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.     

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.     

On the Parameterisation of the Effective Roughness Length for Momentum Transfer over Heterogeneous Terrain

We develop a parameterisation for the effective roughness length of terrain that consists of a repeating sequence of patches, in which each patch is composed of strips of two roughness types. A numerical model with second-order closure in the turbulent stress is developed and used to show that: (i) the normalised Reynolds stress develops as a self-similar profile; (ii) the mixing-length parameterisation is a good first-order approximation to the Reynolds stress. These findings are used to characterise the blending layer, where the stress adjusts smoothly from its local surface value to its effective value aloft. Previous studies have assumed that this adjustment occurs abruptly at a single level, often called the blending height. The blending layer is shown to be characterised by height scales that arise naturally in linear models of surface layer flow over roughness changes, and calculations with the numerical model show that these height scales remain appropriate in the nonlinear regime. This concept of the blending layer allows the development of a new parameterisation of the effective roughness length, which gives values for the effective roughness length that are shown to compare well with both atmospheric measurements and values determined from the second-order model.     

The Askervein Hill Project: Mean wind variations at fixed heights above ground

This is one of a series of papers on the Askervein Hill Project. It presents results on the variations in mean wind speed at fixed heights (z) above the ground from linear arrays of anemometer posts and towers. Most of the data are for z = 10 m but some are for z = 3 m. Selected and directionally grouped data from the 55 Mean Flow runs are presented together with mean flow data from Askervein '83 Turbulence runs. Comparisons are made between the data and guideline estimates of fractional speed-up ratio at hilltop locations and between the data and MS3DJH/3 model predictions along the tower lines. There is good agreement in most cases.     

Near-Wall Flow Development After A Step Change In Surface Roughness

An experimental study of the initial flow field downstream of a step change in surface roughness is presented. The roughness length of the downstream surface was approximately tenfold that of the upstream roughness and, unlike all previous studies, attention was concentrated on the roughness sublayer region beneath the inertial (log-law) region. The experiments were conducted at a boundary layer Reynolds number of about 6 × 10⁴ (based on layer thickness andfree-stream velocity) and around a longitudinal location where the (downstream) roughness length, z_o2, was about 1% of the boundary-layer thickness atthe roughness change point.The thickness of the roughness sublayer was found for the two roughness. It was observed that the vertical profiles of mean velocity and turbulence characteristics started to show similarity after about 160z₀₂ downstream of the roughness change. The presence of a shear stress overshoot is shown to depend strongly on the precise location (with respect to the roughness elements) at which the measurements are made and the thickness of the equilibrium layer is shown to be very sensitive to the way it is defined. It is demonstrated that the growing equilibrium layer has first to encompass the roughness sublayer before any thickness of inertial sublayer can be developed. It follows that, in somepractical cases, like flows across some urban environments, the latter(log-law) region may never exist at all.     

Observed Wind Profiles and Turbulence Fluxes over an ice Surface with Changing Surface Roughness

Wind profile and eddy-correlation data obtained at two sites on a melting glacier surface in Iceland during the summer of 1996 are presented. Throughout the experiment the surface roughness increased rapidly from smooth to very rough, with the largest roughness element height obtained being about 1.7 m. In a layer close to the rough surface we find that the wind speed profiles were disturbed showing horizontal inhomogeneities as in a roughness sublayer. Its height was approximately two times the height of the main roughness elements (h) at both sites throughout the experiment. From the wind profiles and eddy-correlation data we calculated corrections for the displaced zero plane as a function of time and compared these with results obtained from a drag partitioning model. In general, the agreement was reasonable considering the ranges of uncertainty but the results indicate that the increasing horizontal anisotropy of the surface probably limits the use of the model. The values obtained for the roughness lengths are in good agreement with those calculated from a simple linear model, i.e., z₀/h = 0.5 with the frontal area index. Above the roughness sublayer the wind profiles, normalised standard deviations of wind speed, and the balance of the turbulence kinetic energy budget behaved as over an ideal homogeneous surface thereby confirming similarity of the flow.     

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.     

Scalar fluxes from urban street canyons. Part I: Laboratory simulation

Flow over urban surfaces depends on surface morphology and interaction with the boundary layer above. However, the effect of the flow on scalar fluxes is hard to quantify. The naphthalene sublimation technique was used to quantify scalar vertical fluxes out of a street canyon under neutral conditions. For an array of eight canyons with aspect ratio H/W=0.75 (here, H is building height and W is the street width), increased flux was observed in the first two or three canyons for moderate and low roughness upstream. This is consistent with predictions of the length scale for initial adjustment of flow to an urban canopy. The flux was constant after the initial adjustment region and thus dependent only on local geometry. For a street canyon in the equilibrium part of the array, each facet of the street canyon was coated with naphthalene to simulate scalar release from street, walls and roof, to evaluate the effect of street canyon geometry on fluxes for H/W=0.25, 0.6, 1 and 2. Fluxes from the roof and downstream wall were considerably larger than fluxes from the street and upstream wall, and only the flux from the downstream wall exhibited a simple decrease with H/W. For each H/W there was a monotonic decrease between downstream wall, street and upstream wall transfer. This suggests that flow decelerates around the recirculation region in the lee of the upstream building, i.e. a recirculating jet rather than a symmetrical vortex. The addition of a second source within the street canyon resulted in reduced fluxes from each facet for H/W>0.25, due to increased concentration of naphthalene in the canyon air.     

A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces

Recent observations of flux-gradient anomalies in atmospheric flow close to forests, and similar rough surfaces, prompted a wind-tunnel investigation in which cross-wire anemometry was used to study the vertical development and horizontal variability of adiabatic flow over five regularly arrayed rough surfaces, encompassing a 32-fold range of roughness concentration . The roughness elements were cylinders, 6 mm in both height and diameter.Below a layer in which the velocity profile is semi-logarithmic, two surface influences upon the mean velocity field can be distinguished: wake diffusion and horizontal inhomogeneity. The wake diffusion effect causes non-dimensional vertical velocity gradients to be smaller than in the semi-logarithmic region; at least for elements with aspect ratios l/h 1, it is governed by the transverse dimension l of the roughness elements, and is observed when z > h + 1.5l (where z is height above the underlying surface, and h is the height of the roughness elements). A simple diffusivity model successfully describes the horizontally averaged velocity profiles in the region of wake influence, despite conceptual disadvantages. The horizontal inhomogeneity of the flow is negligible when z > h + D (D being the inter-element spacing), and does not entirely mask the wake diffusion effect except over very sparsely roughened surfaces ( 0.02). A criterion for negligibility of both effects, and hence for applicability of conventional turbulent diffusivity theory for momentum, is z > h + 1.5D. These results are compared with atmospheric data, and indicate that wake diffusion may well cause some underestimation of the zero-plane displacement d over typical vegetated surfaces.     

Numerical simulation of turbulent convective flow over wavy terrain

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

Effect of thermal stratification on the growth of the internal boundary layer

The growth of a two-dimensional internal boundary layer (IBL), which develops when a neutral or unstably stratified flow over a uniform terrain encounters a step-change in surface roughness, is numerically investigated by a higher-order turbulence closure theory. It is found that the thickness of the IBL increases as ~ x ⁿ, where x is the downstream distance from the roughness-transition line. For a given set of upstream conditions, the value of the exponent n depends only on the Monin-Obukhov length L, and it is approximately independent of the roughness-change parameter M = In (z01/z02). At large fetches, increases markedly with increasing instability.NRC-NAS Resident Research Associate at AFCRL, 1973–74     

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.     

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 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.     

Studies on critical Reynolds number indices for wind-tunnel experiments on flow within urban areas

Reynolds-number dependence of flow fields within a modelled urban area was studied in a wind tunnel. We measured flow around a single model building and around model city blocks at various wind speeds, and studied Reynolds number indices more appropriate than the building Reynolds number. Our results led to the following conclusions. Firstly, the flow around the models in the wind tunnel was roughly divided into three parts according to the intensities of viscous stress and Reynolds stress as follows: (1) the flow in the vicinity of the ground or the surfaces of the model, where viscous stress became dominant under certain conditions; (2) the flow detached from the surfaces of the model, where Reynolds stress was always dominant; and (3) the flow around the separation bubble at the leading edge of the building model, where the influences of both viscous stress near the wall and the Reynolds stress in the separated boundary layer were mixed.Secondly, the critical Reynolds number of the flow in the modelled urban area could be defined by using both the roughness Reynolds number Re_z0 (= z₀u_*/) and the dimensionless height z₊ (= zu_*/). Reynolds-number independence could be expected for whole flow fields in the modelled urban areas as long as the critical values of Re_z0 and z₊ were satisfied.     

Shear stress results from a mixed spectral finite-difference model: Application to the Askervein Hill project data

Beljaars et al. (1987) developed a model for neutrally stratified boundary-layer flow over roughness changes and topography. It has been discovered that a constant parameter, , was missing in the algebraic-stress closure equations of their paper. This omission also occurred in the MSFD model code but only affects the Askervein Hill shear-stress results for the E-- turbulence closure in Beljaars et al. It also changes the stress results of Karpik (1988), but not his conclusions regarding the robustness of his improved numerical scheme. The present paper demonstrates the effect of the omission of the parameter, , and tests the sensitivity of the model to variations in its value. The new results are compared with the data and model results of Zeman and Jensen (1987).     

Spatial Variability of Turbulent Fluxes in the Roughness Sublayer of an Even-Aged Pine Forest

The spatial variability of turbulent flow statistics in the roughness sublayer (RSL) of a uniform even-aged 14 m (= h) tall loblolly pine forest was investigated experimentally. Using seven existing walkup towers at this stand, high frequency velocity, temperature, water vapour and carbon dioxide concentrations were measured at 15.5 m above the ground surface from October 6 to 10 in 1997. These seven towers were separated by at least 100m from each other. The objective of this study was to examine whether single tower turbulence statistics measurements represent the flow properties of RSL turbulence above a uniform even-aged managed loblolly pine forest as a best-case scenario for natural forested ecosystems. From the intensive space-time series measurements, it was demonstrated that standard deviations of longitudinal and vertical velocities (_u, _w) and temperature (_T) are more planar homogeneous than their vertical flux of momentum (u_* ²) and sensible heat (H) counterparts. Also, the measured H is more horizontally homogeneous when compared to fluxes of other scalar entities such as CO₂ and water vapour. While the spatial variability in fluxes was significant (>15 %), this unique data set confirmed that single tower measurements represent the canonical structure of single-point RSL turbulence statistics, especially flux-variance relationships. Implications to extending the moving-equilibrium hypothesis for RSL flows are discussed. The spatial variability in all RSL flow variables was not constant in time and varied strongly with spatially averaged friction velocity u_*, especially when u_* was small. It is shown that flow properties derived from two-point temporal statistics such as correlation functions are more sensitive to local variability in leaf area density when compared to single point flow statistics. Specifically, that the local relationship between the reciprocal of the vertical velocity integral time scale (I_w) and the arrival frequency of organized structures (/h) predicted from a mixing-layer theory exhibited dependence on the local leaf area index. The broader implications of these findings to the measurement and modelling of RSL flows are also discussed.     

A scheme for computing surface fluxes from mean flow observations

A computational scheme is developed for estimating turbulent surface stress, sensible heat flux and humidity flux from mean velocity, temperature and humidity at a single height in the atmospheric surface layer; conditions at this reference level are presumed known from observations or from a numerical atmospheric circulation model. The method is based on coupling a Monin-Obukhov similarity profile to a force-restore formulation for the evolution of surface soil temperature to yield the local values of shear stress, heat flux and surface temperature. A self-contained formulation is presented including parameterizations for solar and infrared radiant flux at the surface.In addition to reference-level mean flow properties, the parameters needed to implement the scheme are thermal heat capacity of the soil, surface aerodynamic roughness, latitude, solar declination, surface albedo, surface emissivity and atmospheric transmissivity.Sample calculations are presented for (a), constant atmospheric forcing at the reference level, and (b) variable atmospheric forcing corresponding to Kahle's (1977) measurements of windspeed, air temperature and radiometer soil surface temperature under dry vegetatively sparse conditions in the Mohave Desert in California. The latter case simulated the observed diurnal variations resonably well for the parameters used.Consultant, Atmospheric Sciences Division, Department of Energy and Environment, Brookhaven National Laboratory, Upton, N.Y., pc11973, U.S.A.     

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

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