Diffusive filtering theory of gravity wave spectra in the atmosphere

The author presents an alternative to proposed mechanisms explaining horizontal wind gravity wave vertical wavenumber spectra by assuming that the damping effects of molecular viscosity, turbulence, and off-resonance wave-wave interactions can be characterized in terms of a scale-independent diffusivity (D) which increases with altitude. A wave of intrinsic frequency ω and vertical wave number m is assumed to be completely damped when the effective vertical velocity of momentum diffusion (mD) exceeds the vertical phase velocity of the wave (ω/m). Only waves satisfying mD < ω/m, or equivalently m²D < ω and m < ω/D)^1/2 are permitted to grow in amplitude as they propagate upward in the atmosphere. If the gravity wave temporal spectrum of horizontal winds varies as ω^-p, we show that the vertical wave number spectrum must vary as m^-2p+1 and the zonal (or meridional) wave number spectrum must vary as k^-(2p+1)/3. The spectra are proportioinal to ω^-p, m^-3 and k^{-(3p-1)/(p+1)}. Because the joint (m, ω) intrinsic spectra for both scale-independent and scale-dependent diffusive filtering are not separable, the theory predicts that the m spectra of vertical winds are proportional to m^5-2p for scale-independent diffusion and m(^7-3p)/(p-1) for scale-dependent diffusion. -from Author