The Saturation of Gravity Waves in the Middle Atmosphere. Part I: Critique of Linear-Instability Theory

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. Of current theories as to physical cause, the most fully developed and widely employed assumes that saturation results from linear instability: that the waves of the tail grow in amplitude with height (in response to the decrease of atmospheric density) until the system as a whole, or each portion of its tail, is rendered unstable and prevented from growing further. Initially the form and then the intensity of the tail are said to result from this process. The arguments in favor of this view are questioned in the present paper and found wanting (though the claim of instability remains unchallenged and is even reinforced). The waves of the tail are then recognized as being subject to a strong wave?wave interaction arising from the Eulerian advective nonlinearity?from the Doppler shifts that can be imposed upon them by the larger-scale winds of the wave system?a fact recognized in the corresponding oceanographic literature for about a decade now. In a companion paper, a rudimentary analytic approximation to the advective nonlinearity is introduced, and its consequences are shown to yield a spectral form and intensity quite similar to those obtained observationally. The linear instabilities (and some formulas) of the present paper are then invoked to establish the length, rather than the form and intensity, of the tail, at least below the turbopause.