A Wind-Tunnel Investigation of Wind-Turbine Wakes: Boundary-Layer Turbulence Effects

Wind-tunnel experiments were performed to study turbulence in the wake of a model wind turbine placed in a boundary layer developed over rough and smooth surfaces. Hot-wire anemometry was used to characterize the cross-sectional distribution of mean velocity, turbulence intensity and kinematic shear stress at different locations downwind of the turbine for both surface roughness cases. Special emphasis was placed on the spatial distribution of the velocity deficit and the turbulence intensity, which are important factors affecting turbine power generation and fatigue loads in wind energy parks. Non-axisymmetric behaviour of the wake is observed over both roughness types in response to the non-uniform incoming boundary-layer flow and the effect of the surface. Nonetheless, the velocity deficit with respect to the incoming velocity profile is nearly axisymmetric, except near the ground in the far wake where the wake interacts with the surface. It is found that the wind turbine induces a large enhancement of turbulence levels (positive added turbulence intensity) in the upper part of the wake. This is due to the effect of relatively large velocity fluctuations associated with helicoidal tip vortices near the wake edge, where the mean shear is strong. In the lower part of the wake, the mean shear and turbulence intensity are reduced with respect to the incoming flow. The non-axisymmetry of the turbulence intensity distribution of the wake is found to be stronger over the rough surface, where the incoming flow is less uniform at the turbine level. In the far wake the added turbulent intensity, its positive and negative contributions and its local maximum decay as a power law of downwind distance (with an exponent ranging from −0.3 to −0.5 for the rough surface, and with a wider variation for the smooth surface). Nevertheless, the effect of the turbine on the velocity defect and added turbulence intensity is not negligible even in the very far wake, at a distance of fifteen times the rotor diameter.     

A Flume Experiment on the Adjustment of the Mean and Turbulent Statistics to a Transition from Short to Tall Sparse Canopies

Water-flume experiments are conducted to study the structure of turbulent flow within and above a sparse model canopy consisting of two rigid canopies of different heights. This difference in height specifies a two-dimensional step change from a rough to a rougher surface, as opposed to a smooth-to-rough transition. Despite the fact that the flow is in transition from a rough to a rougher surface, the thickness of the internal boundary layer scales as x ^4/5, consistent with smooth-to-rough boundary layer adjustment studies, where x is the downstream distance from the step change. However, the analogy with smooth-to-rough transitions no longer holds when the flow inside the canopy and near the canopy top is considered. Results show that the step change in surface roughness significantly increases turbulence intensities and shear stress. In particular, there is an adjustment of the mean horizontal velocity and shear stress as the flow passes over the rougher canopy, so that their vertical profiles adjust to give maximum values at the top of this canopy. We also observe that the magnitude and shape of the inflection in the mean horizontal velocity profile is significantly affected by the transition. The horizontal and vertical turbulence spectra compare well with Kolmogorov’s theory, although a small deviation at high frequencies is observed in the horizontal spectrum within the canopy. Here, for relatively low leaf area index, shear is found to be a more effective mechanism for momentum transfer through the canopy structure than vortex shedding.     

Measurements of turbulence structure in the boundary layer on a rough surface

Mean products of velocity fluctuations up to fourth order have been measured in a wind tunnel at the trailing edge of a flat plate, one side of which was covered with floor-sanding paper to produce a fully rough surface. This set-up permits easy comparison of structural parameters in smooth-wall and rough-wall boundary layers. The Reynolds-stress profiles and second-order parameters are closely the same on the rough and smooth surfaces; in particular the decrease in Reynolds shear stress near the rough surface, encountered by several other laboratory workers, was not found in the present results. The triple products are spectacularly altered for a distance of up to 10 roughness heights from the rough surface, and imply a large net rate of transport of turbulent energy and shear stress towards the surface. Comparison with other published data shows that the behaviour of this modified region depends on roughness geometry as well as on the roughness height itself; for example, the mean cube of the normal-component fluctuation remains positive (energy transport away from the surface) over sand or gravel roughness but goes negative, like the other energy-transport terms, over crop canopies.     

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.     

Flow over high roughness elements

The mean velocity and longitudinal turbulence-intensity distributions inside the zone of and above high roughness elements were investigated experimentally. This was accomplished by using a model forest canopy. The results indicate that the flow may be divided into transition and fully-developed flow regions, followed by a short adjustment distance near the downstream terminus of the rough boundary. The transition region has a strong effect on the flow characteristics within and above the layer of roughness elements. Generally, a similar qualitative variation for both velocity and turbulence was found inside and above the roughness zone, whose influence extends to more than three times the roughness height.Investigation of the modified universal logarithmic law for describing the velocity variation above the roughness zone revealed that both of the so-called similarity parameters, i.e., friction velocity and roughness length, are not local constants. On the contrary, for a given flow and local conditions they vary drastically with height. It is suspected that this is due to the fact that the classical assumption of constant shear stress throughout the boundary layer or significant portions of it is not satisfied in the case of roughness elements many times greater in height than the thickness of the viscous wall zone.     

Estimates of velocity-pressure and velocity-pressure gradient interactions in the surface layer over plant canopies

The budget equations of turbulent kinetic energy and shear stress contain interaction terms of velocity-pressure and velocity-pressure gradient. These terms were estimated in the surface layer using the air pressure observed at the surface and wind velocity components over plant canopies. The magnitude of the pressure interaction terms was significantly large; it was not negligible compared with the production terms in each budget equation. The present results obtained over a rough surface also confirmed previous results that pressure terms play an important role in the turbulent kinetic energy budgets and the shear stress budget. The height dependency of nondimensional pressure terms versus (z - d)/z ₀ was not clear.     

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

The geostrophic Ekman boundary layer for large Rossby number (Ro) has been investigated by exploring the role played by the mesolayer (intermediate layer) lying between the traditional inner and outer layers. It is shown that the velocity and Reynolds shear stress components in the inner layer (including the overlap region) are universal relations, explicitly independent of surface roughness. This universality of predictions has been supported by observations from experiment, field and direct numerical simulation (DNS) data for fully smooth, transitionally rough and fully rough surfaces. The maxima of Reynolds shear stresses have been shown to be located in the mesolayer of the Ekman boundary layer, whose scale corresponds to the inverse square root of the friction Rossby number. The composite wall-wake universal relations for geostrophic velocity profiles have been proposed, and the two wake functions of the outer layer have been estimated by an eddy viscosity closure model. The geostrophic drag and cross-isobaric angle predictions yield universal relations, which are also supported by extensive field, laboratory and DNS data. The proposed predictions for the geostrophic drag and the cross-isobaric angle compare well with data for Rossby number Ro ≥ 10⁵. The data show low Rossby number effects for Ro < 10⁵ and higher-order effects due to the mesolayer compare well with the data for Ro ≥ 10³.     

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.     

Turbulent flow over a very rough,random surface

A knowledge of the nature of turbulent flow over very rough surfaces is important for an understanding of the environment of crops, forests, and cities. For this reason, a wind-tunnel investigation was carried out on the variations in mean velocity, Reynolds shear-stress, and other turbulence quantities in a deep turbulent flow over a rough surface having a fair degree of randomness in the shapes, sizes, and positions of its elements.There was a layer close to the surface with considerable variations in both mean velocity and shear-stress, and the horizontal scale over which the mean velocity varied was much larger than the average distance between roughness elements. Above this layer, whose depth was of the order of the spacing between roughness elements, shear stress was constant with height, and the velocity profile had a logarithmic form. The usefulness of both mean profile and eddy-correlation methods for estimating fluxes above very rough terrain is discussed in the light of these findings.     

Experimental Study on Effects of Ground Roughness on Flow Characteristics of Tornado-Like Vortices

The three-dimensional wind velocity and dynamic pressure for stationary tornado-like vortices that developed over ground of different roughness categories were investigated to clarify the effects of ground roughness. Measurements were performed for various roughness categories and two swirl ratios. Variations of the vertical and horizontal distributions of velocity and pressure with roughness are presented, with the results showing that the tangential, radial, and axial velocity components increase inside the vortex core near the ground under rough surface conditions. Meanwhile, clearly decreased tangential components are found outside the core radius at low elevations. The high axial velocity inside the vortex core over rough ground surface indicates that roughness produces an effect similar to a reduced swirl ratio. In addition, the pressure drop accompanying a tornado is more significant at elevations closer to the ground under rough compared with smooth surface conditions. We show that the variations of the flow characteristics with roughness are dependent on the vortex-generating mechanism, indicating the need for appropriate modelling of tornado-like vortices.     

Stratified flow over non-uniform surfaces: Turbulent energy model

A turbulent energy model is developed to simulate the response of a neutrally stratified atmospheric boundary layer to sudden changes in surface roughness. A mechanism of turbulent energy transfer is proposed, based upon the results of numerical experiments, that explains the distribution of shear stress and hence the distribution of velocity profiles in the atmospheric surface layer. Two length scales associated with the turbulent energy equation are obtained from experimental data and the law of the wall. Turbulent energy is also predicted.The predicted growth of the internal boundary layer is slower than that obtained from mixing-length models. Also, the predicted surface shear stress obtained from the turbulent energy model is in better agreement with field data than that obtained from mixing-length models.     

The sea surface is aerodynamically rough even under light winds

The sea surface is generally considered to be aerodynamically rough at high winds (U>7 m/s), where the roughness length increases with wind velocity; below this velocity, the atmospheric surface layer enters a transition region and then becomes aerodynamically smooth as the wind velocity further decreases. The sea surface is shown, however, to reach its smoothest condition at a wind velocity of about 5 m/s, and then become rough again at lower velocities. In the latter case, the roughness length increases as the wind velocity decreases in accordance with the surface-tension relation governing wind-wave interactions.     

Subfilter-scale Fluxes over a Surface Roughness Transition. Part I: Measured Fluxes and Energy Transfer Rates

A wind-tunnel experiment was designed and carried out to study the effect of a surface roughness transition on subfilter-scale (SFS) physics in a turbulent boundary layer. Specifically, subfilter-scale stresses are evaluated that require parameterizations and are key to improving the accuracy of large-eddy simulations of the atmospheric boundary layer. The surface transition considered in this study consists of a sharp change from a rough, wire-mesh covered surface to a smooth surface. The resulting magnitude jump in aerodynamic roughnesses, M = ln(z ₀₁/z ₀₂), where z ₀₁ and z ₀₂ are the upwind and downwind aerodynamic surface roughnesses respectively, is similar to that of past experimental studies in the atmospheric boundary layer. The two-dimensional velocity fields used in this study are measured using particle image velocimetry and are acquired at several positions downwind of the roughness transition as well as over a homogeneous smooth surface. Results show that the SFS stress, resolved strain rate and SFS transfer rate of resolved kinetic energy are dependent on the position within the boundary layer relative to the surface roughness transition. A mismatch is found in the downwind trend of the SFS stress and resolved strain rate with distance from the transition. This difference of behaviour may not be captured by some eddy-viscosity type models that parameterize the SFS stress tensor as proportional to the resolved strain rate tensor. These results can be used as a benchmark to test the ability of existing and new SFS models to capture the spatial variability SFS physics associated with surface roughness heterogeneities.     

The flow in a turbulent boundary layer upstream of a change in surface roughness

Modification of a turbulent flow upstream of a change in surface roughness has been studied by means of a stream function-vorticity model.A flow reduction is found upstream of a step change in surface roughness when a fluid flows from a smooth onto a rough surface. Above that layer and above the region of flow reduction downstream of a smooth-rough transition, a flow acceleration is observed. Similar flow modification can be seen at a rough-smooth transition with the exception that flow reduction and flow acceleration are reversed. Within a fetch of –500 < x/z ₀< + 500 (z ₀ is the maximum roughness length, the roughness transition is located at x/z ₀ = 0), flow reduction (flow acceleration) upstream of a roughness transition is one order of magnitude smaller than the flow reduction (flow acceleration) downstream of a smooth-rough (rough-smooth) transition. The flow acceleration (flow reduction) above that layer is two orders of magnitude.The internal boundary layer (IBL) for horizontal mean velocity extends to roughly 300z ₀ upstream of a roughness transition, whereas the IBL for turbulent shear stress as well as the distortion of flow equilibrium extend almost twice as far. For the friction velocity, an undershooting (overshooting) with respect to upstream equilibrium is predicted which precedes overshooting (undershooting) over new equilibrium just behind a roughness transition.The flow modification over a finite fetch of modified roughness is weaker than over a corresponding fetch downstream of a single step change in roughness and the flow stays closer to upstream equilibrium. Even in front of the first roughness change of a finite fetch of modified roughness, a distortion of flow equilibrium due to the second, downwind roughness change can be observed.     

Roughness-Length Model for Organized Rough Walls

A model for the roughness length and its correlation with the roughness shear stress on organized rough walls of varying geometry are presented and verified. The roughness length is nondimensionalized by the characteristic roughness length and is expressed as a function of roughness density with a wake-interference parameter. The dimensionless roughness length is independent of Reynolds number. When the model is applied to the whole range of roughness densities, the rough walls can be smooth, transitionally rough, and fully rough. A large number of data from classical experiments and recent simulations are analyzed to evaluate the proposed correlations, which are found to be consistent with the analyzed datasets. The proposed expression for the dimensionless roughness length and the expression for the dimensionless roughness shear stress, proposed previously by the author (Boundary-Layer Meteorology, 2020, Vol. 174, 393–410), are found to be identical in form. Numerous extant measurements of the two roughness parameters can be reproduced when the wake-interference parameters in the two models are treated as identical. The parameters of the roughness-length model are closely related to the geometry of the roughness elements. Different types of roughness elements can be distinguished by the values of the parameters. These results provide the foundation for constructing the unified roughness model for organized rough walls of varying geometry.

     

Drag due to regular arrays of roughness elements of varying geometry

Comparisons are made of experimental studies on the drag, at high Reynolds number, due to regular arrays of roughness elements of various shapes immersed in a turbulent boundary layer. Using a variant of Millikan's dimensional analysis, the form of the velocity profile is deduced in terms of the dimensions and concentration of the roughness elements. A drag formula results which is shown to be in good agreement with data. Available measurements of the partition of drag between the elements and the intervening surface indicates that equipartition occurs at quite low concentrations. The interaction between elements is then small, so that the drag coefficient of a typical roughness element is nearly constant. A re-examination of some of O'Loughlin's velocity-profile data, obtained below the tops of the roughness elements, suggests the existence of a nearly constant-stress layer scaled to the shear stress of the intervening surface. Above the roughness elements, the mean-velocity profile undergoes a transition to the form appropriate to the total shear stress exerted by the roughened surface. A formula is given which describes the one-dimensional velocity profile over the entire range, excluding the viscous sublayer on the intervening surface. The viscous sublayer appears to correspond quite closely to that on a smooth plate. This work was initiated while the authors were with the Division of Plant Industry, CSIRO. At present on leave at the Natural Resource Ecology Laboratory, Colorado State University, Fort Collins, Colorado, U.S.A.     

Effect of Vertical Wind Shear on Concentration Fluctuation Statistics in a Point Source Plume

Measurements of concentration fluctuation intensity, intermittency factor, and integral time scale were made in a water channel for a plume dispersing in a well-developed, rough surface, neutrally stable, boundary layer, and in grid-generated turbulence with no mean velocity shear. The water-channel simulations apply to full-scale atmospheric plumes with very short averaging times, on the order of 1–4 min, because plume meandering was suppressed by the water-channel side walls. High spatial and temporal resolution vertical and crosswind profiles of fluctuations in the plume were obtained using a linescan camera laser-induced dye tracer fluorescence technique. A semi-empirical algebraic mean velocity shear history model was developed to predict these concentration statistics. This shear history concentration fluctuation model requires only a minimal set of parameters to be known: atmospheric stability, surface roughness, vertical velocity profile, and vertical and crosswind plume spreads. The universal shear history parameter used was the mean velocity shear normalized by surface friction velocity, plume travel time, and local mean wind speed. The reference height at which this non-dimensional shear history was calculated was important, because both the source and the receptor positions influence the history of particles passing through the receptor position.     

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.     

Length-Scale Similarity of Turbulent Organized Structures over Surfaces with Different Roughness Types

We examine the similarity of turbulent organized structures over smooth and very rough wall flows. Turbulent flow fields in horizontal cross-sections were measured using particle image velocimetry, and the characteristics of turbulent organized structures over four types of surfaces were investigated. Measurements were conducted at several measurement heights across the internal boundary layer. The length and width of turbulence structures were quantified using a two-point correlation method. We selected two thresholds of two-point correlation coefficients to consider both large-scale and small-scale structures; the validity of these choices was examined through the analyses using proper orthogonal decomposition. For large-scale structures, the length and aspect ratios (streamwise length/spanwise width) of structures were highly correlated with the velocity gradient for each measurement height and boundary-layer thickness. This relationship was also examined in the results of previous studies, and the scaling of the aspect ratio with the non-dimensional velocity gradient again showed the importance of the velocity gradient, with slight differences found between smooth and rough surfaces. In contrast, the small-scale structures exhibited weak dependency on the velocity gradient and boundary-layer thickness. Instantaneous snapshots of turbulent organized structures at the same shear level also displayed differences in small-scale structures, but the structures of the organized motions resembled each other, as in the results of the two-point correlation method.     

Similarity of large Reynolds number boundary layers

Similarity will exist for both the mean velocity and the turbulent shear stress of a turbulent boundary layer if the following conditions are met: (1) The surface shear is constant. (2) The boundary layer thickness parameters vary linearly with downstream distance. (3) The flow Reynolds number approaches infinity.These conditions may be nearly obtained in atmospheric type boundary layers. Measurements are presented from the Colorado State University Atmospheric Simulation Wind Tunnel which demonstrate the similarity. The wind-tunnel Reynolds number is from one to two orders of magnitude smaller than those of an atmospheric boundary layer.