Turbulence-driven thermal and kinetic energy fluxes in the atmospheres of hot Jupiters

We have performed high resolution $3-$dimensional compressible hydrodynamics simulations to investigate the effects of shocks and turbulence on energy transport into hot Jupiter atmospheres, under a variety of shear gradients. We focus on a local atmospheric region to accurately follow the small-scale structures of turbulence and shocks. We find that the effects of turbulence above and below a shear layer are different in scale and magnitude: below the shear layer, the effects of turbulence on the vertical energy transfer are local, generally $\lesssim2~\times(\text{scale height})$. However, turbulence can have a spatially and thermally-large influence on almost the entire region above the shear layer. We also find that shock formation is local and transient. Once the atmosphere becomes steady, the time-averaged heat energy flux at $P\sim 1$ bar is insignificant, on the order of 0.001\% of the incoming stellar flux with a shear motion at $P\sim 1$ mbar, and 0.1\% with a deeper shear layer at $P\sim 100$ mbar. Accordingly, the diffusion coefficient is higher for the deeper shear layer. Therefore, our results suggest that turbulence near less dense regions ($P\sim 1$ mbar) does not cause a sufficiently deep and large penetration of thermal energy to account for radius inflation in hot Jupiters, regardless of how violent the turbulence is. However, as the shear layer gets deeper, heat energy transfer becomes more effective throughout the atmosphere (upwards and downwards) due to a larger kinetic energy budget. Therefore, it is more important how deep turbulence occurs in the atmosphere, than how unstable the atmosphere is for effective energy transfer.