Circulation and Dissipation on Hot Jupiters

TL;DR

This paper investigates the hydrodynamic dissipation mechanisms in hot Jupiter atmospheres, revealing turbulence and shocks as key factors in wind speed regulation, and emphasizes the importance of including artificial dissipation in simulations.

Contribution

It combines linear analysis and nonlinear simulations to identify turbulence and shocks as primary dissipation processes, highlighting the need for explicit dissipation terms in global models.

Findings

Wind speeds saturate at Mach ~2 and Richardson number ~1/4.

Turbulence and shocks dominate dissipation, driven by Kelvin-Helmholtz instability.

Limited resolution in simulations can lead to overestimated wind speeds.

Abstract

Many global circulation models predict supersonic zonal winds and large vertical shears in the atmospheres of short-period jovian exoplanets. Using linear analysis and nonlinear local simulations, we investigate hydrodynamic dissipation mechanisms to balance the thermal acceleration of these winds. The adiabatic Richardson criterion remains a good guide to linear stability, although thermal diffusion allows some modes to violate it at very long wavelengths and very low growth rates. Nonlinearly, wind speeds saturate at Mach numbers $\approx 2$ and Richardson numbers $\lesssim 1/4$ for a broad range of plausible diffusivities and forcing strengths. Turbulence and vertical mixing, though accompanied by weak shocks, dominate the dissipation, which appears to be the outcome of a recurrent Kelvin-Helmholtz instability. An explicit shear viscosity, as well as thermal diffusivity, is added to ZEUS to capture dissipation outside of shocks. The wind speed is not monotonic nor single valued for shear viscosities larger than about $10^{-3}$ of the sound speed times the pressure scale height. Coarsening the numerical resolution can also increase the speed. Hence global simulations that are incapable of representing vertical turbulence and shocks, either because of reduced physics or because of limited resolution, may overestimate wind speeds. We recommend that such simulations include artificial dissipation terms to control the Mach and Richardson numbers and to capture mechanical dissipation as heat.