The flow in a turbulent boundary layer upstream of a change in surface roughness

Modification of a turbulent flow upstream of a change in surface roughness has been studied by means of a stream function-vorticity model.A flow reduction is found upstream of a step change in surface roughness when a fluid flows from a smooth onto a rough surface. Above that layer and above the region of flow reduction downstream of a smooth-rough transition, a flow acceleration is observed. Similar flow modification can be seen at a rough-smooth transition with the exception that flow reduction and flow acceleration are reversed. Within a fetch of –500 < x/z ₀< + 500 (z ₀ is the maximum roughness length, the roughness transition is located at x/z ₀ = 0), flow reduction (flow acceleration) upstream of a roughness transition is one order of magnitude smaller than the flow reduction (flow acceleration) downstream of a smooth-rough (rough-smooth) transition. The flow acceleration (flow reduction) above that layer is two orders of magnitude.The internal boundary layer (IBL) for horizontal mean velocity extends to roughly 300z ₀ upstream of a roughness transition, whereas the IBL for turbulent shear stress as well as the distortion of flow equilibrium extend almost twice as far. For the friction velocity, an undershooting (overshooting) with respect to upstream equilibrium is predicted which precedes overshooting (undershooting) over new equilibrium just behind a roughness transition.The flow modification over a finite fetch of modified roughness is weaker than over a corresponding fetch downstream of a single step change in roughness and the flow stays closer to upstream equilibrium. Even in front of the first roughness change of a finite fetch of modified roughness, a distortion of flow equilibrium due to the second, downwind roughness change can be observed.