Saturated and unsaturated spectra of gravity waves and scale- dependent diffusion

Abstract

For a highly idealized condition, the spectrum of saturated and unsaturated gravity waves at each height is calculated directly from the wave equation. A principal feature is the inclusion of wave dissipation, although in an approximate form. In the absence of wave absorption, reflection, radiation, wind shears, resonant wave-wave interactions and other sources and sinks, this dissipation at each height is determined solely by the "turbulent' or chaotic state caused by off-resonant wave-wave interactions and instability of the (broad) wave spectrum at that height. The dissipation is approximately accounted for by a diffusion term. The appropriate diffusivity is self-consistent with the continuum of spectral waves that cause the chaotic state and is argued to be scale dependent. -from Author