Shear stress partitioning in large patches of roughness in the atmospheric inertial sublayer

Drag partition measurements were made in the atmospheric inertial sublayer for six roughness configurations made up of solid elements in staggered arrays of different roughness densities. The roughness was in the form of a patch within a large open area and in the shape of an equilateral triangle with 60 m long sides. Measurements were obtained of the total shear stress (τ) acting on the surfaces, the surface shear stress on the ground between the elements (τ_S) and the drag force on the elements for each roughness array. The measurements indicated that τ_S quickly reduced near the leading edge of the roughness compared with τ, and a τ_S minimum occurs at a normalized distance (x/h, where h is element height) of (downwind of the roughness leading edge is negative), then recovers to a relatively stable value. The location of the minimum appears to scale with element height and not roughness density. The force on the elements decreases exponentially with normalized downwind distance and this rate of change scales with the roughness density, with the rate of change increasing as roughness density increases. Average τ_S : τ values for the six roughness surfaces scale predictably as a function of roughness density and in accordance with a shear stress partitioning model. The shear stress partitioning model performed very well in predicting the amount of surface shear stress, given knowledge of the stated input parameters for these patches of roughness. As the shear stress partitioning relationship within the roughness appears to come into equilibrium faster for smaller roughness element sizes it would also appear the shear stress partitioning model can be applied with confidence for smaller patches of smaller roughness elements than those used in this experiment.     

Direct Measurement Of Shear Stress During Snow Saltation

Wind-tunnel experiments were carried out to measure the shear stressduring snow saltation. Shear stress acting on the snow surface, measured directly with a newly developed drag meter system, revealedthat the shear stress increased with the development ofsaltation. This result supports Owen's hypothesis that the saltationlayer acts as an increased roughness to the flow above the saltationlayer, leading to an increase in surface shear stress. To investigate the contribution of the grain borne shear stress_g and the fluid shear stress _f to the increment of the total shear stress _total, _g was calculated from the loss of horizontal momentum of saltating snowparticles. Since _g is the largest contribution to theincrement of _total, the collision of thesaltating particles is dominant for the shear stressmodification. The results qualitatively support the numericalsimulation reported by McEwan and Willetts.     

Interaction between the atmospheric and oceanic boundary layers

The two-layer system of an atmosphere over water bodies is reduced to a single-layer problem. Values of the interfacial quantities, such as the friction velocity, the surface velocity, the angles, and , between the surface shear stress and the geostrophic wind velocity and the surface wind velocity, respectively, and the surface roughness, all of which depend upon external parameters, such as the geostrophic wind and stratifications, are obtained. The geostrophic drag coefficient C _d, the geostrophic wind coefficient C _f, and the angles , and , of the turbulent flow at the sea-air interface are functions of a dimensionless number, mfG/kg, with S ₁ and S ₂ as two free stratification parameters. The surface roughness is uniquely determined from the geostrophic wind rather than from the wind profile in the boundary layer.Formerly Visiting Research Associate, Applied Physics Branch, Earth Observations Division, NASA-Manned Spacecraft Center, Houston, Texas.     

Drag and drag partition on rough surfaces

An analytic treatment of drag and drag partition on rough surfaces is given. The aims are to provide simple predictive expressions for practical applications, and to rationalize existing laboratory and atmospheric data into a single framework. Using dimensional analysis and two physical hypotheses, theoretical predictions are developed for total stress (described by the square root of the canopy drag coefficient), stress partition (described by the ratio _S/ of the stress _s on the underlying ground surface to total stress ), zero-plane displacement and roughness length. The stress partition prediction is the simple equation _S/= 1/(1+), where = C_RC_S the ratio of element and surface drag coefficients. This prediction agrees very well with data and is free of adjustable constants. Other predictions also agree well with a range of laboratory and atmospheric data.     

Shear-Stress Partitioning in Live Plant Canopies and Modifications to Raupach’s Model

The spatial peak surface shear stress t_S^￠￠{\tau _S^{\prime\prime}} on the ground beneath vegetation canopies is responsible for the onset of particle entrainment and its precise and accurate prediction is essential when modelling soil, snow or sand erosion. This study investigates shear-stress partitioning, i.e. the fraction of the total fluid stress on the entire canopy that acts directly on the surface, for live vegetation canopies (plant species: Lolium perenne) using measurements in a controlled wind-tunnel environment. Rigid, non-porous wooden blocks instead of the plants were additionally tested for the purpose of comparison since previous wind-tunnel studies used exclusively artificial plant imitations for their experiments on shear-stress partitioning. The drag partitioning model presented by Raupach (Boundary-Layer Meteorol 60:375–395, 1992) and Raupach et al. (J Geophys Res 98:3023–3029, 1993), which allows the prediction of the total shear stress τ on the entire canopy as well as the peak (t_S ^￠￠/t)^1/2{(\tau _S ^{\prime\prime}/\tau )^{1/2}} and the average (t_S^￠/t)^1/2{(\tau _S^{\prime}/\tau )^{1/2}} shear-stress ratios, is tested against measurements to determine the model parameters and the model’s ability to account for shape differences of various roughness elements. It was found that the constant c, needed to determine the total stress τ and which was unspecified to date, can be assumed a value of about c = 0.27. Values for the model parameter m, which accounts for the difference between the spatial surface average t_S^￠{\tau _S^{\prime}} and the peak t_S ^￠￠{\tau _S ^{\prime\prime}} shear stress, are difficult to determine because m is a function of the roughness density, the wind velocity and the roughness element shape. A new definition for a parameter a is suggested as a substitute for m. This a parameter is found to be more closely universal and solely a function of the roughness element shape. It is able to predict the peak surface shear stress accurately. Finally, a method is presented to determine the new a parameter for different kinds of roughness elements.     

Spatio-Temporal Surface Shear-Stress Variability in Live Plant Canopies and Cube Arrays

This study presents spatiotemporally-resolved measurements of surface shear-stress τ _s in live plant canopies and rigid wooden cube arrays to identify the sheltering capability against sediment erosion of these different roughness elements. Live plants have highly irregular structures that can be extremely flexible and porous resulting in considerable changes to the drag and flow regimes relative to rigid imitations mainly used in other wind-tunnel studies. Mean velocity and kinematic Reynolds stress profiles show that well-developed natural boundary layers were generated above the 8 m long wind-tunnel test section covered with the roughness elements at four different roughness densities (λ = 0, 0.017, 0.08, 0.18). Speed-up around the cubes caused higher peak surface shear stress than in experiments with plants at all roughness densities, demonstrating the more effective sheltering ability of the plants. The sheltered areas in the lee of the plants are significantly narrower with higher surface shear stress than those found in the lee of the cubes, and are dependent on the wind speed due to the plants ability to streamline with the flow. This streamlining behaviour results in a decreasing sheltering effect at increasing wind speeds and in lower net turbulence production than in experiments with cubes. Turbulence intensity distributions suggest a suppression of horseshoe vortices in the plant case. Comparison of the surface shear-stress measurements with sediment erosion patterns shows that the fraction of time a threshold skin friction velocity is exceeded can be used to assess erosion of, and deposition on, that surface.     

Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index

Using a previous treatment of drag and drag partition on rough surfaces, simple analytic expressions are derived for the roughness length (z ₀) and zero-plane displacement (d) of vegetated surfaces, as functions of canopy height (h) and area index (). The resulting expressions provide a good fit to numerous field and wind tunnel data, and are suitable for applications such as surface parameterisations in atmospheric models.     

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.     

Experimental Investigation on Shear-Stress Partitioning for Flexible Plants with Approximately Zero Basal-to-Frontal Area Ratio in a Wind Tunnel

Shear-stress partitioning is investigated for one type of flexible plant for very small values of the basal-to-frontal area ratio σ (0.001–0.007). The plant model is made of plastic with irregular structures, which are different from previously investigated rigid regular or flexible roughness elements with larger σ values. The distribution of the surface shear stress and the total shear stress at four plant densities with five plant heights are measured in a wind tunnel using Irwin-type sensors and a load cell, respectively. The wind-tunnel experiments prove that, for these flexible plants, the plant height and lateral cover usually decrease with increasing friction velocity, especially for taller plants, while the plant coverage generally increases. However, these characteristics may be inconsistent with flexible roughness elements with very large σ values (and usually very low aspect ratios) because these elements are less flexible. The present flexible plants generally result in lower shear-stress ratios compared with other roughness elements, which is also proven by the higher values of β (the ratio of the drag coefficient of an isolated roughness element to that of the bare surface) and a constant m (accounting for the difference between the average and peak surface shear stresses) from the present experiments (β?=?184–210 and m?=?0.68–0.79). The peak mean stress ratio of the present flexible plants is not a constant (1.07–1.54) because it is affected by the lateral cover, which is different from previous studies that consider the ratio to be constant without regard for the lateral cover.     

Drag coefficient modeling for the near coastal zone

Using the JONSWAP spectrum for describing the surface wave state in the near coastal zone, models for the roughness length and the drag coefficient are used to simulate the dependence of the wind stress on fetch and depth. The results of each model are then compared with a compiled set of past investigations of the neutral drag coefficient over a variety of conditions. It is found that the models of Donelan, Hsu, and Kitaigorodskii correctly predict the trends in the drag coefficient with fetch and depth. Although it did not account for all the observed variations in the neutral drag coefficient. Kitaigorodskii's model, when incorporating the JONSWAP spectrum, more accurately simulated the slopes of the various C_DN regressions against windspeed.     

Velocity and Surface Shear Stress Distributions Behind a Rough-to-Smooth Surface Transition: A Simple New Model

A simple new model is proposed to predict the distribution of wind velocity and surface shear stress downwind of a rough-to-smooth surface transition. The wind velocity is estimated as a weighted average between two limiting logarithmic profiles: the first log law, which is recovered above the internal boundary-layer height, corresponds to the upwind velocity profile; the second log law is adjusted to the downwind aerodynamic roughness and local surface shear stress, and it is recovered near the surface, in the equilibrium sublayer. The proposed non-linear form of the weighting factor is equal to ln(z/z ₀₁)/ln(δ _i /z ₀₁), where z, δ _i and z ₀₁ are the elevation of the prediction location, the internal boundary-layer height at that downwind distance, and the upwind surface roughness, respectively. Unlike other simple analytical models, the new model does not rely on the assumption of a constant or linear distribution for the turbulent shear stress within the internal boundary layer. The performance of the new model is tested with wind-tunnel measurements and also with the field data of Bradley. Compared with other existing analytical models, the proposed model shows improved predictions of both surface shear stress and velocity distributions at different positions downwind of the transition.     

A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice

Although the bulk aerodynamic transfer coefficients for sensible (C _H ) and latent (C _E ) heat over snow and sea ice surfaces are necessary for accurately modeling the surface energy budget, they have been measured rarely. This paper, therefore, presents a theoretical model that predicts neutral-stability values of C _H and C _E as functions of the wind speed and a surface roughness parameter. The crux of the model is establishing the interfacial sublayer profiles of the scalars, temperature and water vapor, over aerodynamically smooth and rough surfaces on the basis of a surface-renewal model in which turbulent eddies continually scour the surface, transferring scalar contaminants across the interface by molecular diffusion. Matching these interfacial sublayer profiles with the semi-logarithmic inertial sublayer profiles yields the roughness lengths for temperature and water vapor. When coupled with a model for the drag coefficient over snow and sea ice based on actual measurements, these roughness lengths lead to the transfer coefficients. C _E is always a few percent larger than CH. Both decrease monotonically with increasing wind speed for speeds above 1 m s^–1, and both increase at all wind speeds as the surface gets rougher. Both, nevertheless, are almost always between 1.0 × 10^–3 and 1.5 × 10^–3.     

Numerical simulation of turbulent convective flow over wavy terrain

By means of a large-eddy simulation, the convective boundary layer is investigated for flows over wavy terrain. The lower surface varies sinusoidally in the downstream direction while remaining constant in the other. Several cases are considered with amplitude up to 0.15H and wavelength ofH to 8H, whereH is the mean fluid-layer height. At the lower surface, the vertical heat flux is prescribed to be constant and the momentum flux is determined locally from the Monin-Obukhov relationship with a roughness lengthz _o=10^–4 H. The mean wind is varied between zero and 5w _*, wherew _* is the convective velocity scale. After rather long times, the flow structure shows horizontal scales up to 4H, with a pattern similar to that over flat surfaces at corresponding shear friction. Weak mean wind destroys regular spatial structures induced by the surface undulation at zero mean wind. The surface heating suppresses mean-flow recirculation-regions even for steep surface waves. Short surface waves cause strong drag due to hydrostatic and dynamic pressure forces in addition to frictional drag. The pressure drag increases slowly with the mean velocity, and strongly with /H. The turbulence variances increase mainly in the lower half of the mixed layer forU/w _*>2.     

Wind profile development above a locally adjusted sea surface

Results are presented from a numerical experiment of wind and shear stress profile development away from a shore line; the water surface is assumed to obey the Charnock-Ellison relation between surface roughness and friction velocity. In typical cases the upwind, land surface is rough relative to the sea and the velocity and shear stress results are qualitatively similar to those for flows from relatively rough to relatively smooth solid surfaces. In the present case, however, the downwind surface roughness and friction velocity vary with position and we find that wind profile development may play a significant role in the relationship between sea surface roughness and fetch.     

Wind Stress Structure in the Unstable Marine Surface Layer Detected by Sar

The wind stress in the marine surface layer under unstable conditions and low wind speed has been studied using a Synthetic Aperture Radar (SAR) image of the sea surface and time series of the horizontal and vertical wind velocities and of the wind stress recorded on board the C.N.R. research platform, in the northern Adriatic Sea, during a SAR overflight.A conditional sampling technique has been used on the wind stress time series and on the SAR image to detect downward (sweep) and upward (ejection) bursts of the momentum flux, as well as the two-dimensional structure of the radar backscatter.From the ensemble average of both the wind stress and the backscatter structures, it has been possible to estimate the mean duration of the upward (11 s) and the downward (15 s) wind stress bursts and the mean size of the bright patches of the SAR image (120 m). The front of the mean backscatter structure, associated with the downward wind stress bursts, has been related to the time length of the mean sweep stress structure to get, after accounting for a threshold of the wind stress for the generation of the sea surface wavelets, the translation velocity U_t of the mean wind stress of sweep, very close to the mean wind speed. The vertical coherence of the wind stress structures has permited to refer the translation velocity to a level very close to the sea surface, but above the viscous sublayer. The variability of U_t with height has been studied through comparison with the mean wind speed at different heights z calculated by a boundary-layer model. Accounting for the results reported in the literature, there is an indication that U_t is constant with height in the range 0.5 m z 15 m.The two-dimensional pattern of the wind stress structures has been derived from the SAR image. The structures appear elongated crosswind, as with microfronts, with an average cross- to down-wind ratio of 4. The area covered by the downward wind stress structures represents 13% of the total area.     

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.     

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.     

Regional shear stress of broken forest from radiosonde wind profiles in the unstable surface layer

Mean wind speed profiles were measured by tracking radiosondes in the unstable atmospheric boundary layer (ABL) over the forested Landes region in southwestern France. New Monin-Obukhov stability correction functions, recently proposed following an, analysis by Kader and Yaglom, as well as the Businger-Dyer stability formulation were tested, with wind speeds in the surface sublayer to calculate the regional shear stress. These profile-derived shear stresses were compared with eddy correlation measurements gathered above a mature forest stand, at a location roughly, 4.5 km from the radiosonde launch site. The shear stress values obtained by means of the newly proposed stability function were in slightly better agreement with the eddy correlation values than those obtained by means of a Businger-Dyer type stability function. The general robustness of the profile method can be attributed in part to prior knowledge of the regional surface roughness (z ₀=1.2 m) and the momentum displacement height (d ₀=6.0 m), which were determined from neutral wind profile analysis. The 100 m drag coefficient for the unstable conditions above this broken forest surface was found to beu _* ² /V ₁₀₀ ² =0.0173.     

Field And Wind-Tunnel Studies Of Aerodynamic Roughness Length

The aerodynamic roughness length (z₀) values of three Gobi desert surfaces were obtained by measurement of the boundary-layer wind profile in the field. To clarify the factors affecting the Gobi surface aerodynamic roughness length, a wind-tunnel experiment was conducted. The wind-tunnel simulation shows that z₀ values increase with increasingsize and coverage of roughness elements. Especially, the shape and height of roughnesselements are more important than other factors in affecting roughness length. The roughness length increases with decreasing values of the geometric parameter (the ratio of element horizontal surface area to height, ) of roughness elements. But at a higher free stream velocity, the height is more important than the shape in affecting roughness length.