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A new formulation of the spectral energy budget of kinetic and availablepotential energies of the atmosphere is derived, with spherical harmonics asbase functions. Compared to previous formulations, there are three mainimprovements: (i) the topography is taken into account, (ii) the exactthree-dimensional advection terms are considered and (iii) the vertical flux isseparated from the energy transfer between different spherical harmonics. Usingthis formulation, results from two different high resolution GCMs are analyzed:the AFES T639L24 and the ECMWF IFS T1279L91. The spectral fluxes show that theAFES, which reproduces realistic horizontal spectra with a k^{-5/3} inertialrange at the mesoscales, simulates a strong downscale energy cascade. Incontrast, neither the k^{-5/3} vertically integrated spectra nor the downscaleenergy cascade are produced by the ECMWF IFS.

A new formulation of the atmospheric spectral energy budget, with application to two high-resolution general circulation models