Coupled Analytical Model for the Internal Boundary Layer Height, Wall Shear Stress and Mean Velocity Behind a Surface Roughness Transition in Boundary-Layer Flow

Abstract

A coupled analytical framework is developed to predict the internal boundary layer (IBL) height, wall shear stress and the mean velocity profile downstream of a surface roughness transition in a neutral atmospheric boundary-layer. The new model combines a three-layer analytical velocity formulation with a modified diffusion analogy for the IBL growth rate. The diffusion analogy links the growth rate of the IBL to turbulent diffusion and to mean vertical advection. Our formulation rectifies physical inconsistencies in a previous model that assumed that the turbulent diffusion is controlled only by the upstream surface conditions and that the characteristic streamwise velocity difference caused by streamline displacement is independent of downstream distance from the roughness transition. Key model parameters, namely the turbulent diffusion coefficient and the eddy viscosity augmentation coefficient, are modelled as functions of the upstream-to-downstream aerodynamic roughness length ratio. The coupled model, along with three other analytical models, is tested against twelve datasets covering a wide range of roughness ratios, including wind-tunnel experiments and large-eddy simulations. The new model accurately predicts wall shear stress, mean velocity, and IBL height for all combinations of upstream and downstream roughness values evaluated, for both smooth-to-rough and rough-to-smooth transitions.