Gravity wave breaking has an important influence on both the momentum and the energy budget of the middle atmosphere. While the role of this process is generally accepted, many details of its development, from initial instabilities over turbulent exchange to a final mixed state, are not clear yet. From the theoretical perspective progress is hampered by the enormous range of scales involved. The most prominent gravity waves observed by radar or lidar measurements have horizontal wavelengths of a few 100 km, while their convective instabilities are strongest on scales of a few 10 m. For a complete representation a direct numerical simulation would have to bridge a gap of five orders of magnitude. Since this will, for purely technical reasons, not be possible within an overseeable time, additional methods might be useful. Here an interesting concept is the description of linear wave packets in a slowly-varying background state by an eikonal, WKB-type, approach. By focussing on the large-scale spatial and temporal dependence of local wave number and amplitude it highlights the essentials of propagating linear disturbances while keeping secondary details aside, thereby enabling an efficient description of small-scale features. The roots of this theory in the gravity-wave context go back to a seminal paper by Bretherton (1966) where a wave-activity conservation law has been derived which has later on been generalized further (Bretherton, 1971, Andrews and McIntyre, 1978).

Still, however, a practical theory for the wave amplitude in a background medium with a general space and time dependence does not exist yet. So is the above mentioned law still limited to background states with strictly horizontal flow and it applies not to fields with horizontal gradients in the stratification. Moreover, also divergent background flows are not included. Especially the first two of these limitations seem to be detrimental for a direct application to the propagation of small-scale disturbances in a large-scale gravity wave. With this in mind the presentation discusses the derivation of a general wave-amplitude equation (in the Boussinesq framework) for general convectively stable background fields with arbitrary spatial and time dependence in all components. The effects of friction and heating are included. The predictions of the new theory for the propagation of short gravity waves in a field given by long waves are compared to direct simulations by a spectral wave model resolving the short-wave packet in the long-wave background. Significant improvements over an application of the classical theory are found. In all cases examined there is a good agreement between the new eikonal model and the wave-packet resolving model.