The theoretical scattering of smoke in a turbulent atmosphere

Abstract

The fundamental result of G. I. Taylor’s paper, “ Eddy Motion in the Atmosphere,” is that the scattering in a turbulent atmosphere of suspended matter, or diffusion of potential temperature, may be regarded as analogous to the diffusion of heat in a solid ; on this theory every point in the atmosphere possesses a coefficient of eddy-diffusion, K, which may vary from point to point, and which may further differ for diffusion in different directions at any one point, analogous to the diffusion of heat in crystalline substances. For the case in which K is the same at every point in the atmosphere the density of suspended matter, x gms. per cm. 3 , must satisfy the differential equation :— (∂/∂ t + u ∂/∂ x + v ∂/∂ y + w ∂/∂ z ) x = K∇ 2 x , where u, v, w are the components of mean velocity of the air. The purpose of this paper is to obtain solutions of (1) applicable to several methods of artificial smoke production, viz. : (A) A puff of smoke due to the instantaneous generation of matter at a point; (B) A smoke-cloud produced continuously and uniformly at a fixed point in a uniform wind ; (C) A smoke-cloud produced continuously and uniformly along an unlimited straight line perpendicular to the direction of a uniform wind.