Wave-mean Flow Interactions in the Atmospheric Circulation of Tidally Locked Planets

Abstract

We use a linear shallow-water model to investigate the global circulation of the atmospheres of tidally locked planets. Simulations, observations, and simple models show that if these planets are sufficiently rapidly rotating, their atmospheres have an eastward equatorial jet and a hot-spot east of the substellar point. We linearize the shallow-water model about this eastward flow and its associated height perturbation. The forced solutions of this system show that the shear flow explains the form of the global circulation, particularly the hot-spot shift and the positions of the cold standing waves on the night-side.We suggest that the eastward hot-spot shift seen in observations and 3D simulations of these atmospheres is caused by the zonal flow Doppler-shifting the stationary wave response eastwards, summed with the height perturbation from the flow itself. This differs from other studies which explained the hot-spot shift as pure advection of heat from air flowing eastward from the substellar point, or as equatorial waves travelling eastwards. We compare our solutions to simulations in our climate model Exo-FMS, and show that the height fields and wind patterns match.We discuss how planetary properties affect the global circulation, and how they change observables such as the hot-spot shift or day-night contrast. We conclude that the wave-mean flow interaction between the stationary planetary waves and the equatorial jet is a vital part of the equilibrium circulation on tidally locked planets.

The Atmospheric Circulation of Ultra-hot Jupiters

“…We are also interested in the effects of hydrogen dissociation and recombination on the detailed circulation pattern. At a first glance, the horizontal wind fields at 70 mbar shown in Figure 1 are qualitatively similar between simulations without and with hydrogen dissociation, and most of them exhibit an eastward equatorial jet with the characteristic off-equatorial Rossby waves and equatorial Kelvin waves driven by day-night forcing (e.g., Showman & Polvani 2011, Tsai et al 2014, Hammond & Pierrehumbert 2018. However, at very high equilibrium temperature (T eq 3200 K), the eastward equatorial jets at 70 mbar in simulations with hydrogen dissociation are significantly weakened and even disappears at T eq = 3600 K, while those in simulations without hydrogen dissociation are still well preserved.…”

“…It is likely that the wave dynamics depends on various other parameters in addition to rotation, which could all be affected by changing the equilibrium temperature. Indeed, in the context of shallow water systems (Showman & Polvani 2011, Hammond & Pierrehumbert 2018, the forced-damped wave solutions are affected by the radiative forcing, frictional drag, and rotation, all of which determine the effective deformation radius. Including effects of hydrogen dissociation could only increase the complexity of wave dynamics.…”

Temporal Variability in Hot Jupiter Atmospheres

“…In general, the large-scale equatorial standing wave pattern drives this circulation , Rauscher & Menou 2010, Showman & Polvani 2011, which is known as a Gill pattern in the Earth tropical dynamics literature (Matsuno 1966, Gill 1980). This planetary-scale equatorial standing wave ("Gill") pattern is analogous to those in Earth's tropics in that it is comprised of equatorial Rossby and Kelvin wave modes (Showman & Polvani 2010, 2011, Tsai et al 2014, Hammond & Pierrehumbert 2018. These waves are triggered by the large day-to-night forcing contrast on the planet, and are damped by radiative cooling and frictional drag (Perez-Becker & Showman 2013, Komacek & Showman 2016.…”

A New Line-by-line General Circulation Model for Simulations of Diverse Planetary Atmospheres: Initial Validation and Application to the Exoplanet GJ 1132b

“…Moreover, the longitudinal tilting of the hotspot correlates well with this equatorial super-rotating jet, because the hotspot shift is the consequence of atmospheric dynamics. Previous studies suggested that the eastward hotspot shift is caused by the equatorial super-rotating jet (e.g., Zhang & Showman 2017;Hammond & Pierrehumbert 2018), with Zhang & Showman (2017) focusing on the heat advection by the equatorial super-rotating jet and Hammond & Pierrehumbert (2018) focusing on the Doppler-shifting stationary wave response. Note that until now theoretical work has only been done in the shallowwater framework.…”