Tile cause of the fast zonal winds on the large gas planets is disputed. To
investigate their possible origin by convection in the planets' molecular
hydrogen layer, I study simple numerical models of thermal convection in a
rotating sphere at low Ekman numbers for Rayleigh numbers up to 100 times c
ritical. With stress-free boundaries and high Rayleigh number it is possibl
e to reproduce the observed magnitudes of tile zonal and non-zonal flow com
ponents at the surfaces of Jupiter and Saturn. While only three flow bands
are found for a thick convecting shell, the number increases to seven for a
shell with an inner-to-outer radius of 0.6.