  The banded structures observed on the surfaces of the gas giants are
associated with strong zonal winds alternating in direction with latitude. We
use three-dimensional numerical simulations of compressible convection in the
anelastic approximation to explore the properties of zonal winds in rapidly
rotating spherical shells. Since the model is restricted to the electrically
insulating outer envelope, we therefore neglect magnetic effects.
  A systematic parametric study for various density scaleheights and Rayleigh
numbers allows to explore the dependence of convection and zonal jets on these
parameters and to derive scaling laws.
  While the density stratification affects the local flow amplitude and the
convective scales, global quantities and zonal jets properties remain fairly
independent of the density stratification. The zonal jets are maintained by
Reynolds stresses, which rely on the correlation between zonal and
cylindrically radial flow components. The gradual loss of this correlation with
increasing supercriticality hampers all our simulations and explains why the
additional compressional source of vorticity hardly affects zonal flows.
  All these common features may explain why previous Boussinesq models were
already successful in reproducing the morphology of zonal jets in gas giants.
