Analysis of the Relation Between Doppler Spectral Width and Thunderstorm Turbulence

Abstract

A technique to separate ordered flow in a tornadic thunderstorm from the random velocities associated with turbulence is described. The relative importance of the ordered flow shear and turbulence in the broadening of the Doppler velocity spectrum is evaluated by least-squares fitting an assumed linear model of radial velocities to measured ones over an angular analysis domain (about 3° in azimuth and 3° in elevation). Fields and cumulative probabilities of Doppler spectral widths associated with turbulence and velocity shear, of root-mean-square (rms) velocity residuals, and of the turbulent kinetic energy dissipation rates ? are presented. In order to estimate ? from measurements of Doppler spectral width, the outer scale of the inertial subrange of turbulence must be at least three times larger than the size of the radar's resolution volume. Wind fields synthesized from the Doppler data of two radars are related to the turbulent kinetic energy dissipation rate and rms velocity residual fields. The observed relationship between wind gradients, rms residuals, and dissipation rates suggests the expected cascade of turbulent kinetic energy as it moves from the largest length scales down to the smallest. Within this storm, turbulence contributed much more to spectral broadening than ordered flow shear. However, in a very small portion of the storm, shear and nonturbulent eddies are responsible for nearly all spectral broadening. Fifty percent of the volume of this tornadic storm had ? larger than 0.1 m2 s?3.