A new surface boundary condition for LES over a rough-to-smooth transition: experimental and numerical tests

Understanding the effects of surface roughness transitions on the spatial distribution of surface shear stress and velocity is key to improving prediction of turbulent transport in the atmospheric boundary layer (ABL). For example, large-eddy simulations (LESs) rely on the application of Monin-Obukhov similarity theory (the log law under neutral conditions) to calculate the local surface shear stress as a function of the resolved velocity field. However, this approach is questionable since it is valid only over homogeneous surfaces. Improvement of this boundary condition in simulations of ABL flow over heterogeneous surfaces requires a better understanding of the effects of surface roughness transitions on the relation between surface shear stress and velocity fields. Motivated by this, a simple new model is proposed to predict the distribution of wind velocity and surface shear stress downwind of a rough-to-smooth surface transition. The model estimates the wind velocity as a weighted average between two limiting logarithmic profiles: the first log law, which is recovered above the internal boundary layer height, corresponds to the upwind velocity profile; the other log law is adjusted to the downwind aerodynamic roughness and local surface shear stress, and it is recovered near the surface, in the equilibrium sublayer. The proposed non-linear form of the weighting factor is equal to ln(z/z₀₁)/ln(δ_i/z₀₁), where z, δ_i and z₀₁ are the elevation of the prediction location, the internal boundary layer height at that downwind distance, and the upwind surface roughness, respectively. The performance of the new model is tested with our wind tunnel measurements and also with the field data of Bradley (1968). Compared with other existing analytical models, the proposed model gives improved predictions of both surface shear stress and velocity distribution at different positions downwind of the transition. A posteriori tests using LES with different boundary conditions show that the new model gives improved predictions of both velocity and surface shear stress distributions compared with the standard log-law formulation. In addition, these results show little sensitivity to grid resolution.