  A new formulation of the spectral energy budget of kinetic and available
potential energies of the atmosphere is derived, with spherical harmonics as
base functions. Compared to previous formulations, there are three main
improvements: (i) the topography is taken into account, (ii) the exact
three-dimensional advection terms are considered and (iii) the vertical flux is
separated from the energy transfer between different spherical harmonics. Using
this formulation, results from two different high resolution GCMs are analyzed:
the AFES T639L24 and the ECMWF IFS T1279L91. The spectral fluxes show that the
AFES, which reproduces realistic horizontal spectra with a k^{-5/3} inertial
range at the mesoscales, simulates a strong downscale energy cascade. In
contrast, neither the k^{-5/3} vertically integrated spectra nor the downscale
energy cascade are produced by the ECMWF IFS.
