Flow Over Hills

Abstract

We now move on to the next obstacle to understanding how the boundary layer behaves in general through the study of flow over ridges and hills. In Chapter 4 we examined simple changes in surface conditions and showed how their effects extend upwards with increasing downwind distance. The distinguishing features of the flow over those changes were a small perturbation in the pressure field and an internal boundary layer, the depth of which was controlled by turbulent diffusion from the new surface. Here, we confront not a change in surface properties but a change in surface elevation that forces large-scale changes in the pressure field. The response to this forcing is more complicated than any we have tackled so far, but the work of many scientists over the past 25 years gives us a measure of understanding of the processes involved. In addition to extending to hillsides the kind of analyses of wind and turbulence we have already presented, there are new questions that only arise in the context of hill flows. One, with ramifications for large-scale prediction of the weather and climate, is how much drag hills exert on the atmosphere flowing over them. For large hills and mountains this problem is dominated by the behavior of the internal gravity waves initiated by hills; over lower topography, however, it involves a subtle balance between changes in the surface stress distribution and the pressure field. In questions of wind turbine siting, understanding the position and magnitude of accelerations in the mean wind becomes crucial, whereas changes to both the mean wind and turbulence are important when predicting the fate of atmospheric pollutants in hilly terrain or estimating wind loads on buildings. The pattern of airflow around a hill is determined not only by the hill shape but also by its size. A characteristic feature of the atmosphere as a whole is its static stability, extending all the way to the ground at night-time and down to zi during the day. As a result, the vertical movement of air parcels that must occur as the wind flows over a hill is accompanied by a gravitational restoring force.