The datasets on the forced two-dimensional turbulence on a rotating sphere obtained in our recent numerical experiments were analyzed to study the energy density distribution in the wavenumber space. Its dependence on two experimental parameters of the rotation rate and the forcing wavenumber is clarified.

Owing to the effect of rotation the upward energy cascade ceases around a characteristic total wavenumber $n_\beta$ at which the ``$\beta$-term'' is comparable to the nonlinear Jacobian term. The energy density of zonal components ( $m = 0$ ) is dominant in the range of $n \lsim n_\beta$ while the energy is very small in a segment-shaped region at the lower edge in the wavenumber space $(m,n)$. Anisotropic distribution of the energy is also found in high wavenumber region $n \gsim n_\beta$ ; the energy density decreases as the zonal wavenumber $m$ increases.

The flow field on the spherical geometry is projected on some tangential planes from the equator to the poles to compare the energy density distributions in two-dimensional wavenumber space with those obtained in some $\beta$-plane experiments. The energy distribution becomes anisotropic to have dominant zonal components as the local $\beta$-effect increases ( or, the tangential plane is put closer to the equator ). In the case on equatorial tangential planes, the region in which the energy density is very small shows a dumbbell shape indicating strong anisotropy.