Three-Dimensional Structures of Equatorial Waves and the Resulting Super-Rotation in the Atmosphere of a Tidally Locked Hot Jupiter

Abstract

Three-dimensional equatorial trapped waves excited by stellar isolation and the resulting equatorial superrotating jet in a vertical stratified atmosphere of a tidally-locked hot Jupiter are investigated. Taking the hot Jupiter HD 189733b as a fiducial example, we analytically solve linear equations subject to stationary stellar heating with a uniform zonal-mean flow included. We also extract wave information in the final equilibrium state of the atmosphere from our radiative hydrodynamical simulation for HD 189733b. Our analytic wave solutions are able to qualitatively explain the three-dimensional simulation results. Apart from previous wave studies, investigating the vertical structure of waves allows us to explore new wave features such as the wavefronts tilts related to the Rossbywave resonance as well as dispersive equatorial waves. We also attempt to apply our linear wave analysis to explain some numerical features associated with the equatorial jet development seen in the general circulation model by Showman and Polvani. During the spin-up phase of the equatorial jet, the acceleration of the jet can be in principle boosted by the Rossby-wave resonance. However, we also find that as the jet speed increases, the Rossby-wave structure shifts eastward, while the Kelvin-wave structure remains approximately stationary, leading to the decline of the acceleration rate. Our analytic model of jet evolution implies that there exists only one stable equilibrium state of the atmosphere, possibly implying that the final state of the atmosphere is independent of initial conditions in the linear regime. Limitations of our linear model and future improvements are also discussed.

Results from a set of three-dimensional numerical experiments of a hot Jupiter atmosphere

“…Therefore, to analyse the transport of momentum in the atmosphere we shift to using height, z, as a vertical coordinate. The simulations of Tsai et al (2014), however, are performed using a height-based model, and the results interpolated onto a pressure Table 2 for explanation of simulation names). In terms of AAM conservation the Std Full simulation is representative of our simulation set, and the remaining three included simulations (Std Prim, Deep ∆T eq→pole and Reduced p max ) the only examples where AAM conservation is much poorer.…”

“…The remaining important terms can be classified as mean flow terms involving the zonal velocity paired with either the meridional or vertical flow (− (ρv u cos 2 φ) ,φ r cos 2 φ , − (ρw ur 3 ) ,r r 3 ), or the mean Coriolis terms derived from the contributions of the Coriolis terms of the momentum equations (+2Ωρv sin φ, −2Ωρw cos φ). Tsai et al (2014) test the presence in their simulations, of the proposed pumping mechanism of Showman & Polvani (2011) in the context of the β-plane where the Coriolis parameter is assumed to vary linearly with latitude (as opposed to ∝ cos φ). Tsai et al (2014) present figures of the meridional and vertical eddy momentum transport (strictly the divergence of the eddy momentum fluxes), supporting an eddy-driven jet, although they do not present contributions from mean flow terms.…”

“…The equations and simulations of Showman & Polvani (2011) are, however, based on the primitive equations of motion (a simplified version of the equations of motion for an atmosphere, see Mayne et al 2014a, for a full discussion in relation to hot Jupiters), incorporating the assumption of vertical hydrostatic equilibrium, a shallow atmosphere and constant gravity. Further testing of this mechanism has been performed using results from a more dynamically complete model by Tsai et al (2014). Tsai et al (2014) adopt the β-plane approximation and investigate the momentum fluxes in 3D, in an assumed steady state.…”

“…Further testing of this mechanism has been performed using results from a more dynamically complete model by Tsai et al (2014). Tsai et al (2014) adopt the β-plane approximation and investigate the momentum fluxes in 3D, in an assumed steady state. In the β-plane approximation the Coriolis force is taken to vary linearly with latitude, φ (actual variation is ∝ cos φ).…”

Atmospheric Electrification in Dusty, Reactive Gases in the Solar System and Beyond

“…The coupling between the (slow) planetary rotation and the temperature differential results in the development of a broad, supersonic, super-rotating equatorial jets (Tsai et al 2014). Gas velocities at pressure levels of 0.1 bars in the wellknown HD189733b can reach 5 km/s (e.g., Dobbs-Dixon and Agol 2013).…”