Atmospheric turbulent boundary layer development due to a change in surface roughness

The turbulent wind flow passing from a surface of one roughness to another is investigated analytically. The wind flow is modelled by a deep atmospheric turbulent boundary layer that assumes the possibility of self-preserving development in the course of flow modification. Closed form solutions are obtained describing the entire flow development and the characteristics of the wind velocity, surface stress changes and frictional velocity changes. It is found that as the wind flows past the roughness discontinuity, the flow adapts to the new surface roughness through adjustment by a vertical displacement of streamlines. This leads to a change in boundary layer thickness and the length of the acceleration region, in which the adjustments depend obviously on the difference in roughness between the new and the original region. By including the effect of frictional velocity and higher-order terms, the theory also shows that a greatly different value of shear stress is possible in the new regime, as opposed to what Townsend [J. Fluid Mech. 26 (1966) 255] has predicted.