A wind tunnel study of turbulent flow over a two-dimensional ridge

Abstract

We present a wind-tunnel simulation of adiabatic atqospheric flow normal to a rough, twodimensional ridge. The data are analyzed in physical streamline coordinates, which are described in some detail. The mean velocity speed-up on the hill top is adequately predicted by existing formulae while the behaviour of the wake flow fits into a pattern that emerges from other wind-tunnel experiments. The turbulent stresses evolve in response to the extra strain rates induced by the hill, streamline curvature and acceleration: 3 is coupled strongly to acceleration while z and 7 follow curvature. These differing responses lead to significant phase differences between the changes in the component stresses as the hill is traversed. An analogous response is seen in the components of turbulent stress divergence, which are computed as part of streamwise momentum budgets. Only very close to the surface is turbulent stress divergence comparable to the inertial and pressure terms in the momentum budget; over most of the flow regime, the mean flow response is approximately inviscid. Finally, we compare our results with data from other wind tunnel models and from real hills.

Measurements of Flows Over Isolated Valleys

“…There is thus very little detailed data available on the way on which the hill affects the characteristics of the upstream flow. However, the experiments of Finnigan et al (1990) showed that at the upstream edge of an isolated hill of height 0.1δ the velocity 'speed-down' at z/H = 0.1 (with H here equal to the hill height) was about 13%, similar to the levels of speed-up seen for the valleys discussed here.…”

“…The perturbation pressure field will undoubtedly extend upstream so one expects to see an increase in near surface velocities upstream of the valley. The effects are illustrated by the 'inverse' case of flow over an isolated hill, as discussed by Finnigan et al (1990), for example, who show an increase in surface pressure as the hill is approached (see below). For steeper hills or valleys, but still not steep enough (for the valley case) to promote separation, the effect will be greater.…”

The height of maximum speed-up in the atmospheric boundary layer flow over low hills

“…3. The agreement is only acceptable for the BR(max), BR(min), Black Mountain and Finnigan et al (1990) wind tunnel data. Mickle et al (1988), Beljaars and Taylor (1989) and Taylor and Walmsley (1996) has come up with this same conclusion, except for the wind tunnel data, which was not included in their works.…”

“…Kaimal and Finnigan (1994) point out that, as a hill is scaled down to fit into a wind tunnel, the surface roughness (grass, heather, stones) usually shrinks too much to satisfy the aerodynamically fully rough condition that ensure flow similarity. This fact, widely recognized in the literature (Britter et al, 1981;Gong and Ibbetson, 1989;Finnigan et al, 1990), reduces the applicability of such measurements. As Athanassiadou and Castro (2001) observe, 'Laboratory experiments … concentrate on flow that is not always fully rough and, as a result, not directly applicable to the atmosphere.'…”

“…Another possibility is to use fully rough models to represent hills covered with rather tall vegetation. Finnigan et al (1990) and Gong and Ibbetson (1989) report measurements of this kind and their results are included here. These measurements add data to the 'rough surface end' of the range, as Figures 2-4 show.…”