A stochastic model of gravity-wave-induced clear-air turbulence

We examine the consequences of using a vertical wavenumber spectral model to describe variations of vertical profiles of atmospheric variables (horizontal and vertical wind, temperature, and other scalars) about a mean profile. At high wavenumbers the model exhibits a wavenumber to the -3 dependence, which is characteristic of a continuum of internal gravity waves whose amplitudes are controlled by a breaking process. By employing a random phase between wavenumber amplitude components, a reverse Fourier transform of the spectrum yields simulated profiles of velocity and thermal variability as well as shear and Brunt-Vaisala frequency variability. Individual components of the vertical shear of the horizontal wind and the Brunt-Vaisala frequency exhibit Gaussian distributions; the square of the magnitude of the shear exhibits a Rice-Nakagami distribution. Assuming regions with Ri