Turbulent diffusion from a point source in stratified and neutral flows around a three-dimensional hill—part I. Diffusion equation analysis

Abstract

In stable stratified flow around three dimensional hills vertical motion and vertical diffusion is negligible. Consequently turbulent diffusion from a point source can be modelled by considering horizontal flow and horizontal diffusion. Using an eddy diffusivity the advective diffusive equation around a three dimensional hill which is axisymmetric about a vertical axis is solved to show how source positions on and off the centre line affect the trajectories and splitting of impinging plumes and the value and position of the maximum surface concentration on the hill. In the second part of the paper we analyse a plume in a neutrally stable potential flow around an axisymmetric obstacle such as a hemisphere, also using the diffusion equation. The solutions show how, because streamlines approach the surface of a 3-dimensional hill much more closely than the surface of a 2-dimensional hill, the maximum surface concentrations on the hill can become very much greater than in the absence of the hill. But this only occurs for a limited range of source heights.