Stratified and turbulent wind flow over two-dimensional topographies : a numerical model

Typescript (photocopy).A method for analyzing a two-dimensional flow over non-uniform surfaces has been developed. The method of analysis includes: (1) the development of a general transformation in which variable spacing in the streamwise and vertical directions is provided by a geometric point distribution with different initial spacing; (2) an exploration into a family of finite difference methods suitable for solving atmospheric lee-wave problems; and (3) the development of a turbulence model for stratified flow. The turbulence model consists of a k-(epsilon) model of turbulence and two empirical algebraic models relating stratified turbulent exchange coefficients to the neutrally stable exchange coefficients. The numerical models developed have been employed to investigate three problems involving the wind flow over different surface topographies. These problems are: (1) turbulent atmospheric flow in a neutrally stable condition; (2) laminar stratified atmospheric and channel flow in which the external forcing functions are the surface topography and potential temperature nonhomogeneity; and (3) turbulent stratified atmospheric flow over surface topographies. It has been found that as the flow becomes more subcritical (F(,r) < 1/(pi)), the maximum speed-up ratio occurs further downstream of the topography crest. Furthermore, for stratified turbulent atmospheric flow, the speed-up ratio not only decreases with a decrease in densimetric Froude number but also with an increase in the roughness element sizes. The results have been found to be in good agreement with both experimental and numerical results of other researchers. The amplitude of the predicted waves is approximately the same order of magnitude as the obstacle height. The present model predicts a break down in the flow for a subcritical densimetric Froude numbers that are less than or equal to 0.070. High values of velocity and potential temperature resulted at the lee of the topography for a F(,r) < 0.070. The numerical models developed have been applied to isolated topographies but they can easily be modified to study flow over multiple two-dimensional topographies (analytic topographies) and other phenomena, such as the heat island