Comments on the paper by C. S. Gardner, “Testing theories of atmospheric gravity wave saturation and dissipation”

Abstract

Gardner (1996, henceforth G96), examines a number of theories that seek to account for the vertical-wavenumber (m) spectrum of horizontal wind perturbations (u′) induced by gravity waves in the middle atmosphere. He notes that all the theories predict much the same spectra, and so he seeks to “identify the experimental data required to test the fundamental physics upon which these theories are based …” While I applaud Gardner's goal and will at a later stage contribute to it, I must first comment adversely on some aspects of his preliminary summaries and of his observational inferences. My remarks are limited almost exclusively to his discussion of the linear instability theory of Dewan and Good (1986, henceforth DG86) and Smith et al. (1987, henceforth SFV87), called by him the LIT, the diffusive filtering theory (DFT) of Gardner (1994, henceforth G94), and the Doppler spread theory (DST) initiated by Hines (1991b). In all of the theories under discussion, the u′ power spectral density (PSD) is taken in G96 to exhibit an increase with m at m values less than some characteristic value m∗ and a decrease, more-or-less proportional to m−3, in a ‘tail’ region at greater m values up to some upper limit mM, whereafter turbulence is said to set in. The transition at m∗ may be thought of, for convenience of discussion, as being abrupt, though each theory in fact either assumes or derives a smooth transition. The various theories differ from one another in the physical processes that are assumed to establish the tail portion of the spectrum, the tail's range in m, and the intensity of the PSD of the tail. That intensity has been said observationally to be invariant under changes of circumstance and height, a characteristic that is widely attributed to a ‘saturation’ of the spectrum or of the corresponding waves. The tail portion of the spectrum is therefore said by many to be saturated, though the theory of G94 purports to disagree with this concept and in fact provides possible alternatives to the m−3 form (as, indeed, does DG86). The LIT, DFT and DST will be discussed below in sequence.