Diffusion of gaussian puffs

Abstract A formula for the relative diffusion of a puff is proposed in which the rate of growth is related to common, one‐dimensional velocity spectra obtainable, for instance, from direct measurements in the atmosphere. Often, an equation of this type is in demand for modelling of instant or short‐term release of potentially harmful gases or smoke, for example, in connection with a puff diffusion model. A simple expression like Taylor's equation for single‐particle diffusion is not obtainable in general for relative diffusion. Therefore, the present approach is based on a kinematic‐statistical model in which a Gaussian approximation has been applied to the relative displacement process of the fluid particles. This is along lines suggested previously, where the expansion of a Gaussian puff has been related to the kinematic energy spectrum in three‐dimensional, isotropic turbulence. Here, however, we attempt to relate the growth rate directly to the one‐dimensional velocity spectra (or their corresponding correlations) most commonly available in the atmosphere. In particular, this is of value for the surface layer, where diffusions in the horizontal and vertical directions are different (anisotropy) due to the presence of the ground. Experimental evaluation is based on a series of smoke release experiments carried out in the surface layer over homogeneous terrain in Denmark. Solutions of the puff growth rate equation with the measured correlations are found to compare well with the experimental data of cross‐wind relative diffusion over the limited scale of the experiments.