The energy spectra of the observed zonal flows on Jupiter and Saturn are shown to obey the scaling law EZ(n)5CZ(V/R)2n25 in the range of total wave numbers n not affected by large scale friction ~here, V and R are the rotation rate and the radius of the planet, and CZ is an order-one constant!. These spectra broadly resemble their counterpart in recent simulations of turbulent flows on the surface of a rotating sphere [Huang et al., Phys. Fluids 13, 225 ~2001] that represents a strongly anisotropic flow regime evoked by the planetary vorticity gradient. It is conjectured that this regime governs the large scale circulations and the multiple zonal jets on giant planets. The observed strong equatorial jets that were not produced in the nearly inviscid simulations by Huang et al. are attributed to the combined effect of the energy condensation in the lowest zonal modes and the large scale friction.