The atmospheric gravity wave energy spectra often show power law dependencies with wavenumbers and frequencies. A simple mechanism involving off-resonant scale-separated interactions is proposed for their formation, namely the refraction of the wave packets in pseudorandom shears encountered during their vertical propagation. In the Boussinesq and rotating frame approximation the evolution of the spectral distribution of wave action is calculated within the eikonal formalism, i.e., via the simulation of the ray paths for an ensemble of elementary wave packets. The energy spectra are then easily built from the wave action spectra. Experiments are conducted where wave packets propagate away from Dirac delta function, or spectrally uniform sources at low altitudes, in realistic atmospheric background flows. The energy spectra show dependencies with the vertical wavenumber m and horizontal wavenumber k that are consistent with the most widely recognized empirical spectral models. A specific focus is given on the vertical evolution of the vertical wavenumber spectrum. The spectrum shows an invariant scaling as N²/m³ at large wavenumbers. It possesses a central wavenumber whose value depends on the total wave energy and is controlled by the statistics of the background mean flow. Similarly, the wave packet azimuths show an increasingly strong anisotropy resulting from the wave mean flow interaction at critical levels.