▪ AbstractWe review the experimental evidence on turbulent flows over rough walls. Two parameters are important: the roughness Reynolds number ks+, which measures the effect of the roughness on the buffer layer, and the ratio of the boundary layer thickness to the roughness height, which determines whether a logarithmic layer survives. The behavior of transitionally rough surfaces with low ks+ depends a lot on their geometry. Riblets and other drag-reducing cases belong to this regime. In flows with δ/k ≲ 50, the effect of the roughness extends across the boundary layer, and is also variable. There is little left of the original wall-flow dynamics in these flows, which can perhaps be better described as flows over obstacles. We also review the evidence for the phenomenon of d-roughness. The theoretical arguments are sound, but the experimental evidence is inconclusive. Finally, we discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness element...

Turbulent flows over rough walls

An analytical solution is presented for the flow of an adiabatic turbulent boundary layer on a uniformly rough surface over a two-dimensional hump with small curvature, e.g. a low hill. The theory is valid in the limit L/y0 → ∞ when h/L 2k2/ln(δ/y0) where L and h are the characteristic length and height of the hump, y0 the roughness length of the surface and δ the thickness of the boundary layer. For rural terrain, taking δ ∼ 600m these conditions imply that 102 < L < 104m and h/L < 0·05. Considerations of the turbulent energy balance suggest that the eddy viscosity distribution for equilibrium flow near a wall may still be used to a good approximation to determine the changes in Reynolds stress. This result is only required in a thin layer adjacent to the surface - in the main part of the boundary layer the perturbation stresses are shown to be negligible and the disturbance to be almost irrotational. The theory shows that for a log-profile upwind the increase in wind speed near the surface of the hill is O((h/L)u0(L)) where u0(L) is the velocity of the incident wind at a height L. Thus the increase in surface winds can be considerably greater than is predicted by potential flow theory based on an upwind velocity u0(h). It is also found that, at the point above the top of a low hill at which the increase in velocity is a maximum, the velocity is approximately equal to the velocity at the same elevation above level ground upwind of the hill. The surface stress is highly sensitive to changes in the surface elevation, being doubled by a slope as small as one in five. The turning of the wind in the Ekman layer may induce a change in direction of the wind above the hill.

The main object of this analysis is to show how the changes in wind speed and shear stress are related to the size and shape of the hill and to the roughness of the surface. Some comparisons are made with measurements of the natural wind and wind tunnel flows. These suggest that the theory may be useful in giving rough estimates of the effect of hills on the wind. The theory and the quoted measurements suggest that the present design recommendation for the increase in wind speeds over hills to be used in wind loading calculations may be an underestimate. It is to be hoped that this analysis will encourage more detailed measurements to be made of the wind over hills.

Turbulent wind flow over a low hill

The bursting process in turbulent boundary layers provides new insight on turbulence phenomena, mechanics of sedimentation, and genesis of bedforms in natural geophysical flows. Recent visualization experiments suggest that the turbulent boundary layer can be divided into an inner zone, whose essential characteristics scale with inner (wall) variables, and an outer zone, whose properties scale with the fluid-dynamic variables of the entire flow. The inner zone is distinguished by (i) a viscous sublayer displaying spanwise alternations of high-and low-speed streaks and (ii) episodic disruption by lift-ups of low-speed streaks. Oscillatory growth and breakup stages of the Stanford model of bursting characterize the turbulent structure of the outer zone. The burst cycle exists in turbulent boundary layers of all natural flows except perhaps (i) open-channel flows in the upper part of the upper flow regime and (ii) wind-generated surface waves. Fluid motions described as kolks and boils in incompressible open-channel flows correspond to the oscillatory growth stage and the late oscillatory growth and breakup stages, respectively, of the Stanford model of bursting. Supporting evidence includes (i) close similarity of gross fluid motions, (ii) equivalent scaling of boils and bursts, and (iii) intensification of boils and bursts in adverse pressure gradients and over rough beds. McQuivey's (1973) turbulence measurements show that the Eulerian integral time scale T E scales with the same outer variables as boil periodicity and burst periodicity. It is hypothesized that T E equals the mean duration of bursts at a point in the flow. Bedforms governed by the turbulent structure of the inner zone (microforms) cannot form if the sublayer is disrupted by bed roughness. The conditions for the existence of two common microforms and their spacings scale with the inner variables. Grain roughness increases the vertical intensity of the turbulence (by enhancing lift-ups) within the inner zone, thereby explaining textural differences between the coarse ripple and fine ripple bed stages of Moss (1972). Mesoforms respond to the fluid-dynamical regime in the outer zone and scale with the outer variables. The mean spacing of dunelike large-scale ripples in equilibrium open-channel flows is proportional to the boundary-layer thickness and equals the length scale formed by the product of the free-stream velocity and the boil period. Strong upward flow in a burst provides the vertical anisotropy in the turbulence which is needed to suspend sediment. Bursting promotes the entrain-ment of more and coarser sediment than tractive forces alone can accomplish.

Sedimentological and fluid-dynamic implications of the turbulent bursting phenomenon in geophysical flows

This is a review of the mechanisms that control neutrally stable turbulent boundary-layer flow over hills and waves, their relative magnitudes, and how they exert their greatest effects in different regions of the flow. We compare calculations based on various analytical and computational models with each other and with relevant experimental data. We discuss practical applications of these studies.

Turbulent flow over hills and waves

This is the first of a series of three papers describing experiments on the dispersion of trace heat from elevated line and plane sources within a model plant canopy in a wind tunnel. Here we consider the wind field and turbulence structure. The model canopy consisted of bluff elements 60 mm high and 10 mm wide in a diamond array with frontal area index 0.23; streamwise and vertical velocity components were measured with a special three-hot-wire anemometer designed for optimum performance in flows of high turbulence intensity. We found that:

(i)

The momentum flux due to spatial correlations between time-averaged streamwise and vertical velocity components (the dispersive flux) was negligible, at heights near and above the top of the canopy.




(ii)

In the turbulent energy budget, turbulent transport was a major loss (of about one-third of local production) near the top of the canopy, and was the principal gain mechanism lower down. Wake production was greater than shear production throughout the canopy. Pressure transport just above the canopy, inferred by difference, appeared to be a gain in approximate balance with the turbulent transport loss.




(iii)

In the shear stress budget, wake production was negligible. The role of turbulent transport was equivalent to that in the turbulent energy budget, though smaller.




(iv)

Velocity spectra above and within the canopy showed the dominance of large eddies occupying much of the boundary layer and moving downstream with a height-independent convection velocity. Within the canopy, much of the vertical but relatively little of the streamwise variance occurred at frequencies characteristic of wake turbulence.




(v)

Quadrant analysis of the shear stress showed only a slight excess of sweeps over ejections near the top of the canopy, in contrast with previous studies. This is a result of improved measurement techniques; it suggests some reappraisal of inferences previously drawn from quadrant analysis.

H A Panofsky

Papers

The Atmospheric Boundary Layer Below 150 Meters