A Numerical Computation of Air Flow over a Sudden Change of Surface Roughness

Abstract

This paper deals with a numerical study of the influence of changes in surface roughness on the turbulent boundary layer in the lower layer of the atmosphere under neutral conditions. The whole set of equations governing the flow is solved by a finite-difference method. The turbulent energy equation is included to provide a better understanding of turbulent mechanisms. The pressure gradient is treated implicitly. Computational results agree well with Bradley's observations. A local minimum of surface stress is found at a short distance from the edge (dividing line) in the case of smooth-to-rough transition. Two boundary layers, a velocity layer and a stress layer, are found. The height of the velocity layer is about one-half that of the stress layer. Both layers follow the 4/5 power law. The height-to-fetch ratio for the internal boundary layer is found to be about 1/10 for the stress and 1/20 for the velocity. The height-to-fetch ratio for a new nearly equilibrium layer is about 1/100 for the smooth-to-rough case and 1/200 for the rough-to-smooth case far downwind. The stress is close to the upstream value for the upper portion of the transition layer. An inflection point of the velocity profile occurs in the transition region. The non-dimensional wind shear is significantly different from the value of unity which exists in an equilibrium flow.