Shear-driven instabilities and shocks in the atmospheres of hot Jupiters

Abstract

Context. General circulation models of the atmosphere of hot Jupiters have shown the existence of a supersonic eastward equatorial jet. These results have been obtained using numerical schemes that filter out vertically propagating sound waves and assume vertical hydrostatic equilibrium, or were acquired with fully compressive codes that use large dissipative coefficients. Aims. We remove these two limitations and investigate the effects of compressibility on the atmospheric dynamics by solving the standard Euler equations. Methods. This was done by means of a series of simulations performed in the framework of the equatorial β-plane approximation using the finite-volume shock-capturing code RAMSES. Results. At low resolution, we recover the classical results described in the literature: we find a strong and steady supersonic equatorial jet of a few km s −1 that displays no signature of shocks. We next show that the jet zonal velocity depends significantly on the grid meridional resolution. When this resolution is fine enough to properly resolve the jet, the latter is subject to a Kelvin-Helmholtz instability. The jet zonal mean velocity displays regular oscillations with a typical timescale of a few days and a significant amplitude of about 15% of the jet velocity. We also find compelling evidence for the development of a vertical shear instability at pressure levels of a few bars. It seems to be responsible for an increased downward kinetic energy flux that significantly affects the temperature of the deep atmosphere and appears to act as a form of drag on the equatorial jet. This instability also creates velocity fluctuations that propagate upward and steepen into weak shocks at pressure levels of a few mbars. Conclusions. We conclude that hot-Jupiter equatorial jets are potentially unstable to both a barotropic Kelvin-Helmholtz instability and a vertical shear instability. Upon confirmation using more realistic models, these two instabilities could result in significant time variability of the atmospheric winds, may provide a small-scale dissipation mechanism in the flow, and might have consequences for the internal evolution of hot Jupiters.

Atmospheric Circulations of Hot Jupiters as Planetary Heat Engines

“…Such a damping length could be either due to a horizontal Kelvin-Helmholtz instability or due to the steepening of day-night standing waves into shocks. We note that the shock-resolving simulations in Fromang et al (2016) also found a dominant scale for horizontal shear instabilities of L a 2 5 p , and are thus consistent with our results. The upper end of our wind speed estimate is additionally consistent with the bulk flow becoming supersonic, and thus prone to dissipation via shocks ( Figure 5).…”

Atmospheric Circulation of Hot Jupiters: Dayside–Nightside Temperature Differences. II. Comparison with Observations

“…As in Perez-Becker & Showman (2013), they showed that the combined effects of increasing relative efficacy of radiative cooling and increasing drag strength can explain the increase in dayside-nightside temperature contrast with increasing equilibrium temperature, as both mechanisms damp wave adjustment processes. This drag is likely due to either Lorentz forces in an ionized atmosphere threaded by a dipolar magnetic field (Perna et al 2010;Batygin et al 2013;Rauscher & Menou 2013;Rogers & Komacek 2014;Rogers & Showman 2014) or smallscale instabilities (Li & Goodman 2010;Youdin & Mitchell 2010;Fromang et al 2016), including shocks, which largely are expected to occur on the dayside of the planet (Heng 2012;Fromang et al 2016). However, Komacek & Showman (2016) found that drag only affects dayside-nightside temperature differences if it occurs on a characteristic timescale much shorter than the rotation period of the planet.…”

Hot Jupiter atmospheric flows at high resolution

“…Our T85 and T127 runs do reach the latitudinal regime at which one might expect the dynamical transition witnessed by Fromang et al (2016) to manifest. However, as exemplified in the lower two panels of Figure 2, even at high resolution, we do not find any evidence for the oscillatory/cyclic behavior of the equatorial regions reported by Fromang et al (2016).…”

“…These results are worth discussing in the context of the study of Fromang et al (2016), who find a transition to a markedly different regime of circulation at latitudinal resolutions in excess of 64-128 cell elements (see their Figure 4). Our T85 and T127 runs do reach the latitudinal regime at which one might expect the dynamical transition witnessed by Fromang et al (2016) to manifest. However, as exemplified in the lower two panels of Figure 2, even at high resolution, we do not find any evidence for the oscillatory/cyclic behavior of the equatorial regions reported by Fromang et al (2016).…”

“…While we know and have an understanding of what drives winds in these atmospheres (Showman & Polvani 2011;Hammond & Pierrehumbert 2018), the dominant form of dissipation for wind kinetic energy is still the subject of intense debate. Indeed new physics is at play in these atmospheres: shocks (Li & Goodman 2010;Dobbs-Dixon & Agol 2013;Fromang et al 2016) MHD effects (Batygin & Stevenson 2010;Perna et al 2010;Menou 2012;Thorngren & Fortney 2018) and vertical transport (Menou 2019) could all play a role in limiting the wind speeds on these planets.…”