# A random walk model for dispersion in inhomogeneous turbulence in a convective boundary layer

- Authors
- Type
- Published Article
- Journal
- Atmospheric Environment (1967)
- Publisher
- Elsevier
- Publication Date
- Jan 01, 1989
- Volume
- 23
- Issue
- 9
- Pages
- 1911–1924
- Identifiers
- DOI: 10.1016/0004-6981(89)90516-7
- Source
- Elsevier
- Keywords
- License
- Unknown

## Abstract

It is necessary for a random walk model to satisfy the well-mixed criterion which requires that if particles of a tracer are initially well mixed in the ambient fluid they will remain so. Models applied so far to dispersion in a convective boundary layer where the turbulence is inhomogeneous and skew require a non-Gaussian random forcing and do not satisfy this well-mixed condition. In this work a random walk model is developed based on the approach of Thomson (1987, J. Fluid Mech. 180,529–556) which satisfies the well-mixed condition, incorporates skewness in the vertical velocity and has Gaussian random forcing. The skewed probability distribution function (PDF) equation of Baerentsen and Berkowicz (1984, Atmospheric Environment 18, 701–712) is used to derive the model equation. The model is applied to diffusion in a convective boundary layer. The validity of the closure assumption that σ A = w ̄ A and σ b = w ̄ A , where σ A and σ B are the updraft and downdraft velocity standard deviations, respectively and w ̄ A and w ̄ B are the mean updraft and downdraft velocities, respectively, is analyzed quantitatively with the measured values of various statistical parameters involved in the PDF equation. Results reveal that the assumption is quite satisfactory. The new model is general and reduces to the one-dimensional model equations of Wilson et al. (1983, Boundary-Layer Met. 27,163–169) and Thomson (1987, J. Fluid Mech. 180, 529–556) when the turbulence is Gaussian without any mean flow, and to the basic Langevin equation when the turbulence is homogeneous. Predictions are made for the dimensionless crosswind integrated concentrations, mean particle height, and particle spread for three source heights and three step sizes. The comparison of the model results with laboratory measurements of Willis and Deardorff(1976, Q. Jl R. met. Soc. 102,427–445; 1978, Atmospheric Environment 12,1305–1311; 1981, Atmospheric Environment 15,109–117) and the random walk results of de Baas et al. (1986, Q. Jl R. met. Soc. 112,165–180) and Sawford and Guest (1987, J. atmos. Sci. 44,1152–1165) in which the models require non-Gaussian random forcing, shows that the new model simulates the experimental features quite well. The particle distribution becomes homogeneous after X≈6. The maximum ground level concentrations are better predicted by the new model.