Wind-Tunnel Simulation of Weakly and Moderately Stable Atmospheric Boundary Layers

The simulation of horizontally homogeneous boundary layers that have characteristics of weakly and moderately stable atmospheric flow is investigated, where the well-established wind engineering practice of using ‘flow generators’ to provide a deep boundary layer is employed. Primary attention is given to the flow above the surface layer, in the absence of an overlying inversion, as assessed from first- and second-order moments of velocity and temperature. A uniform inlet temperature profile ahead of a deep layer, allowing initially neutral flow, results in the upper part of the boundary layer remaining neutral. A non-uniform inlet temperature profile is required but needs careful specification if odd characteristics are to be avoided, attributed to long-lasting effects inherent of stability, and to a reduced level of turbulent mixing. The first part of the wind-tunnel floor must not be cooled if turbulence quantities are to vary smoothly with height. Closely horizontally homogeneous flow is demonstrated, where profiles are comparable or closely comparable with atmospheric data in terms of local similarity and functions of normalized height. The ratio of boundary-layer height to surface Obukhov length, and the surface heat flux, are functions of the bulk Richardson number, independent of horizontal homogeneity. Surface heat flux rises to a maximum and then decreases.     

Surface Heterogeneity Effects on Regional-Scale Fluxes in the Stable Boundary Layer: Aerodynamic Roughness Length Transitions

The effects of abrupt streamwise transitions of the aerodynamic roughness length ( $z_\mathrm{o}$ z o ) on the stable atmospheric boundary layer are evaluated using a series of large-eddy simulations based on the first Global Energy and Water Cycle Experiment Atmospheric Boundary Layer intercomparison study (GABLS1). Four $z_\mathrm{o}$ z o values spanning three orders of magnitude are used to create all possible binary distributions with each arranged into patches of characteristic length scales equal to roughly one-half, one, and two times the equivalent homogeneous boundary-layer height. The impact of the heterogeneity on mean profiles of wind speed and temperature, on surface fluxes of heat and momentum, and on internal boundary-layer dynamics are considered. It is found that $z_\mathrm{o}$ z o transitions do not significantly alter the functional relationship between the average surface fluxes and the mean profiles of wind speed and potential temperature. Although this suggests that bulk similarity theory is applicable for modelling the stable boundary layer over $z_\mathrm{o}$ z o heterogeneity, effective surface parameters must still be specified. Existing models that solve for effective roughness lengths of momentum and heat are evaluated and compared to values derived from the simulation data. The existing models are unable to accurately reproduce both the values of the effective aerodynamic roughness lengths and their trends as functions of patch length scale and stability. A new model for the effective aerodynamic roughness length is developed to exploit the benefits of the other models tested. It accurately accounts for the effects of the heterogeneity and stratification on the blending height and effective aerodynamic roughness length. The new model provides improved average surface fluxes when used with bulk similarity.     

Effect of Roughness on Surface Boundary Conditions for Large-Eddy Simulation

An important parameterization in large-eddy simulations (LESs) of high- Reynolds-number boundary layers, such as the atmospheric boundary layer, is the specification of the surface boundary condition. Typical boundary conditions compute the fluctuating surface shear stress as a function of the resolved (filtered) velocity at the lowest grid points based on similarity theory. However, these approaches are questionable because they use instantaneous (filtered) variables, while similarity theory is only valid for mean quantities. Three of these formulations are implemented in simulations of a neutral atmospheric boundary layer with different aerodynamic surface roughness. Our results show unrealistic influence of surface roughness on the mean profile, variance and spectra of the resolved velocity near the ground, in contradiction of similarity theory. In addition to similarity-based surface boundary conditions, a recent model developed from an a priori experimental study is tested and it is shown to yield more realistic independence of the results to changes in surface roughness. The optimum value of the model parameter found in our simulations matches well the value reported in the a priori wind-tunnel study.     

Equilibrium Atmospheric Boundary-Layer Flow: Computational Fluid Dynamics Simulation with Balanced Forces

Forcing relationships in steady, neutrally stratified atmospheric boundary-layer (ABL) flow are thoroughly analyzed. The ABL flow can be viewed as balanced between a forcing and a drag term. The drag term results from turbulent stress divergence, and above the ABL, both the drag and the forcing terms vanish. In computational wind engineering applications, the ABL flow is simulated not by directly specifying a forcing term in the ABL but by specifying boundary conditions for the simulation domain. Usually, these include the inflow boundary and the top boundary conditions. This ‘boundary-driven’ ABL flow is dynamically different from its real counterpart, and this is the major reason that the simulated boundary-driven ABL flow does not maintain horizontal homogeneity. Here, first a dynamical approach is proposed to develop a neutrally stratified equilibrium ABL flow. Computational fluid dynamics (CFD) software (Fluent 6.3) with the standard \(k\) – \(\varepsilon \) turbulence model is employed, and by applying a driving force profile, steady equilibrium ABL flows are simulated by the model. Profiles of wind speed and turbulent kinetic energy (TKE) derived using this approach are reasonable in comparison with the conventional logarithmic law and with observational data respectively. Secondly, the equilibrium ABL profiles apply as inflow conditions to simulate the boundary-driven ABL flow. Simulated properties between the inlet and the outlet sections across a fetch of 10 km are compared. Although profiles of wind speed, TKE, and its dissipation rate are consistently satisfactory under higher wind conditions, a deviation of TKE and its dissipation rate between the inlet and outlet are apparent (7–8 %) under lower wind-speed conditions (2 m s \(^{-1}\) at 10 m). Furthermore, the simulated surface stress systematically decreases in the downwind direction. A redistribution of the pressure field is also found in the simulation domain, which provides a different driving pattern from the realistic case in the ABL.     

The internal boundary layer — A review

A review is given of relevant work on the internal boundary layer (IBL) associated with:

1. Small-scale flow in neutral conditions across an abrupt change in surface roughness,
2. Small-scale flow in non-neutral conditions across an abrupt change in surface roughness, temperature or heat/moisture flux,
3. Mesoscale flow, with emphasis on flow across the coastline for both convective and stably stratified conditions.

The major theme in all cases is on the downstream, modified profile form (wind and temperature), and on the growth relations for IBL depth.     

Thermal Stratification Effects on Flow Over a Generic Urban Canopy

The influence of local surface heating and cooling on flow over urban-like roughness is investigated using large-eddy simulations. By adjusting the incoming or outgoing heat flux from the ground surface, various degrees of local thermal stratification, represented by a Richardson number \((Ri_\tau )\) , were attained. Drag and heat transfer coefficients, turbulence structure, integral length scales, and the strength of quadrant events that contribute to momentum and heat fluxes were obtained and are compared with locally stable, neutral and unstable flows. With increasing \(Ri_\tau \) , or equivalently as the flow characteristics change from local thermal instability to stability, a gradual decline in the drag and heat transfer coefficients is observed. These values are found to be fairly independent of the type of thermal boundary condition (constant heat flux or constant temperature) and domain size. The maps of anisotropy invariants showed that for the values of \(Ri_\tau \) considered, turbulence structures are almost the same in shape for neutral and unstable cases but differ slightly from those in the stable case. The degree of anisotropy is found to decrease as \(Ri_\tau \) increases from \(-2\) to 2.5. Compared to the neutral case, the integral length scales are shortened in the streamwise and vertical direction by ground cooling, but enhanced in the vertical direction with ground heating. Quadrant analysis showed that an increase in floor heating increases the strength of ejections above the canopy. However, the contributions of updrafts or downdrafts to the heat flux are found not to be significantly influenced by the type of local thermal stratification for the values of \(Ri_\tau \) considered. From the octant analysis, the transport mechanisms of momentum and heat above the canopy are found to be very similar in both locally unstable and stable flows.     

The characteristics of a laboratory produced turbulent Ekman layer

The characteristics of the atmospheric turbulent Ekman boundary layer have been qualitatively simulated in an annular rotating wind tunnel. Observed velocity spirals found to exist within the wind tunnel resembled qualitatively those found in the atmosphere in that a two-layer structure was evident, consisting of a log-linear portion topped by an outer spiral layer. The magnitude of the friction velocity u _* obtained from the log-linear profile agreed with that measured directly, i.e., that obtained from the relation: u _* = (u′w′)^1/2. Also, the effects of surface roughness on the characteristics of the boundary layer agreed with expected results. In cases where the parametric behaviour predicted by theory departed from the observed behaviour, the probable cause was the inherent size limitations of the wind tunnel. The ability to maintain dynamic similarity is constrained by the limited radius of curvature of the wind tunnel. The vertical distribution of turbulent intensity in the wind tunnel was found to agree qualitatively with an observed atmospheric distribution. Also, a vertical distribution of eddy diffusivity was calculated from tunnel data and found to give qualitatively what one might expect in the atmosphere.     

Velocity profiles,the resistance law and the dissipation rate of mean flow kinetic energy in a neutrally and stably stratified planetary boundary layer

The logarithmic + polynomial approximation is suggested for vertical profiles of velocity components in a planetary boundary layer (PBL) at neutral and stable stratification. The resistance law functions A and B are determined on the basis of this approximation, using integral relations derived from the momentum equations, the Monin-Obukhov asymptotic formula for the wind profile in a stably stratified near-surface layer and the known expressions for the PBL depth. This result gives a realistic and convenient method for calculating the surface friction velocity and direction and the total dissipation rate of mean flow kinetic energy in terms of geostrophic velocity, buoyancy flux at the surface, the roughness parameter and the Coriolis parameter. In the course of these derivations a review is given of current views on the main problems of the neutral and stable PBL.     

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.     

Investigation of the Stable Atmospheric Boundary Layer at Halley Antarctica

Boundary-layer measurements from the Brunt Ice Shelf, Antarctica are analyzed to determine flux–profile relationships. Dimensionless quantities are derived in the standard approach from estimates of wind shear, potential temperature gradient, Richardson number, eddy diffusivities for momentum and heat, Prandtl number, mixing length and turbulent kinetic energy. Nieuwstadt local scaling theory for the stable atmospheric boundary-layer appears to work well departing only slightly from expressions found in mid-latitudes. An $E$ E – $l_{\mathrm{m}}$ l m single-column model of the stable boundary layer is implemented based on local scaling arguments. Simulations based on the first GEWEX Atmospheric Boundary-Layer Study case study are validated against ensemble-averaged profiles for various stability classes. A stability-dependent function of the dimensionless turbulent kinetic energy allows a better fit to the ensemble profiles.     

Observations of the barotropic Ekman layer over an urban terrain

Data from low-level soundings over Cambridge, U.S.A. were selected on the basis of an Ekman-like variation of the wind vector with altitude combined with evidence of a barotropic atmosphere. The method of geostrophic departure was used to determine the shear-stress distribution. The analysis yields the dimensionless properties of the barotropic Ekman layer under neutral and stable stratification. Some important results include: the geostrophic drag coefficient displays no dependence on the degree of static stability; the dimensionless height of the boundary layer decreases with increasing stability in agreement with the prediction of Zilitinkevich; the properties of the urban surface layer, where the roughness elements are multistory buildings, show no dependence on atmospheric stability under the moderate wind conditions which display the Ekman-like wind profile; and the directions of the horizontal shear stress and the vertical derivative of the velocity vector usually tend to be parallel only near the surface layer. Values of the two constants of the Rossby number similarity theory are found for the neutral barotropic Ekman layer at a surface Rossby number equal to 2 × 10⁵. The implications of the work with respect to wind-tunnel simulation of the flow over models of urban areas are discussed.     

Weibull-k Revisited: “Tall” Profiles and Height Variation of Wind Statistics

The Weibull distribution is commonly used to describe climatological wind-speed distributions in the atmospheric boundary layer. While vertical profiles of mean wind speed in the atmospheric boundary layer have received significant attention, the variation of the shape of the wind distribution with height is less understood. Previously we derived a probabilistic model based on similarity theory for calculating the effects of stability and planetary boundary-layer depth upon long-term mean wind profiles. However, some applications (e.g. wind energy estimation) require the Weibull shape parameter (k), as well as mean wind speed. Towards the aim of improving predictions of the Weibull- \(k\) profile, we develop expressions for the profile of long-term variance of wind speed, including a method extending our probabilistic wind-profile theory; together these two profiles lead to a profile of Weibull-shape parameter. Further, an alternate model for the vertical profile of Weibull shape parameter is made, improving upon a basis set forth by Wieringa (Boundary-Layer Meteorol, 1989, Vol. 47, 85–110), and connecting with a newly-corrected corollary of the perturbed geostrophic-drag theory of Troen and Petersen (European Wind Atlas, 1989, Risø National Laboratory, Roskilde). Comparing the models for Weibull-k profiles, a new interpretation and explanation is given for the vertical variation of the shape of wind-speed distributions. Results of the modelling are shown for a number of sites, with a discussion of the models’ efficacy and applicability. The latter includes a comparative evaluation of Wieringa-type empirical models and perturbed-geostrophic forms with regard to surface-layer behaviour, as well as for heights where climatological wind-speed variability is not dominated by surface effects.     

Temporal Evolution of Low-Level Winds Induced by Two-dimensional Mesoscale Surface Heat-Flux Heterogeneity

Using large-eddy simulation (LES), the effects of mesoscale local surface heterogeneity on the temporal evolution of low-level flows in the convective boundary layer driven by two-dimensional surface heat-flux variations are investigated at a height of about 100 m over flat terrain. The surface variations are prescribed with sinusoids of wavelength 32 km and varying amplitudes of 0, 50, 100, and 200 W m $^{-2}$ . The Weather Research and Forecasting numerical model is used as a mesoscale-domain LES model that has a grid spacing fine enough to explicitly resolve energy-containing turbulent eddies and a model domain large enough to include mesoscale circulations. Mesoscale circulations induced by the two-dimensional surface heterogeneity may undergo a flow transition and an associated spectral energy cascade, which has been found previously but only with one-dimensional surface heat-flux variations. Over a strongly heterogeneous surface prescribed with a two-dimensional sinusoid of amplitude 200 W m $^{-2}$ , the domain-averaged variance of the horizontal wind component initially grows rapidly, then undergoes a flow transition and subsequently rapidly decays. With a background wind, the induced mesoscale circulations are inhibited in the streamwise direction. However in the spanwise direction, somewhat stronger mesoscale circulations are induced, compared with those with no background wind. The background wind attenuates the significant reduction of the low-level temperature gradient by the fully-developed mesoscale horizontal flow. Spectral decomposition reveals that this rapid transition also exists in the mesoscale horizontal flows induced by the intermediate surface heterogeneity prescribed with a sinusoid of amplitude 100 W m $^{-2}$ . However the transition is masked by continuously growing turbulence.     

Stability Dependence and Diurnal Change of Large-Scale Turbulence Structures in the Near-Neutral Atmospheric Boundary Layer Observed from a Meteorological Tower

Based on the analysis of observations from a 213-m tall meteorological tower at Tsukuba, Japan, we have investigated the favourable conditions for the predominant existence of large-scale turbulence structures in the near-neutral atmospheric boundary layer (ABL). From the wavelet variance spectrum for the streamwise velocity component ( $u$ ) measured by a sonic anemometer-thermometer at the highest level (200 m), large-scale structures (time-scale range of 100–300 s) predominantly exist under slightly unstable and close to neutral conditions. The emergence of large-scale structures also can be related to the diurnal evolution of the ABL. The large-scale structures play an important role in the overall flow structure of the lower boundary layer. For example, $u$ velocity components at the 200-m and 50-m levels show relatively high correlation with the existence of large-scale structures. Under slightly unstable (near-neutral) conditions, a low-speed region in advance of the high-speed structure shows a positive deviation of temperature and appears as the plume structure that is forced by buoyancy in the heated lower layer. In spite of the difference in buoyancy effects between the near-neutral and unstable cases, large-scale structures are frequently observed in both cases and the same vertical correlation of $u$ components is indicated. However, the vertical wind shear is smaller in the unstable cases. On the other hand, in near-neutral cases, the transport efficiency of momentum at the higher level and the flux contribution of sweep motions are larger than those in the unstable cases.     

A simple unified theory for flow in the canopy and roughness sublayer

The mean flow profile within and above a tall canopy is well known to violate the standard boundary-layer flux–gradient relationships. Here we present a theory for the flow profile that is comprised of a canopy model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing layer analogy for the flow at a canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the flow just above the canopy, within the so-called roughness sublayer, depends. A natural form for the vertical profiles within the roughness sublayer follows that overcomes problems with many earlier forms in the literature. Predictions of the mean flow profiles are shown to match observations over a range of canopy types and stabilities. The unified theory predicts that key parameters, such as the displacement height and roughness length, have a significant dependence on the boundary-layer stability. Assuming one of these parameters a priori leads to the incorrect variation with stability of the others and incorrect predictions of the mean wind speed profile. The roughness sublayer has a greater impact on the mean wind speed in stable than unstable conditions. The presence of a roughness sublayer also allows the surface to exert a greater drag on the boundary layer for an equivalent value of the near-surface wind speed than would otherwise occur. This characteristic would alter predictions of the evolution of the boundary layer and surface states if included within numerical weather prediction models.     

A boundary-layer analysis of atmospheric motion over a semi-elliptical surface obstruction

Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, V/STOL vehicles, etc.). The purpose of this analysis is to determine the kinds of flow fields that can result from surface obstructions in an otherwise horizontally homogeneous statistically stationary flow. The technique is based on the boundary-layer/Boussinesq-approximated equations of motion. The pressure gradient resulting from the surface obstruction is that consistent with a potential flow over a two-dimensional cylinder with elliptical cross-section, an approach commonly used for boundary-layer analyses in the engineering community. The dissipative effects of atmospheric turbulence on the mean flow are represented with eddy-viscosity models of the Reynolds stresses. The upstream flow is a neutral one and is characterized by a logarithmic profile for the mean wind. The following conclusions result from the analysis: (1) localized maxima in wind speed occur at the top of a surface obstruction, which are expected in physically real flow situations, (2) an increase in the elliptical aspect ratio decreases the wind speed within the boundary layer at the top of the ellipse and returns it to the logarithmic distribution characteristic of undisturbed flow, (3) increases in surface roughness affect the flow by decreasing the velocity in the boundary layer, with the most pronounced effect occurring near the surface of the smaller aspect-ratio ellipse, (4) Reynolds number has a negligible effect on the overall flow for the range of Reynolds numbers considered in this study, (5) a decrease in the elliptical aspect ratio and an increase in the surface roughness cause larger separation regions.     

The Effect of Surface Heterogeneity on the Structure Parameters of Temperature and Specific Humidity: A Large-Eddy Simulation Case Study for the LITFASS-2003 Experiment

We conduct a high-resolution large-eddy simulation (LES) case study in order to investigate the effects of surface heterogeneity on the (local) structure parameters of potential temperature \(C_T^2\) and specific humidity \(C_q^2\) in the convective boundary layer (CBL). The kilometre-scale heterogeneous land-use distribution as observed during the LITFASS-2003 experiment was prescribed at the surface of the LES model in order to simulate a realistic CBL development from the early morning until early afternoon. The surface patches are irregularly distributed and represent different land-use types that exhibit different roughness conditions as well as near-surface fluxes of sensible and latent heat. In the analysis, particular attention is given to the Monin–Obukhov similarity theory (MOST) relationships and local free convection (LFC) scaling for structure parameters in the surface layer, relating \(C_T^2\) and \(C_q^2\) to the surface fluxes of sensible and latent heat, respectively. Moreover we study possible effects of surface heterogeneity on scintillometer measurements that are usually performed in the surface layer. The LES data show that the local structure parameters reflect the surface heterogeneity pattern up to heights of 100–200 m. The assumption of a blending height, i.e. the height above the surface where the surface heterogeneity pattern is no longer visible in the structure parameters, is studied by means of a two-dimensional correlation analysis. We show that no such blending height is found at typical heights of scintillometer measurements for the studied case. Moreover, \(C_q^2\) does not follow MOST, which is ascribed to the entrainment of dry air at the top of the boundary layer. The application of MOST and LFC scaling to elevated \(C_T^2\) data still gives reliable estimates of the surface sensible heat flux. We show, however, that this flux, derived from scintillometer data, is only representative of the footprint area of the scintillometer, whose size depends strongly on the synoptic conditions.     

Intercomparison of Methods for the Simultaneous Estimation of Zero-Plane Displacement and Aerodynamic Roughness Length from Single-Level Eddy-Covariance Data

We applied three approaches to estimate the zero-plane displacement $d$ through the aerodynamic measurement height $z$ (with $z = z_{m}- d$ and $z_{m}$ being the measurement height above the surface), and the aerodynamic roughness length $z_{0}$ , from single-level eddy covariance data. Two approaches (one iterative and one regression-based) were based on the universal function in the logarithmic wind profile and yielded an inherently simultaneous estimation of both $d$ and $z_{0}$ . The third approach was based on flux–variance similarity, where estimation of $d$ and consecutive estimation of $z_{0}$ are independent steps. Each approach was further divided into two methods differing either with respect to the solution technique (profile approaches) or with respect to the variable (variance of vertical wind and temperature, respectively). All methods were applied to measurements above a large, growing wheat field where a uniform canopy height and its frequent monitoring provided plausibility limits for the resulting estimates of time-variant $d$ and $z_{0}$ . After applying, for each approach, a specific data filtering that accounted for the range of conditions (e.g. stability) for which it is valid, five of the six methods were able to describe the temporal changes of roughness parameters associated with crop growth and harvest, and four of them agreed on $d$ to within 0.3 m most of the time. Application of the same methods to measurements with a more heterogeneous footprint consisting of fully-grown sugarbeet and a varying contribution of adjacent harvested fields exhibited a plausible dependence of the roughness parameters on the sugarbeet fraction. It also revealed that the methods producing the largest outliers can differ between site conditions and stability. We therefore conclude that when determining $d$ for canopies with unknown properties from single-level measurements, as is increasingly done, it is important to compare the results of a number of methods rather than rely on a single one. An ensemble average or median of the results, possibly after elimination of methods that produce outliers, can help to yield more robust estimates. The estimates of $z_{0}$ were almost exclusively physically plausible, although $d$ was considered unknown and estimated simultaneously with the methods and results described above.     

Momentum- and Heat-Flux Parametrization at Dome C,Antarctica: A Sensitivity Study

An extensive meteorological observational dataset at Dome C, East Antarctic Plateau, enabled estimation of the sensitivity of surface momentum and sensible heat fluxes to aerodynamic roughness length and atmospheric stability in this region. Our study reveals that (1) because of the preferential orientation of snow micro-reliefs (sastrugi), the aerodynamic roughness length \(z_{0}\) varies by more than two orders of magnitude depending on the wind direction; consequently, estimating the turbulent fluxes with a realistic but constant \(z_{0}\) of 1 mm leads to a mean friction velocity bias of \(24\,\%\) in near-neutral conditions; (2) the dependence of the ratio of the roughness length for heat \(z_{0t}\) to \(z_{0}\) on the roughness Reynolds number is shown to be in reasonable agreement with previous models; (3) the wide range of atmospheric stability at Dome C makes the flux very sensitive to the choice of the stability functions; stability function models presumed to be suitable for stable conditions were evaluated and shown to generally underestimate the dimensionless vertical temperature gradient; as these models differ increasingly with increases in the stability parameter z / L, heat flux and friction velocity relative differences reached \(100\,\%\) when \(z/L > 1\); (4) the shallowness of the stable boundary layer is responsible for significant sensitivity to the height of the observed temperature and wind data used to estimate the fluxes. Consistent flux results were obtained with atmospheric measurements at heights up to 2 m. Our sensitivity study revealed the need to include a dynamical parametrization of roughness length over Antarctica in climate models and to develop new parametrizations of the surface fluxes in very stable conditions, accounting, for instance, for the divergence in both radiative and turbulent fluxes in the first few metres of the boundary layer.