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.     

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 Study of the Internal Boundary Layer due to a Roughness Change in Neutral Conditions Observed During the LINEX Field Campaigns

Summary As an aspect of the LINEX field studies (1996–1997; Lindenberg near Beeskow, Germany), the characteristics of the internal boundary layer (IBL) that is associated with a step change of the surface roughnesses in neutral constant stress layers was investigated and is reported in this paper. Both smooth to rough (in 1996) and rough to smooth (in 1997) types of flow, have been studied based upon the profiles of mean wind and temperature realised from a 10-m mast and eddy correlation measurements taken at two levels (2 m and 5 m). Depending upon wind direction, the fetch at the site varied between 140 m and 315 m within the wind sector (200° to 340°) used for the field investigations. The height of the IBL, δ, had been determined from the intersect of the logarithmic wind-profiles below (< 2 m) and above (> 6 ) the interface. Values of δ obtained at the experimental site compared fairly well to the existing theoretical/empirical fetch-height relationships of the form: δ=aċx ^b , where a, b, are empirical constants. The ratio for the friction velocities below and above the IBL as measured directly by the eddy correlation techniques showed that for fetches less than 250 m there was an increase (decrease) of about 20% of the momentum flux arising from the smooth to rough (rough to smooth) transitions. Influences of distant obstructions (e.g., bushes, pockets of trees) on the surface flow were markedly important on the examined wind profiles and such can be indicative as multiple IBLs. Received September 1, 1997 Revised August 5, 1998     

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.     

Flow splitting at the bifurcation between two valleys: idealized simulations in comparison with Mesoscale Alpine Programme observations

Summary This paper investigates the characteristics of channelled airflow in the vicinity of a junction of three idealized valleys (one valley carrying the incoming flow and two tributaries carrying the outflow), using a two-dimensional single-layer shallow water model. Particular attention is given to the flow splitting occurring at the junction. Nondimensionalized, the model depends on the valley geometry, the Reynolds number, which is related to the eddy viscosity, and on the difference of the hydrostatic pressure imposed at the exit of the tributaries. At the spatial scale considered in this study, the Rossby number relating the inertial and Coriolis forces is always larger than 1, implying that the effect of earth rotation can be neglected to a first approximation. The analysis of the flow structure within the three valleys as well as the calculation of the split ratio (fraction of the air flow diverted into one of the two downstream valleys with respect to the total mass flux in the upstream valley) show that (i) the flow pattern depends strongly on the Reynolds number while the split ratio is comparatively insensitive; (ii) the valley geometry and the difference between the upstream and downstream hydrostatic pressures affect the flow pattern, the location of the split point and the split ratio; (iii) the relative contribution of flow deflection by the sidewalls and the blocking/splitting mechanism differs between the settings of a “Y-shape” valley and a “T-shape” valley. Quantitative comparison of the present results with numerical simulations of realistic cases and with observations collected in the region of the Rhine and Seez valleys (Switzerland) (“Y-shape” valley) and in the region of the Inn and Wipp valleys (Austria) (“T-shape” valley) during the Mesoscale Alpine Programme (MAP) field experiment shows good agreement provided that the normalized valley depth NΔH/U_u significantly exceeds 1, i.e., when “flow around” is expected. A structural disagreement between the idealized simulations and the observed wind field is found only when NΔH/U_u ≃ 1, that is, in the “flow over” regime. This shows that the dimensionless valley depth is indeed a good indicator for flow splitting, implying that the stratification is a key player in reality.     

Stratified flow over non-uniform surface conditions: Mixing-length model

The response of a neutrally stratified atmospheric surface layer to sudden changes in surface roughness and temperature is investigated by solving the steady-state boundary-layer equations. Near the discontinuities, the distributions of velocity and shear stress are found to be critically dependent upon whether or not the pressure and buoyancy terms are retained in the governing equations. Computed distributions of velocity and shear stress are found to be in good agreement with windtunnel and field data. The growth of the internal boundary layer under neutral conditions for smooth to rough transitions follows the 0.8 power law; however, rough to smooth transitions are associated with a 0.7 power law.     

Particle-Image Velocimetry Measurements of Separation and Re-attachment of Airflow over Two-Dimensional Hills with Various Slope Angles and Approach-Flow Characteristics

Airflow over two-dimensional hills was investigated in a wind tunnel using particle image velocimetry. We focus on the flow separation behaviour. A trapezoidal hill shape was used in most of the experimental runs, but the critical slope angle for flow separation was approximately the same as that established for smooth hill shapes. The re-attachment point of the separated flow became farther from the hill as the slope angle $\theta $ increased, reaching a saturation of about seven times the hill height for $\theta \gtrsim 60^\circ $ . Increasing the upwind surface roughness length was found to suppress flow separation. This tendency is analogous to the previous experimental results for turbulent boundary layers on flat plates. The boundary-layer thickness varied by the presence or absence of Counihan-type spires and a castellated fence at the test-section entrance had negligible effect on the flow separation.     

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.     

Note on a Parametric Relation for Separating Flow over a Rough Hill

A parametrization method used to account for the effects of flow separation and wall roughness on the lower boundary condition for turbulent boundary layers is investigated against direct numerical simulation and laser Doppler anemometry data. The numerical simulation represents flow over a smooth, flat surface with a prescribed external adverse pressure gradient. The water-channel experiments cover flow over smooth and rough hills for two specified Reynolds numbers. Global optimization algorithms based on four different direct search methods are used to assess the parametrization function, C, in terms of local mean velocity profiles and the parametrization parameters u _* (friction velocity), ∂ _x p (local pressure gradient), z ₀ (effective roughness) and d (zero-plane displacement). The study investigates regions of attached and reversed flows, and forty-two velocity profiles are compared with the proposed expression for the function C, including two profiles that satisfy the solution of Stratford.     

Water-Tank Studies of Separating Flow Over Rough Hills

The present work investigates the lower boundary condition for flows over a steep, rough hill. Simple asymptotic arguments together with the mixing-length hypothesis are used to derive a local analytical solution that is tested against three different flow conditions. In all, 36 velocity profiles are compared with the proposed expression. The experiments were carried out in a water channel and velocity measurements were made through laser Doppler anemometry. The extent of separated flow was made to vary as a function of the roughness and the Reynolds number. The analysis includes regions of attached as well as separated flow. In particular, the solution of Stratford is studied at the points of separation and re-attachment and found to apply equally well in rough walls.     

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.     

The Askervein Hill Project: Wind-tunnel simulations at three length scales

Wind-tunnel simulations of neutrally-stable atmospheric boundary-layer flow over an isolated, low hill (Askervein) have been carried out at three different length scales in two wind-tunnel facilities. The objectives of these simulations were to assess the reliability with which changes in mean wind and turbulence structure induced by the prototype hill on boundary-layer flow can be reproduced in the wind tunnel, and to determine the relative impact of certain modelling approaches (surface roughness, model scale, measurement techniques, etc.) on the quality of the simulations. The wind-tunnel results are compared with each other and with full-scale data and are shown in general to model the prototype flow very well. The effects of relaxing the criterion of aerodynamic roughness of the model surface were limited to certain regions in the lee of the hill and were linked to separation phenomena.     

Non-Linear, Microscale Modelling of the Flow Over Askervein Hill

The flow solver “3DWind” is used to explore new aspects of the Askervein hill flow case. Previous work has investigated sensitivities to the grid, the inflow boundary profile, the roughness and the turbulence model. Several different linear and non-linear numerical models have also been validated by means of the Askervein hill case. This analysis focuses on the flow sensitivity to the grid spacing, the incident wind direction and the vertical resolution of topographic data. The horizontal resolution is found to be fine enough to cause only minor differences compared to a grid where every second node is removed. The vertical resolution dependence is mainly attributed to the wall functions. Simulations are performed for wind directions 200°, 205°, 210° and 215° at the reference station. The smallest directional biases compared to experimental values along a line through the hilltop are found for the directions 200° and 205°. There are larger wind direction changes along this line through the hilltop in the 200° case than in the 215° case. Still the simulation results give less veering than found in the experimental results, and this is maybe caused by a slightly stable atmosphere. The sensitivity to the vertical resolution of the topographical data is found to be particularly high close to the ground at the top of the hill; this is where the speed-up is most important. Differences decrease with the height from the ground. At higher levels the speed-ups are smaller and caused by terrain formations with larger scales.     

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.     

A case study of stably stratified airflow over the pennines using an instrumented glider

In this paper we present data gathered during a weak case of the Helm wind, an example of supercritical airflow, in the vicinity of Cross Fell in Northern England. Airborne measurements have been made using an instrumented glider with simultaneous ground-based measurements both on a hill summit and on the valley floor downwind of the hill.It is found that the major features of the airflow both near the surface and aloft, including the lee-wave activity are well reproduced by the airflow model of Carruthers and Choularton (1982). Secondary features including several higher modes of lee-waves and changes in the valley flow associated with nocturnal cooling were observed which could not be accounted for by the simple model.     

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.

     

Observations of Boundary-Layer Wind-Tunnel Flow over Isolated Ridges of Varying Steepness and Roughness

Boundary-layer wind-tunnel flow is measured over isolated ridges of varyingsteepness and roughness. The steepness/roughness parameter space is chosento produce flows that range from fully attached to strongly separated. Measurementsshow that maximum speedup at the hill crest is significantly lower than predictedby linear theory and that recovery in the lee of the hill is much slower for stronglyseparated flow over steep terrain. The measurements also show that behaviour ofthe mean and turbulent components of the flow on the downwind side of the ridgeis fundamentally different between separated and non-separated flows. This suggeststhe dominance of much increased turbulence time and length scales in the lee of thehill in association with a production mechanism that scales with the hill length ratherthan the proximity to the surface as on the windward side of the hill crest.     

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.     

光滑海面上风、温、湿廓线的层结订正模式及海气整体交换系数

详细介绍了光滑面标量粗糙度ＺＴ,Ｚｑ与风速粗糙度Ｚ０的相似表达式,论述了把Ｍｏｎｉｎ－Ｏｂｕｋｈｏｖ相似理论推广到光滑面上湍流气层的合理性,从而得到光滑面风、温、湿层结订正廓线与粗糙面廓线相统一的形式。总结了用该模式处理的三个海上梯度观测资料的计算结果,揭示出了微风时通过光滑海面的海气通量及整体交换系数受层结影响远大于风速影响的特征。并给出光滑界面上不同层结的整体交换系数随风速变化的拟合公式。