THE SATURATION OF GRAVITY-WAVES IN THE MIDDLE ATMOSPHERE .4. CUTOFF OF THE INCIDENT WAVE SPECTRUM

A Doppler-spread theory for the saturation of middle atmosphere gravit y waves was presented in an earlier member of this sequence of papers. It employed a model in which a broad spectrum of waves subject to lin ear theory is incident from below. The spectral distribution (in verti cal wavenumber m) is deformed, as it propagates upward, in response to the growing importance of the Eulerian advective nonlinearity imposed on each wave by the total wave-induced wind. The deformation is such as to statistically spread the spectrum towards larger m, with the lar gest-m waves being progressively obliterated in quasi-critical-layer i nteractions. The model invoked a cutoff of the incident spectrum at a vertical wavenumber specified as lying in the range 0.5-1.0 times the local buoyancy frequency divided by the rms wind speed, with the choic e 0.5 being adopted tentatively. A qualitative argument for the chosen cutoff wavenumber was presented but was not supported by any more cer tain quantitative analysis at the time. The present paper derives an a nalytic form for the cutoff function, illustrates it in application, a nd provides quantitative support for a value possibly as low as 0.5 in the stratosphere and a value possibly as high as 1.0 in the mesospher e. In addition, it slightly recasts the heuristic approach to the Dopp ler-spread analysis, and it admits to certain difficulties, associated with the largest-m waves, whose circumvention appears to require a fa r more detailed analysis of wave-wave interaction through the advectiv e nonlinearity.