  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.
