A Critical Comparison of Theories of Gravity Wave Saturation

Abstract

The vertical-wavenumber (m) power spectral density (PSD) of irregular winds in the middle atmosphere often or even usually exhibits a large-m “tail” region with a log-log slope of about -3 and with an intensity that is roughly invariant under changes of meteorological conditions, time, location and even height (despite the intrinsic growth with height anticipated for individual waves in response to the diminishing gas density). This “saturated” portion of the PSD is usually represented by the form AN2m-3, where N2 is the atmospheric stability (buoyancy frequency squared) and A is a constant typically found to lie well within the range 0.1 < A < 1.0. (See and compare, for example, Dewan et al. (1984), Wu and Widdel (1989) and Tsuda et al. (1989).) At vertical wavenumbers less than some transitional value m*, the PSD is variable with conditions and grows with height -- i.e., is “unsaturated”, with m* decreasing as height increases to provide continuity of PSD through the transition (e.g., Tsuda et al. (1989)). The present paper is concerned with theoretical attempts to explain the characteristic behavior of the saturated portion of the spectrum, assuming the spectrum to be produced by gravity waves. It should be noted, however, that some datasets (e.g., Wilson et al. (1991) and Beatty et al. (1992)) yield large-m portions of the spectrum with slopes that remain relatively constant but appreciably different from -3, and/or with intensities that may increase with height; a successful theory may have to explain this behavior as well, otherwise than by claiming that the relevant PSDs are unsaturated.