A Stochastic Model of Gravity-Wave-Induced Clear-Air Turbulence

Abstract

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?Väisälä frequency variability. Individual components of the vertical shear of the horizontal wind and the Brunt?Väisälä frequency exhibit Gaussian distributions; the square of the magnitude of the shear exhibits a Rice?Nakagami distribution. Assuming regions with Ri < 0.25 are turbulent, we can examine a number of aspects of the occurrence of clear-air turbulent breakdown in the stratified free atmosphere. For a typical tropospheric condition, the average turbulent layer thickness turns out to be about 35 m and about 20% of the troposphere appears to be actively turbulent. The majority of the turbulent layers appear to be due to autoconvective overturning instead of Kelvin-Helmholtz dynamic instability. Computations of profiles of the refractive index structure function parameter, Cn2, and the rate of dissipation of turbulent kinetic energy, ?, are found to be quite sensitive to the assumptions of the relationship of turbulent length scale to layer thickness, the growth of turbulent layers after breakdown, and the threshold sensitivity and sampling strategy of measurement systems (e.g., clear-air radar).