Spectral methods for atmospheric diffusion modeling

The rate of diffusion of a cloud depends on cloud dimensions. As the cloud enlarges, larger eddies come into play and the rate of diffusion increases. The turbulent diffusion process is scale-dependent. The gradient-transfer theory (K-theory) is only appropriate when the dimensions of the dispersed material are much larger than the size of the turbulent eddies. Introduction of a spectral turbulent diffusivity function (STD) makes it possible to treat the diffusive transport in a Eulerian system, with diffusivity effectively dependent on the actual size of the concentration distribution. The basic innovation is that diffusion is treated in the Fourier space and the diffusion coefficient is dependent on the wave number of the Fourier components of the concentration distribution. It is shown that the concept of the wave-number-dependent diffusivity leads to a non-local flux-gradient relation.