The Saturation of Gravity Waves in the Middle Atmosphere. Part II: Development Of Doppler-Spread Theory

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Abstract
The irregular winds of the middle atmosphere are commonly attributed to an upwardly propagating system of atmospheric gravity waves. Their one-dimensional (in vertical wavenumber m) power spectrum has been reported to exhibit a nearly universal behavior in its “tail” region of large m: both the form (∼m−3) and the intensity of the tail are approximately invariant with meteorological conditions, time, place and height. This universality is often described as resulting from “saturation” of the system, with the physical cause of saturation being left for separate identification and analysis. Here the cause is attributed to nonlinear interaction between the waves of the full spectrum, most specifically to the advective nonlinearity of the Eulerian fluid-dynamic equations. This nonlinearity has the effect of Doppler shifting the local intrinsic frequency of any given wave in the wind field imposed by all waves. Only an approximation to its effects is sought here, the wind field of the full spectrum be... Abstract The irregular winds of the middle atmosphere are commonly attributed to an upwardly propagating system of atmospheric gravity waves. Their one-dimensional (in vertical wavenumber m) power spectrum has been reported to exhibit a nearly universal behavior in its “tail” region of large m: both the form (∼m−3) and the intensity of the tail are approximately invariant with meteorological conditions, time, place and height. This universality is often described as resulting from “saturation” of the system, with the physical cause of saturation being left for separate identification and analysis. Here the cause is attributed to nonlinear interaction between the waves of the full spectrum, most specifically to the advective nonlinearity of the Eulerian fluid-dynamic equations. This nonlinearity has the effect of Doppler shifting the local intrinsic frequency of any given wave in the wind field imposed by all waves. Only an approximation to its effects is sought here, the wind field of the full spectrum be...

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