Dispersion of a dense cylindrical cloud in a turbulent atmosphere

Abstract

This paper describes the development of a simple analytical dense gas model. It calculates the height, radius, and instantaneous concentration within a drifting cloud. The initial state is a cylinder of gas of arbitrary aspect ratio. Upon release, the cylinder collapses due to its excess density. The collapse generates internal turbulence which entrains air and dilutes the cloud. Within the core or central part of the cloud, top entrainment controls concentration decay. The core concentration decays as t −1 (where t denotes time). Side entrainment generates a radial transition zone between the radially uniform core and the atmosphere. The core radius increases due to gravitational slumping and is eroded by side entrainment. Both the vertical and radial transition zones are chosen to be Gaussian. As the gravitational collapse continues, self-generated turbulence grows weaker. Internal turbulence, and hence entrainment, then becomes proportional to the ambient atmospheric turbulence divided by the Richardson number Ri where Ri is large and decreasing. This causes a vertical growth proportional to t 2 of the relatively thin disk. Gravitational slumping continues to maintain the radial growth such that R 2∼ t ( R is the mean radius of cloud). Hence, concentration decays as t −3. As Ri falls below the critical value Ri c, the core vanishes and there is a smooth and gradual transition to a Gaussian puff description of the cloud. The nondimensional concentration is shown to be primarily a function of non-dimensional time and a characteristic Richardson number. In addition to predicting the concentration field, the model calculates the cloud position as it accelerates from rest due to momentum entrainment from the ambient wind. Four data sets are used to calibrate and evaluate the model. The data are derived from laboratory studies at the University of Arkansas and at Colorado State University and from field studies at Porton Down and Thorney Island. The initial volumes of the gas clouds span eight orders of magnitude. Uncertainty of physical measurements and model estimates is discussed in detail. A mechanism for comparing modelled and measured concentrations (the ratio method) is used to quantify the uncertainty in a concentration estimate. Components of uncertainty are examined (inherent, model, observational, and input).