The effect of wind shear on horizontal spread from an instantaneous ground source

Abstract

The medium range spread of a cloud of material released in a turbulent wind is considered theoretically. Attention is directed to the effect of systematic wind shear with height to see whether this may be important. It is shown that there are two cases, according to whether the height to which the material may rise is effectively bounded or not. In the first case when the height is bounded, the situation is in essentials the same as for flow in a pipe (Taylor 1953, 1954). After a sufficient length of time, the horizontal spread is described by a diffusivity which is the linear sum of two components, one representing the effect of horizontal turbulent fluctuations of the wind, and the other the effect of an interaction between the systematic wind shear and the vertical transport of material by the turbulence. For given mean wind profile, the latter effect is proportional in an inverse way to the coefficient of vertical diffusion. In the second case, when the material may rise to any height, it is shown that the horizontal spread cannot be described, in general, by a constant diffusivity, and that the horizontal mean-square spread or dispersion does not increase linearly with the time. However, the horizontal fluctuations and the interaction of wind shear with vertical transport still contribute independently to the horizontal dispersion. It is found that the interaction effect now depends in a direct way on the coefficient of vertical diffusion. It is also concluded that for medium-range diffusion the effect of the interaction of wind shear with vertical transport is dominant.