Neutral turbulent flow over forested hills

Numerical simulations of neutral, turbulent flow over periodic forested hills are carried out using a first-order turbulence closure scheme. The forest is represented by the inclusion in the model of a canopy near the surface where additional drag is exerted on the flow as a result of the trees. Simulations with a more traditional roughness-length parametrization of the surface, which does not explicitly model the flow within the forest, are also carried out for comparison. Comparison of simulations with existing wind-tunnel data shows that the simple mixing-length canopy closure scheme provides a good estimate of the mean flow over a forested hill and is a significant improvement on a traditional roughness-length parametrization in this case. The numerical results are seen to be in close agreement with existing linear analytical solutions for flow over a low and wide forested hill. The model is used to investigate the breakdown of the analytical solution when the hill becomes steep and the perturbations to the flow are no longer linear. Even in the case of a gentle slope, the analytical solution can break down when the hill is narrow or the canopy is deep and the vertical velocities near the top of the canopy become large. This leads to a downwind shift in the surface pressure perturbation and an enhanced drag compared to a roughness-length model. Model results also show enhanced flow separation in the presence of a canopy. These results are important for a range of meteorological problems including the interpretation of flux measurements, parametrization of orographic drag, predicting wind damage to trees and calculating the yield from wind turbines.