# The Effect of a Group of Obstacles on a Flow and Dispersion over a Surface

Thesis

In this thesis we develop analytical models for boundary layer flow through a two dimensional group of obstacles , based on the "distributed force" model. An array of obstacles is represented as a region without solid obstructions but with distributed body forces resisting the flow. Linear analyses are presented of inviscid, laminar (or constant eddy viscosity) and turbulent flow through such force distributions. For any group of obstacles, we show how to calculate the model force distribution which becomes the input for the linear analyses. The entire procedure can be iterated to take account of non-linear upstream sheltering effects. In general the model distributed force integrates to equal the actual force exerted by obstacles on the flow divided by the fraction of the array volume not occupied by solid obstacles. Turbulent stresses are modelled using a mixing length that is uniform up to a specified height and increases linearly above. Our physical arguments for a displaced mixing length above the obstacles provide an explanation for the observed coincidence between displacement height and the level of mean momentum absorption. Comparisons of the turbulent analysis results with numerical simulations and experimental data show very encouraging agreement and so support both the distributed force model and the assumptions of the mathematical analysis. From the results of the turbulent flow analysis, effective roughness and displacement heights can be calculated for the flow above the obstacles. When the displacement of the turbulent mixing length is correctly taken into account, the calculated parameters are comparable with those obtained experimentally. An analysis of plume dispersion through a group of obstacles shows how the flow field results can be applied to practical situations, and highlights the dominant effect of enhanced perturbation shear stress, especially in the obstacle roof top layer, on changes to the downstream evolution of the plume.