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General circulation models of the atmosphere of hot Jupiters have shown theexistence of a supersonic eastward equatorial jet. In this paper, weinvestigate the effects of compressibility on the atmospheric dynamics bysolving the standard Euler equations. This is done by means of a series ofsimulations performed in the framework of the equatorial beta-planeapproximation using the finite volume shock-capturing code RAMSES. At lowresolution, we recover the classical results described in the literature: wefind a strong and steady supersonic equatorial jet of a few km/s that displaysno signature of shocks. We next show that the jet zonal velocity dependssignificantly on the grid meridional resolution. When that resolution is fineenough to properly resolve the jet, the latter is subject to a Kelvin-Helmholtzinstability. The jet zonal mean velocity displays regular oscillations with atypical timescale of few days and a significant amplitude of about 15% of thejet velocity. We also find compelling evidence for the development of avertical shear instability at pressure levels of a few bars. It seems to beresponsible for an increased downward kinetic energy flux, significantlyaffecting the temperature of the deep atmosphere, and appears to act as a formof drag on the equatorial jet. This instability also creates velocityfluctuations that propagate upward and steepen into weak shocks at pressurelevels of a few mbars. We conclude that hot Jupiter equatorial jets arepotentially unstable to both a barotropic Kelvin-Helmholtz instability and avertical shear instability. Upon confirmation using more realistic models, bothinstabilities could result in significant time variability of the atmosphericwinds, may provide a small scale dissipation mechanism in the flow, and mighthave consequences for the internal evolution of hot Jupiters.

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