 71–94] 研究潮汐锁定系外行星的薄上层大气层的行为；特别是“热木星”大气的行为，气态巨行星靠近恒星运行并潮汐锁定它们，有白天和黑夜。我们有兴趣试图阐明 Showman 和 Polvani 发现的在此类行星上产生赤道超自转的机制，即。赤道附近地区的一股快速的东流。我们扩展了他们对论文附录中研究的两个简单线性案例的分析，包括了（小）非线性项，这些项随后相互作用以产生平均流量。在第一种情况下，我们扩展了小辐射时间尺度，发现赤道的平均流向东，这种情况可能与最热的潮汐锁定系外行星特别相关。在另一种情况下，我们使用多参数渐近扩展，其中拖动时间尺度非常大，但远小于扩展的小幅度尺度的倒数。在这种情况下，我们再次发现非线性项产生了赤道向东的平均流。这些结果可能有助于为赤道超旋转提供可能的解释。