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.     

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.     

Subfilter-Scale Fluxes over a Surface Roughness Transition. Part II: A priori Study of Large-Eddy Simulation Models

The ability of subfilter-scale (SFS) models to reproduce the statistical properties of SFS stresses and energy transfers over heterogeneous surface roughness is key to improving the accuracy of large-eddy simulations of the atmospheric boundary layer. In this study, several SFS models are evaluated a priori using experimental data acquired downwind of a rough-to-smooth transition in a wind tunnel. The SFS models studied include the eddy-viscosity, similarity, non-linear and a mixed model consisting of a combination of the eddy-viscosity and non-linear models. The dynamic eddy-viscosity model is also evaluated. The experimental data consist of vertical and horizontal planes of high-spatial-resolution velocity fields measured using particle image velocimetry. These velocity fields are spatially filtered and used to calculate SFS stresses and SFS transfer rates of resolved kinetic energy. Coefficients for each SFS model are calculated by matching the measured and modelled SFS energy transfer rates. For the eddy-viscosity model, the Smagorinsky coefficient is also evaluated using a dynamic procedure. The model coefficients are found to be scale dependent when the filter scales are larger than the vertical measurement height and fall into the production subrange of the turbulence where the flow scales are anisotropic. Near the surface, the Smagorinsky coefficient is also found to decrease with distance downwind from the transition, in response to the increase in mean shear as the flow adjusts to the smooth surface. In a priori tests, the ability of each model to reproduce statistical properties of the SFS stress is assessed. While the eddy-viscosity model has low spatial correlation with the measured stress, it predicts mean stresses with the same accuracy as the other models. However, the deficiency of the eddy-viscosity model is apparent in the underestimation of the standard deviation of the SFS stresses and the inability to predict transfers of kinetic energy from the subfilter scales to the resolved scales. Overall, the mixed model is found to have the best performance.     

Large-Eddy Simulation of the Stable Atmospheric Boundary Layer using Dynamic Models with Different Averaging Schemes

Large-eddy simulation (LES) of a stable atmospheric boundary layer is performed using recently developed dynamic subgrid-scale (SGS) models. These models not only calculate the Smagorinsky coefficient and SGS Prandtl number dynamically based on the smallest resolved motions in the flow, they also allow for scale dependence of those coefficients. This dynamic calculation requires statistical averaging for numerical stability. Here, we evaluate three commonly used averaging schemes in stable atmospheric boundary-layer simulations: averaging over horizontal planes, over adjacent grid points, and following fluid particle trajectories. Particular attention is focused on assessing the effect of the different averaging methods on resolved flow statistics and SGS model coefficients. Our results indicate that averaging schemes that allow the coefficients to fluctuate locally give results that are in better agreement with boundary-layer similarity theory and previous LES studies. Even among models that are local, the averaging method is found to affect model coefficient probability density function distributions and turbulent spectra of the resolved velocity and temperature fields. Overall, averaging along fluid pathlines is found to produce the best combination of self consistent model coefficients, first- and second-order flow statistics and insensitivity to grid resolution.     

Wind flow over ridges in simulated atmospheric boundary layers

The flows over four two-dimensional triangular hills and three two-dimensional bell-shaped hills have been investigated in a simulated rural atmospheric boundary layer modelled to a scale of 1:300: Further measurements were made over two of the triangular hills in a simulated rural boundary layer of 1: 3000 scale and in a simulated urban boundary layer modelled to a scale of 1:400. The effect of the model hill surface roughness was also investigated. Flow measurements were restricted to the mean velocity U, RMS velocity fluctuations u and the energy spectra for the streamwise velocity component Measurements were made at a number of longitudinal positions in the approach flow, over the model hills and downstream of the model hills. For each model hill, the crest was the region of largest mean velocity and smallest velocity fluctuations. The largest mean velocities over the model hills occurred for hills of intermediate slope rather than for the steepest hills. A decrease in the scale of the simulated atmospheric boundary layer led to a reduction in the amplification factors at the hill crests, whereas an increase in the surface roughness of the approach flow resulted in increased amplification factors at the hill crests.     

The Adaptation of the Atmospheric Boundary Layer to a Change in Surface Roughness

The adaptation of the atmospheric boundary layer to a change in the underlying surface roughness is an interesting problem and hence much research, theoretical, experimental, and numerical, has been undertaken. Within the atmospheric boundary layer an accurate numerical model for the turbulent properties of the atmospheric boundary layer needs to be implemented if physically realistic results are to be obtained. Here, the adaptation of the atmospheric boundary layer to a change in surface roughness is investigated using a first-order turbulence closure model, a one-and-a-half-order turbulence closure model and a second-order turbulence closure model. Perturbations to the geostrophic wind and the pressure gradients are included and it is shown that the second-order turbulence closure model, namely the standard k - model, is inferior to a lower-order closure model if a modification to limit the turbulent eddy size within the atmospheric boundary layer is not included within the model.     

The Turbulence Structure of the Stable Atmospheric Boundary Layer Around a Coastal Headland: Aircraft Observations and Modelling Results

The turbulence structure of a stable marine atmospheric boundary layer in the vicinity of a coastal headland is examined using aircraft observations and numerical simulations. Measurements are drawn from a flight by the NCAR C-130 around Cape Mendocino on the coast of northern California on June 7 1996 during the Coastal Waves 96 field program. Local similarity scaling of the velocity variances is found to apply successfully within the continuously turbulent layer; the empirical scaling function is similar to that found by several previous studies. Excellent agreement is found between the modelled and observed scaling results. No significant change in scaling behaviour is observed for the region within the expansion fan that forms downstream of the Cape, suggesting that the scaling can be applied to horizontally heterogeneous conditions; however, the precise form of the function relating scaled velocities and stability is observed to change close to the surface. This result, differences between the scaling functions found here and in other studies, and the departure of these functions from the constant value predicted by the original theory, leads us to question the nature of the similarity functions observed. We hypothesize that the form of the functions is controlled by non-local contributions to the velocity variance budgets, and that differences in the non-local terms between studies explain the differences in the observed scaling functions.     

Scale effects in wind tunnel modeling of an urban atmospheric boundary layer

Precise urban atmospheric boundary layer (ABL) wind tunnel simulations are essential for a wide variety of atmospheric studies in built-up environments including wind loading of structures and air pollutant dispersion. One of key issues in addressing these problems is a proper choice of simulation length scale. In this study, an urban ABL was reproduced in a boundary layer wind tunnel at different scales to study possible scale effects. Two full-depth simulations and one part-depth simulation were carried out using castellated barrier wall, vortex generators, and a fetch of roughness elements. Redesigned “Counihan” vortex generators were employed in the part-depth ABL simulation. A hot-wire anemometry system was used to measure mean velocity and velocity fluctuations. Experimental results are presented as mean velocity, turbulence intensity, Reynolds stress, integral length scale of turbulence, and power spectral density of velocity fluctuations. Results suggest that variations in length-scale factor do not influence the generated ABL models when using similarity criteria applied in this study. Part-depth ABL simulation compares well with two full-depth ABL simulations indicating the truncated vortex generators developed for this study can be successfully employed in urban ABL part-depth simulations.     

Similarity theory and resistance laws for the planetary boundary layer

Methods are developed for the determination of parameters of the atmospheric planetary boundary layer, within the framework of similarity theory based on the external parameters — wind velocity at the upper boundary of the layer, its thickness, air temperature difference between the upper and the lower boundaries, roughness of the underlying surface, and buoyancy forces. The form of the resistance laws is discussed. Determination of the thickness of the stationary and horizontally homogeneous (Ekman) boundary layer is analyzed and generalizations of the latter are suggested for non-stationary and inhomogeneous boundary layers.     

Study of near-surface models for large-eddy simulations of a neutrally stratified atmospheric boundary layer

In large-eddy simulations (LES) of the atmospheric boundary layer (ABL), near-surface models are often used to supplement subgrid-scale (SGS) turbulent stresses when a major fraction of the energetic scales within the surface layer cannot be resolved with the temporal and spatial resolution at hand. In this study, we investigate the performance of both dynamic and non-dynamic eddy viscosity models coupled with near-surface models in simulations of a neutrally stratified ABL. Two near-surface models that are commonly used in LES of the atmospheric boundary layer are considered. Additionally, a hybrid Reynolds- averaged/LES eddy viscosity model is presented, which uses Prandtl’s mixing length model in the vicinity of the surface, and blends in with the dynamic Smagorinsky model away from the surface. Present simulations show that significant portions of the modelled turbulent stresses are generated by the near-surface models, and they play a dominant role in capturing the expected logarithmic wind profile. Visualizations of the instantaneous vorticity field reveal that flow structures in the vicinity of the surface depend on the choice of the near-surface model. Among the three near-surface models studied, the hybrid eddy viscosity model gives the closest agreement with the logarithmic wind profile in the surface layer. It is also observed that high levels of resolved turbulence stresses can be maintained with the so-called canopy stress model while producing good agreement with the logarithmic wind profile.     

Long-Term Mean Wind Profiles Based on Similarity Theory

We provide general forms for long-term mean wind profiles from similarity-based wind profiles, beginning with a probabilistic adaptation of Monin–Obukhov similarity theory. We develop an analytical formulation for the stability distributions prevailing in the atmospheric surface layer, which in turn facilitates the derivation of a long-term mean wind profile based on Monin–Obukhov similarity theory. The modelled stability distributions exhibit good agreement with measurements from sites having different local conditions. The long-term wind profile formulation is further extended to include the influence of the depth of the atmospheric boundary layer (h), which becomes relevant for heights above h/3, and the resultant long-term ‘tall’ profile form also matches observations.     

Statistics of shallow convection on Mars based on large-eddy simulations. Part 2: effects of wind shear

Effects of wind on quasi-steady, shallow convection in the Martian boundary layer are studied using a large-eddy simulation model. Convection in the model is generated by the radiative flux divergence and the strength of the surface heat flux, which do not vary in time. The resulting convective boundary layer exhibits transient, irregular, horizontal cellular structures, transported by wind, and a lack of well-pronounced regular horizontal rolls, observed for analogous conditions on Earth. The dimensionless statistics of turbulence are generally similar to those generated in the windless conditions, and depend on the ratio F, defined in terms of the integrated radiative and turbulent heating rates in the boundary layer. The simulations show that variations of the radiative heating influence the temperature statistics, while their effects on the wind velocity are relatively small. The horizontal velocity variances do not show a strong dependence on parameter F, in contrast with the vertical velocity variances, which are strongly dependent on F.     

Internal Boundary Layers: I. Height Formulae for Neutral and Diabatic Flows

The notion of an internal boundary layer (IBL) appeared in studies of local advection within the atmospheric boundary layer when air flows over a change in surface conditions. These include surface roughness, thermal and moisture properties. An ability to predict the height of the IBL interface in the atmosphere under neutral stability, accompanied by certain assumptions on the form of the mean flow parameters, have been a means of obtaining information on the velocity profile after step changes in roughness for more than half a century. A compendium of IBL formulae is presented. The approach based on the diffusion analogy of Miyake receives close attention. The empirical expression of Savelyev and Taylor (2001, Boundary Layer Meteorol. 101, 293–301) suggested that turbulent diffusion is not the only factor that influences IBL growth. An argument is offered that an additional element, mean vertical velocity or streamline displacement, should be taken into account. Vertical velocity is parameterized in terms of horizontal velocity differences employing continuity constraints and scaling. Published data are analyzed from a new point of view, which produces two new neutral stratification formulae. The first implies that the roughness lengths of adjacent surfaces are equally important and a combined length scale can be constructed. In addition new formulae to predict the height of the region of diabatic flow affected by a step change in surface conditions are obtained as an extension of the neutral flow case.     

Large-eddy simulations of thermally forced circulations in the convective boundary layer. Part I: A small-scale circulation with zero wind

We have conducted large-eddy simulations (LES) of the atmospheric boundary layer with surface heat flux variations on a spatial scale comparable to the boundary layer depth.We first ran a simulation with a horizontally homogeneous heat flux. In general the results are similar to those of previous large-eddy simulations. The model simulates a field of convective eddies having approximately the correct velocity and spatial scales, and with the crucial property that kinetic energy is transported vigorously upwards through the middle levels. However, the resolved temperature variance is only about half what is observed in the laboratory or the atmosphere. This deficiency — which is shared by many other large-eddy simulations — has dynamic implications, particularly in the pressure/temperature interaction terms of the heat flux budget. Recent simulations by other workers at much higher resolution than ours appear to be more realistic in this respect.The surface heat flux perturbations were one-dimensional and sinusoidal with a wavelength equal to 1.3 times the boundary-layer depth. The mean wind was zero. Results were averaged over several simulations and over time. There is a mean circulation, with ascent over the heat flux maxima (vertical velocity ~0.1w _*) and descent over the heat flux minima. Turbulence is consistently stronger over the heat flux maxima. The horizontal velocity variance components (calculated with respect to the horizontal average) become unequal, implying that convective eddies are elongated parallel to the surface heat flux perturbations.A consideration of the budgets for temperature and velocity suggests several simplifying concepts.The research reported in this paper was conducted while the first author was on study leave at Colorado State University.     

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.     

ON SIMILARITY AND THE TURBULENT STRUCTURE IN THE STABLE BOUNDARY LAYER

In the stably stratified boundary layer,the vertical flux profiles for momentum and heat can be obtained froman atmospheric boundary layer model which includes parameterization of the long-wave radiation.In addi-tion,the Monin-Obukhov similarity theory can be extended to the whole boundary layer by using the local tur-bulent scales L(z),U.(z)and 0.(z)in place of surface layer scales.The similarity predictions are ingood agreement with observational data.     

Stratified Atmospheric Boundary Layers

Various features of different stability regimes of the stable boundary layer are discussed. Traditional layering is examined in terms of the roughness sublayer, surface layer, local similarity, z-less stratification and the region near the boundary-layer top. In the very stable case, the strongest turbulence may be detached from the surface and generated by shear associated with a low level jet, gravity waves or meandering motions. In this case, similarity theory and the traditional concept of a boundary-layer break down. The elevated turbulence may intermittently recouple to the surface. Inability to adequately measure turbulent fluxes in very stable conditions limits our knowledge of this regime.     

A Modulated-Gradient Parametrization for the Large-Eddy Simulation of the Atmospheric Boundary Layer Using the Weather Research and Forecasting Model

The performance of the modulated-gradient subgrid-scale (SGS) model is investigated using large-eddy simulation (LES) of the neutral atmospheric boundary layer within the weather research and forecasting model. Since the model includes a finite-difference scheme for spatial derivatives, the discretization errors may affect the simulation results. We focus here on understanding the effects of finite-difference schemes on the momentum balance and the mean velocity distribution, and the requirement (or not) of the ad hoc canopy model. We find that, unlike the Smagorinsky and turbulent kinetic energy (TKE) models, the calculated mean velocity and vertical shear using the modulated-gradient model, are in good agreement with Monin–Obukhov similarity theory, without the need for an extra near-wall canopy model. The structure of the near-wall turbulent eddies is better resolved using the modulated-gradient model in comparison with the classical Smagorinsky and TKE models, which are too dissipative and yield unrealistic smoothing of the smallest resolved scales. Moreover, the SGS fluxes obtained from the modulated-gradient model are much smaller near the wall in comparison with those obtained from the regular Smagorinsky and TKE models. The apparent inability of the LES model in reproducing the mean streamwise component of the momentum balance using the total (resolved plus SGS) stress near the surface is probably due to the effect of the discretization errors, which can be calculated a posteriori using the Taylor-series expansion of the resolved velocity field. Overall, we demonstrate that the modulated-gradient model is less dissipative and yields more accurate results in comparison with the classical Smagorinsky model, with similar computational costs.