The focusing of gravity-wave energy by a gravity-wave spectrum

The vertical distribution of the mean-flow acceleration contributed by gravity waves is of primary importance to the study of middle-atmosphere circulation. There remain significant uncertainties regarding the non-conservative processes that determine this distribution. One point of consensus is that these processes are profoundly sensitive to the environment through which the wave energy propagates. Waves rising through the middle atmosphere encounter not only large vertical variations in the large-scale flow, but also substantial fluctuations due to numerous other waves, which vary both spatially and temporally. We have demonstrated, using raytracing techniques, that a wave's response to this combination is fundamentally different in character from its response to simpler background fields. It is distinct from the simple refractive behaviour that occurs in a steady background featuring mean shear. It is also completely different from the response to a single quasi-monochromatic wave, or any combination of such ``pairwise'' interactions. In particular, as the background spectrum becomes broader, the action density variations appear to lose all semblance of a simple relationship with vertical group speed. One consequence of this complexity is that wave energy is focused in some regions and times, and defocused in others. Unlike the steady-background case, the focusing events are not confined to the neighbourhood of critical approaches, where the vertical wavenumber becomes large. Our results suggest a highly inhomogeneous field of wave energy density, with both critical and non-critical opportunities for wavebreaking throughout a broader vertical region, compared to theories that are based on simpler approximations to the observed flow field. We have identified commonly observed features of the atmospheric winds that contribute to non-critical focusing. We examine these effects in a variety of models, with a view to understanding how non-critical focusing contributes to wavebreaking and momentum-flux divergence in the middle atmosphere. This mechanism for mean-flow acceleration has not been included in existing gravity-wave-drag parameterizations.