Gravity wave focusing in the middle atmosphere

We investigate effects of time-dependent wave-wave interactions on the propagation and dissipation of gravity wave energy in the middle atmosphere. By including wave motions in the effective background seen by a given member of the spectrum, the raytracing technique employed can represent strongly nonlinear interactions in which the frequency, wavenumber, and amplitude of a test wave vary significantly. Careful attention is paid to WKB considerations. Our inclusion of temporal as well as spatial variations in the background removes the inverse relationship between wave action density and vertical group velocity, which has been used in previous studies to restrict wave dissipation to critical approaches. Instead, Hayes' conservation equations for wave action density are used to directly calculate wave amplitude variation over the ray path. We show that as the model is made more realistic in representing the complexity typically observed in the gravity wave spectrum, wave action density variations become increasingly independent of wavenumber variations; the time-varying background fluctuations focus wave energy both when the wavenumber is increasing and when it is decreasing. Moreover, the resulting caustics are fundamentally different from those found in previous time-dependent studies using simpler quasi-monochromatic backgrounds. We examine ray solutions in a variety of background models to identify commonly observed features of the wind field that contribute to this focusing. These results suggest that wave dissipation may not be primarily restricted to critical approaches (even those of the spectrum-induced kind); and that temporal focusing may contribute significantly to wave drag in the middle atmosphere.