Modification of mean flow and turbulent energy by a change in surface roughness under conditions of neutral stability

A theory is developed which describes the adjustment of the flow of a hydrostatically neutral fluid in the lower portion of a fully-turbulent boundary layer, after an abrupt change in surface roughness. The model is based on the hypothesis that the horizontal shear stress is proportional to the turbulent energy. The theory postulates that the flow is primarily governed by the dominant terms of the horizontal-momentum, continuity, and turbulent-energy equations. The model was solved by numerical techniques on a digital computer. Unlike previous models there are no a priori assumptions about the distribution of velocity or stress, the behaviour of the nondimensional wind shear, mixing length, or momentum-exchange coefficient in the transition region. The theory, in contrast to earlier theories, suggests the distribution of turbulent energy, as well as velocity. An inflection point is predicted in the transition velocity-profile. The nondimensional wind shear is found to differ significantly from unity in the transition region. These predictions agree with observation.