Note on Spectral Diffusivity Theory

Abstract

The diffusion equation with a wavenumber-dependent diffusivity is derived as an approximation to the statistical theory of plume dispersion from a continuous point source. The travel time explicitly appearing in the statistical theory is implicitly included in the wavenumber-dependent diffusivity K(k). By suitable choice of this function it is possible within a few percent to reproduce the centerline concentration. Due to the approximate nature of the method, however, it yields a non-Gaussian concentration shape close to the source. Results for the case of a crosswind extended source are compared to other commonly used methods for this problem. Some considerations are presented on the proper choice of averaging time for the concentration field.