  The surface winds of Jupiter and Saturn are primarily zonal. Each planet
exhibits strong prograde equatorial flow flanked by multiple alternating zonal
winds at higher latitudes. The depth to which these flows penetrate has long
been debated and is still an unsolved problem. Previous rotating convection
models that obtained multiple high latitude zonal jets comparable to those on
the giant planets assumed an incompressible (Boussinesq) fluid, which is
unrealistic for gas giant planets. Later models of compressible rotating
convection obtained only few high latitude jets which were not amenable to
scaling analysis.
  Here we present 3-D numerical simulations of compressible convection in
rapidly-rotating spherical shells. To explore the formation and scaling of
high-latitude zonal jets, we consider models with a strong radial density
variation and a range of Ekman numbers, while maintaining a zonal flow Rossby
number characteristic of Saturn.
  All of our simulations show a strong prograde equatorial jet outside the
tangent cylinder. At low Ekman numbers several alternating jets form in each
hemisphere inside the tangent cylinder. To analyse jet scaling of our numerical
models and of Jupiter and Saturn, we extend Rhines scaling based on a
topographic $\beta$-parameter, which was previously applied to an
incompressible fluid in a spherical shell, to compressible fluids. The
jet-widths predicted by this modified Rhines length are found to be in
relatively good agreement with our numerical model results and with cloud
tracking observations of Jupiter and Saturn.

Earth and Planetary Astrophysics;Fluid Dynamics;Geophysics