Rough-Wall Turbulent Boundary Layers
01 Jan 1991-Applied Mechanics Reviews (American Society of Mechanical Engineers)-Vol. 44, Iss: 1, pp 1-25
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TL;DR: In this article, the authors reviewed progress in urban climatology over the two decades since the first publication of the International Journal of Climatology (IJC) and highlighted the role of scale, heterogeneity, dynamic source areas for turbulent fluxes and the complexity introduced by the roughness sublayer over the tall, rigid roughness elements of cities.
Abstract: Progress in urban climatology over the two decades since the first publication of the International Journal of Climatology is reviewed. It is emphasized that urban climatology during this period has benefited from conceptual advances made in microclimatology and boundary-layer climatology in general. The role of scale, heterogeneity, dynamic source areas for turbulent fluxes and the complexity introduced by the roughness sublayer over the tall, rigid roughness elements of cities is described. The diversity of urban heat islands, depending on the medium sensed and the sensing technique, is explained. The review focuses on two areas within urban climatology. First, it assesses advances in the study of selected urban climatic processes relating to urban atmospheric turbulence (including surface roughness) and exchange processes for energy and water, at scales of consideration ranging from individual facets of the urban environment, through streets and city blocks to neighbourhoods. Second, it explores the literature on the urban temperature field. The state of knowledge about urban heat islands around 1980 is described and work since then is assessed in terms of similarities to and contrasts with that situation. Finally, the main advances are summarized and recommendations for urban climate work in the future are made. Copyright © 2003 Royal Meteorological Society.
2,723 citations
Cites background from "Rough-Wall Turbulent Boundary Layer..."
...…buildings of different heights and physical characteristics, separated by trees, canyons and open spaces, makes it particularly susceptible to the development of a roughness sublayer of significant depth, perhaps several times the average building height (Raupach et al., 1980, 1991; Roth, 2000)....
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TL;DR: In this article, the mean velocity profile is inflected, second moments are strongly inhomogeneous with height, skewnesses are large, and second-moment budgets are far from local equilibrium.
Abstract: ▪ Abstract The single-point statistics of turbulence in the ‘roughness sub-layer’ occupied by the plant canopy and the air layer just above it differ significantly from those in the surface layer. The mean velocity profile is inflected, second moments are strongly inhomogeneous with height, skewnesses are large, and second-moment budgets are far from local equilibrium. Velocity moments scale with single length and time scales throughout the layer rather than depending on height. Large coherent structures control turbulence dynamics. Sweeps rather than ejections dominate eddy fluxes and a typical large eddy consists of a pair of counter-rotating streamwise vortices, the downdraft between the vortex pair generating the sweep. Comparison with the statistics and instability modes of the plane mixing layer shows that the latter rather than the boundary layer is the appropriate model for canopy flow and that the dominant large eddies are the result of an inviscid instability of the inflected mean velocity profi...
1,484 citations
TL;DR: In this article, the authors review the experimental evidence on turbulent flows over rough walls and discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness element.
Abstract: ▪ 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...
1,389 citations
TL;DR: In this paper, several methods to determine the aerodynamic characteristics of a site through analysis of its surface form (morphometry) are considered in relation to cities, including zero-plane displacement length (zd), roughness length(z0), depth of the roughness sublayer, and aerodynamic conductance.
Abstract: Several methods to determine the aerodynamic characteristics of a site through analysis of its surface form (morphometry) are considered in relation to cities. The measures discussed include zero-plane displacement length (zd), roughness length (z0), depth of the roughness sublayer, and aerodynamic conductance. A sensitivity analysis is conducted on seven formulas to estimate zd and nine to estimate z0, covering a wide range of probable urban roughness densities. Geographic information systems developed for 11 sites in 7 North American cities are used to characterize their morphometry—the height, shape, three-dimensional area, and spatial distribution of their roughness elements (buildings and trees). Most of the sites are in residential suburbs, but one is industrial and two are near city centers. This descriptive survey of urban geometric form is used, together with the morphometric formulas, to derive the apparent aerodynamic characteristics of the sites. The resulting estimates of zd and z0 a...
1,108 citations
Cites background from "Rough-Wall Turbulent Boundary Layer..."
...The magnitude of zr is thought to depend on the height and spatial arrangement of the elements (for a review see Raupach et al. 1991; Claussen 1995)....
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...Typical values of frontal area index are in the range 0.1– 0.25 for crops and about 1–10 for forests (Raupach et al. 1991)....
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...Comparing these urban z0 values with those of natural surfaces given by other tables of typical roughness (e.g., Oke 1987; Stull 1988; Raupach et al. 1991; Garratt 1992; Wieringa 1993) confirms that cities and forests are near the top end of the scale....
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...Raupach et al. (1991) note that surveys of measured coefficients give f d ; 0.64 and f 0 ; 0.13 for field crops and grass canopies and f d ; 0.8 and f 0 ; 0.06 for forests....
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...However, as Raupach et al. (1991) note, even over less heterogeneous terrain than cities, windbased estimates (especially profile methods) are known to be inaccurate....
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TL;DR: In this paper, the authors argue that the active turbulence and coherent motions near the top of a vegetation canopy are patterned on a plane mixing layer, because of instabilities associated with the characteristic strong inflection in the mean velocity profile.
Abstract: This paper argues that the active turbulence and coherent motions near the top of a vegetation canopy are patterned on a plane mixing layer, because of instabilities associated with the characteristic strong inflection in the mean velocity profile. Mixing-layer turbulence, formed around the inflectional mean velocity profile which develops between two coflowing streams of different velocities, differs in several ways from turbulence in a surface layer. Through these differences, the mixing-layer analogy provides an explanation for many of the observed distinctive features of canopy turbulence. These include: (a) ratios between components of the Reynolds stress tensor; (b) the ratio K H /K M of the eddy diffusivities for heat and momentum; (c) the relative roles of ejections and sweeps; (d) the behaviour of the turbulent energy balance, particularly the major role of turbulent transport; and (e) the behaviour of the turbulent length scales of the active coherent motions (the dominant eddies responsible for vertical transfer near the top of the canopy). It is predicted that these length scales are controlled by the shear length scale L s = U(h)/U′(h) (where h is canopy height, U(z) is mean velocity as a function of height z, and U′ = dU/dz). In particular, the streamwise spacing of the dominant canopy eddies Λ x = mL s , with m = 8.1. These predictions are tested against many sets of field and wind-tunnel data. We propose a picture of canopy turbulence in which eddies associated with inflectional instabilities are modulated by larger-scale, inactive turbulence, which is quasi-horizontal on the scale of the canopy.
1,094 citations