A wind-tunnel boundary-layer study of the effects of a surface roughness change: Rough to smooth

The changes imposed on mean velocities and turbulence statistics in the lower atmosphere by an abrupt change in surface roughness, from very rough to smooth, were modelled in a wind tunnel. The influence of a change in the effective surface level, which often accompanies such a variation in surface roughness, was also studied. A deep, turbulent flow was generated upstream of the change, which had a logarithmic mean velocity profile and constant shear-stress for approximately 200 mm above the floor, except for a region near the surface which was influenced by the three-dimensional nature of the random rough surface.When the surface roughness change coincided with a change in surface level, the downstream flow close to the surface was in the wake of the upstream roughness elements, and measured Reynolds shear-stress values were lower than those obtained when the downstream surface was raised. Otherwise, the influence of a change in surface level was small.In all cases, Reynolds shear-stress varied approximately linearly with height in the lower two-thirds of the internal layer and no constant stress region was apparent near the surface, even 2 m downstream of the roughness change. When the roughness change was not accompanied by a change in level, Reynolds shear-stress values extrapolated to the surface agreed well with surface shear-stress inferred from the law of the wall.Changes in mean squares of vertical and lateral velocity fluctuations and in integral time scales, as the flow passed downstream of the roughness change, were surprisingly small.     

Surface drag and turbulence over an inhomogeneous land surface

Data collected over an inhomogeneous semi-rural area are presented. The data are compared with previous surface-layer data to determine how representative the fixed-point flux measurements are of area averages. Departures from the standard surface-layer results are found to be relatively small (~10–20%), which supports the concept of a blending height above which the flow ceases to respond to variations in the underlying surface and becomes horizontally homogeneous.Effective roughness lengths are derived for different wind directions and the relationship between the effective roughness length and upwind surface is examined in the light of recent ideas on averaging surface roughness lengths. It is found that by averaging drag coefficients, realistic values of the effective roughness length can be calculated which are not very sensitive to the precise choice of the component roughness lengths.     

Studies on critical Reynolds number indices for wind-tunnel experiments on flow within urban areas

Reynolds-number dependence of flow fields within a modelled urban area was studied in a wind tunnel. We measured flow around a single model building and around model city blocks at various wind speeds, and studied Reynolds number indices more appropriate than the building Reynolds number. Our results led to the following conclusions. Firstly, the flow around the models in the wind tunnel was roughly divided into three parts according to the intensities of viscous stress and Reynolds stress as follows: (1) the flow in the vicinity of the ground or the surfaces of the model, where viscous stress became dominant under certain conditions; (2) the flow detached from the surfaces of the model, where Reynolds stress was always dominant; and (3) the flow around the separation bubble at the leading edge of the building model, where the influences of both viscous stress near the wall and the Reynolds stress in the separated boundary layer were mixed.Secondly, the critical Reynolds number of the flow in the modelled urban area could be defined by using both the roughness Reynolds number Re_z0 (= z₀u_*/) and the dimensionless height z₊ (= zu_*/). Reynolds-number independence could be expected for whole flow fields in the modelled urban areas as long as the critical values of Re_z0 and z₊ were satisfied.     

Numerical modeling of the nocturnal urban boundary layer

A numerical case study with a second-order turbulence closure model is proposed to study the role of urban canopy layer (UCL) for the formation of the nocturnal urban boundary layer (UBL). The turbulent diffusion coefficient was determined from an algebraic stress model. The concept of urban building surface area density is proposed to represent the UCL. Calculated results were also compared with field observation data. The height of the elevated inversion above an urban center was simulated and found to be approximately twice the average building height. The turbulent kinetic energy k, energy dissipation rate , and turbulence intensities u ² and w ² increase rapidly at the upwind edge of the urban area. The Reynolds stress uw displayed a nearly uniform profile inside the UBL, and the vertical sensible heat flux w had a negative value at the inversion base height. This indicates that the downward transport of sensible heat from the inversion base may play an important role in the formation of the nocturnal UBL.     

On the memory of wind standard deviation for upstream roughness

Big eddies in the outer part of the atmospheric boundary layer contribute to the variance of the horizontal velocity fluctuations near the surface. Because of the slow adjustment of these eddies to new boundary conditions, they carry the roughness characteristics of a large upstream terrain. A scaling relation is proposed that accounts for the memory effects in the big eddies. It is concluded that the standard deviation of the horizontal wind ( _u ) measured at a given height is representative for the shear stress at greater height. This gives at least qualitative support to existing work where u is used for exposure correction of mean wind.     

Accuracy of moments of velocity and scalar fluctuations in the atmospheric surface layer

A detailed accuracy analysis is presented for moments, up to order four, of both velocity (horizontal u and vertical w) and scalar (temperature and humidity q) fluctuations, as well as of the products uw, w and wq, in the atmospheric surface layer. The high-order moments and integral time scales required for this analysis are evaluated from data obtained at a height of about 5 m above the ocean surface under stability conditions corresponding to Z/L \- –0.05. Measured moments and probability density functions of some of the individual fluctuations show departures from Gaussianity, but these are sufficiently small to enable good estimates to be obtained using Gaussian instead of measured moments. For the products, the assumption of joint Gaussianity for individual fluctuations provides a reasonable, though somewhat conservative, estimate for the integration times required. The concept of Reynolds number similarity implies that differences in integration time requirements for flows at different Reynolds numbers arise exclusively from differences in integral time scales. A first approximation to the integral time scales relevant to atmospheric flows is presented.     

A note on the analogy between momentum transfer across a rough solid surface and the air-sea interface

The aerodynamic classification of the resistance laws above solid surfaces is based on the use of a so-called Reynolds roughness number Re _s =h _s u _*/, whereh _s is the effective roughness height, -viscosity,u _*-friction velocity. The recent experimental studies reported by Toba and Ebuchi (1991), demonstrated that the observed variability of the sea roughness cannot be explained only on the basis of the classification of aerodynamic conditions of the sea surface proposed by Kitaigorodskii and Volkov (1965) and Kitaigorodskii (1968) even though the latter approach gains some support from recent experimental studies (see for example Geernaertet al. 1986). In this paper, an attempt is made to explain some of the recently observed features of the variability of surface roughness (Toba and Ebuchi, 1991; Donelanet al., 1993). The fluctuating regime of the sea surface roughness is also described. It is shown that the contribution from the dissipation subrange to the variability of the sea surface can be very important and by itself can explain Charnock's (1955) regime.     

Modelling of turbulence over low hills and varying surface roughness

Neutral surface layer flow over low hills and varying surface roughness is considered with emphasis on closure schemes in relation to the prediction of turbulence quantities. The equations are linearised, Fourier transformed in the two horizontal directions and solved by means of a finite difference method in the vertical. Three closure schemes are. employed, namely mixing length, E- and e-- closure where E, and indicate that differential equations are used for turbulent kinetic energy, dissipation rate and shear stress. Model calculations are compared with experimental data for the step in roughness problem and for the Askervein hill. The mean flow results turn out to be relatively insensitive to the closure scheme. The shear stress and the dimensionless shear, however, are much better predicted with the E- equations than with mixing length closure. In the outer layer of the hill problem, advection of shear stress becomes important. An equation for is needed here.     

Turbulence Reynolds number and the turbulent kinetic energy balance in the atmospheric surface layer

The relation between the turbulence Reynolds numberR and a Reynolds numberz* based on the friction velocity and height from the ground is established using direct measurements of the r.m.s. longitudinal velocity and turbulent energy dissipation in the atmospheric surface layer. Measurements of the relative magnitude of components of the turbulent kinetic energy budget in the stability range 0 >z/L 0.4 indicate that local balance between production and dissipation is maintained. Approximate expressions, in terms of readily measured micrometeorological quantities, are proposed for the Taylor microscale and the Kolmogorov length scale .     

Vertical Structure in the Marine Atmospheric Boundary Layer and its Implication for the Inertial Dissipation Method

The structure of the marine atmospheric boundarylayer and the validity ofMonin–Obukhov similarity theory over the seahave been investigated using longterm measurements. Three levels of turbulencemeasurements (at 10 m, 18 mand 26 m) at Östergarnsholm in themiddle of the Baltic Sea have beenanalysed. The results show that turbulentparameters have a strong dependenceon the actual height due to wave influence.The wind profile and thus thenormalised wind gradient are very sensitiveto wave state. The lower part of theboundary layer can be divided into three heightlayers, a wave influenced layerclose to the surface, a transition layer andan undisturbed ordinary surfacelayer; the depth of the layers is determinedby the wave state. This heightstructure can, however, not be found for thenormalised dissipation, which is onlya function of the stability, except duringpronounced swell where the actualheight also has to be accounted for. Theresults have implications for the heightvariation of the turbulent kinetic energy(TKE) budget. Thus, the imbalancebetween production and dissipation willalso vary with height according to thevariation of wave state. This, in turn,will of course have strong implicationsfor the inertial dissipation method, inwhich a parameterisation of the TKEbudget is used.     

The bulk aerodynamic formulation over heterogeneous surfaces

This interpretative literature survey examines problems with application of the bulk aerodynamic method to spatially averaged fluxes over heterogeneous surfaces. This task is approached by tying together concepts from a diverse range of recent studies on subgrid parameterization, the roughness sublayer, the roll of large inactive boundary-layer eddies, internal boundary-layer growth, the equilibrium sublayer, footprint theory and the blending height. Although these concepts are not completely compatible, qualitative scaling arguments based on these concepts lead to a tentative unified picture of the qualitative influence of surface heterogeneity for a wide spectrum of spatial scales.Generalization of the velocity scale is considered to account for nonvanishing heat and moisture fluxes in the limit of vanishing time-averaged wind speed and to account for the influence of subgrid mesoscale motions on the grid-averaged turbulent flux. The bulk aerodynamic relationship for the heat flux usually employs the surface radiation temperature or, equivalently, the temperature from the modelled surface energy budget. The corresponding thermal roughness length is quite variable and its dependence on available parameters is predictable only in special cases.An effective transfer coefficient to relate the spatially averaged surface fluxes to spatially averaged air-ground differences of temperature and other scalars can be most clearly defined when the blending height occurs below the reference level (observational level or first model level). This condition is satisfied only for surface heterogeneity occurring over horizontal scales up to a few times the boundary-layer depth, depending on the stability and height of the reference level. For surface heterogeneity on larger scales (small mesoscale), an effective transfer coefficient for the spatially averaged flow must be defined, for which predictive schemes are unavailable. For surface variations on large mesoscales, homogeneous subareas may be maintained where traditional similarity theory is locally applicable. Surface variations on these scales may generate thermally-driven mesoscale motions.     

Landscape Roughness Parameters for Sherwood Forest – Experimental Results

The aim of this work is to present experimentally evaluated effective roughnesses (zoe) of a partly forested landscape. Although the ratio of boundary-layer height to obstacle size was only of the order of 50, there still seemed to exist a height range of 75–200 m where surface-layer similarity was approximately valid. Attempts were made to use conventional wind profile analysis to evaluate zoe, but the small height range and the large number of variables initially led to unacceptable uncertainties. Fixing the displacement height zd, rather than fitting it, reduced the data scatter to an acceptable level. The profile-derived roughness lengths zop obtained in this way were in good agreement with previous work, and with an alternative roughness length estimate zof for which flux-derived profile parameters u* and * were used. This implies that the profile-derived roughnesses were consistent with the measured surface-layer momentum flux. Comparison of both roughness estimates also yielded an improved estimate of the displacement height. Besides this, the authors tested a landscape roughness evaluation method which makes use of the gustiness parameter Tu = u/U in the surface layer. The results obtained by this method were in fair agreement with the profile-derived data. In previous work, the gustiness method was advocated because it could be used at relatively low levels, perhaps even within the roughness sub-layer. At the present measuring site, this was not the case as the gustiness method was only valid in an approximate way, and for a limited height range.     

Flux–Profile Relationships Over a Fetch Limited Beech Forest

The influence of an internal boundary layer and a roughness sublayer on flux–profile relationships for momentum and sensible heat have been investigated for a closed beech forest canopy with limited fetch conditions. The influence was quantified by derivation of local scaling functions for sensible heat flux and momentum (_h and _m) and analysed as a function of atmospheric stability and fetch. For heat, the influences of the roughness sublayer and the internal boundary layer were in agreement with previous studies. For momentum, the strong vertical gradient of the flow just above the canopy top for some wind sectors led to an increase in _m, a feature that has not previously been observed. For a fetch of 500 m over the beech forest during neutral atmospheric conditions, there is no height range at the site where profiles can be expected to be logarithmic with respect to the local surface. The different influence of the roughness sublayer on _h and _m is reflected in the aerodynamic resistance for the site. The aerodynamic resistance for sensible heat is considerably smaller than the corresponding value for momentum.     

Observed Wind Profiles and Turbulence Fluxes over an ice Surface with Changing Surface Roughness

Wind profile and eddy-correlation data obtained at two sites on a melting glacier surface in Iceland during the summer of 1996 are presented. Throughout the experiment the surface roughness increased rapidly from smooth to very rough, with the largest roughness element height obtained being about 1.7 m. In a layer close to the rough surface we find that the wind speed profiles were disturbed showing horizontal inhomogeneities as in a roughness sublayer. Its height was approximately two times the height of the main roughness elements (h) at both sites throughout the experiment. From the wind profiles and eddy-correlation data we calculated corrections for the displaced zero plane as a function of time and compared these with results obtained from a drag partitioning model. In general, the agreement was reasonable considering the ranges of uncertainty but the results indicate that the increasing horizontal anisotropy of the surface probably limits the use of the model. The values obtained for the roughness lengths are in good agreement with those calculated from a simple linear model, i.e., z₀/h = 0.5 with the frontal area index. Above the roughness sublayer the wind profiles, normalised standard deviations of wind speed, and the balance of the turbulence kinetic energy budget behaved as over an ideal homogeneous surface thereby confirming similarity of the flow.     

A dynamical analysis of the drag conditions at the sea surface

When applied to a sea surface, shortcomings are noted for the ordinary classification of drag conditions at rigid underlying surfaces according to the Reynolds roughness number Re _s . It is shown that in the case of mobile underlying surfaces, it would be more natural to use the dynamical classification of drag conditions according to the order of magnitude of the ratio ( = /) of the momentum flux toward the waves ( _w) to the viscous momentum flux through the surface ( _w). The relevant estimates of for the main stages of development of the wind waves indicate that the observed values of the drag coefficient of the sea surface correspond to the case of underdeveloped roughness.     

Similarity of atmospheric Reynolds shear stress and heat flux fluctuations over a rough surface

Horizontal u and vertical w velocity fluctuations have been measured together with temperature fluctuations in the atmospheric surface layer, at a small height above a wheat crop canopy. Marginal probability density functions are presented for both individual fluctuations u, w, and for the instantaneous Reynolds stress uw, and heat fluxes w and u. Probability density functions of the velocity fluctuations deviate less significantly from the Gaussian form than the probability density of temperature. There appears to be closer similarity between statistics of the instantaneous heat fluxes than between the momentum flux and either of the heat fluxes investigated. The mean momentum flux receives equal contributions from the events referred to as ejections and sweeps in laboratory boundary layers. Sweeps provide the largest contribution to the heat fluxes.     

Note on the Growth Rate of Water Waves Propagating at an Arbitrary Angle to the Wind

The dependence of the turbulent airflow over water waves on the angle,, between mean wind and wavedirections is investigated. To this end,an existing semi-analytical model is extended. In this model, the main simplification of the problem is obtained by using the well-established divisionof the wave boundary layer into inner and outer regions for modelling turbulence. The effect of waves on turbulence is restricted to the thin inner region. Simulations show that the influence of the wind speed component transverse to the wave direction on the air flow, and hence on the growth rate of the waves, is small. This is confirmed by calculations with a numerical model that solves the full Reynolds equations using a second-order turbulence closure scheme. The growth rate of slowly moving waves (as compared to the wind speed) is then proportional to cos², whereas, for faster waves, it has a narrower angular distribution.     

Variangular wind spirals

The term variangular is introduced to emphasize a significant difference between the present and certain earlier solutions to the problem of organized airmotion within the planetary boundary layer. The latter belong to the family of equiangular wind spirals and have the characteristic that the angle () formed by the vectors of shearing stress and geostrophic departure is invariant with height; it is shown that in this spiral-family, parabolic height-dependency of the effective (eddy) diffusivity (K) alone is permitted, including the asymptotic case of constant K; the famous Ekman spiral as well as the Rossby spiral are two prominent members of the family of equiangular wind spirals. The new variangular theory, as the name implies, permits variation of with height (z) and produces more versatile profiles of wind and stress due to less restraint in K (z). As an example of comparison with observed data, monthly mean wind profiles obtained at Plateau Station, Antarctica, are selected since they exhibit a noteworthy degree of variangularity, in relatively satisfactory agreement with properties of the new theoretical model for wind spirals.National Research Council Visiting Scientist Research Associate, Regional Environments Division, Earth Sciences Laboratory.