Turbulent flow over a very rough,random surface

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

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

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

Mesoscale model response to random,surface-based perturbations — A sea-breeze experiment

The introduction into a mesoscale model of random (in space) variations in roughness length, or random (in space and time) surface perturbations of temperature and friction velocity, produces a measurable, but barely significant, response in the simulated flow dynamics of the lower atmosphere. The perturbations are an attempt to include the effects of sub-grid variability into the ensemble-mean parameterization schemes used in many numerical models. Their magnitude is set in our experiments by appeal to real-world observations of the spatial variations in roughness length and daytime surface temperature over the land on horizontal scales of one to several tens of kilometers. With sea-breeze simulations, comparisons of a number of realizations forced by roughness-length and surface-temperature perturbations with the standard simulation reveal no significant change in ensemble mean statistics, and only small changes in the sea-breeze vertical velocity. Changes in the updraft velocity for individual runs, of up to several cms^-1 (compared to a mean of 14 cms^-1), are directly the result of prefrontal temperature changes of 0.1 to 0.2K, produced by the random surface forcing. The correlation and magnitude of the changes are entirely consistent with a gravity-current interpretation of the sea breeze.     

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.     

上海徐家汇地区台风“灿鸿”与良态风风速特征

上海徐家汇地区建筑分布密集且高低不一,是典型的具有非均一下垫面特征的城市地貌。本文利用该地区的地理信息研究了粗糙度长度的分布规律,并基于80m高度的风速实测数据,对台风"灿鸿"和良态风作用下的平均风速、湍流强度、阵风因子等参数与粗糙度长度之间的关系进行了分析。结果表明:不同风向角对应的计算扇区内建筑物高度、分布密度的差别导致了粗糙度长度值随风向角发生明显变化,但是变化幅度随着计算扇区的增大而减小;台风"灿鸿"作用下的平均风速最大值大于良态风,两者对应的粗糙度长度变化范围差别甚微,但是台风作用下的粗糙度长度中位数较小且分布相对集中;台风"灿鸿"作用下各向湍流强度均随着平均风速的增加呈明显的减小趋势,但不随粗糙度长度变化;良态风作用下,各向湍流强度不随平均风速变化,而随着粗糙度长度的增加而增加;台风"灿鸿"和良态风作用下,各向阵风因子均随湍流强度的增加而增大,但前者作用下的阵风因子略大于后者。     

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.     

Stability Dependence of Height Scales and Effective Roughness Lengths of Momentum and Heat Transfer Over Roughness Changes

It is widely accepted that the correct formulation of an effective roughness length, defined as the area average of the roughness length in heterogeneous terrain, relies upon the appropriate de-termination of a height scale. At this height a meteorological quantity is approximately in equilibrium with local surface conditions and independent of horizontal position. This research note determines explicitly the different height scales from the perturbation solutions of flow velocity and temperature, as well as the fluxes of momentum and heat, in a stratified boundary layer. These solutions are derived from the asymptotic approximation theory and shown to capture major characteristics of momentum and heat transfer over heterogeneous terrain with changes of the underlying roughness lengths. The effective roughness lengths can then be computed by use of these height scales. The dependence of height scales and effective roughness lengths upon stratification is also discussed briefly.     

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.     

Remarks on the Definition and Estimation of Friction Velocity

One of the mainscaling parameters in similarity theory of the atmospheric boundary layer is friction velocity. Unfortunately, several definitions of friction velocity exist in the literature. Some authors use the component of the horizontal Reynolds stress vector in the direction of the mean wind vector to define friction velocity. Others define the friction velocity by means of the absolute value of the horizontal Reynolds stress vector. The two definitions coincide only if the direction of the mean wind vector is parallel to the horizontal Reynolds stress vector. In general, the second definition gives larger values for the friction velocity. Over complex terrain the situation is further complicated by the fact that the terrain following flow is not necessarily horizontal. Thus, several authors have proposed to use terrain following coordinate systems for the definition of friction velocity. By means of a large dataset of fast-response wind measurements with an ultrasonic anemometer the friction velocities resulting from the different definitions are compared. Furthermore, it is shown that friction velocity can be well estimated from horizontal wind speed, and even better from simple horizontal or vertical turbulence parameters.     

Are Urban-Canopy Velocity Profiles Exponential?

Using analyses of data from extant direct numerical simulations and large-eddy simulations of boundary-layer and channel flows over and within urban-type canopies, sectional drag forces, Reynolds and dispersive shear stresses are examined for a range of roughness densities. Using the spatially-averaged mean velocity profiles these quantities allow deduction of the canopy mixing length and sectional drag coefficient. It is shown that the common assumptions about the behaviour of these quantities, needed to produce an analytical model for the canopy velocity profile, are usually invalid, in contrast to what is found in typical vegetative (e.g. forest) canopies. The consequence is that an exponential shape of the spatially-averaged mean velocity profile within the canopy cannot normally be expected, as indeed the data demonstrate. Nonetheless, recent canopy models that allow prediction of the roughness length appropriate for the inertial layer’s logarithmic profile above the canopy do not seem to depend crucially on their (invalid) assumption of an exponential profile within the canopy.     

Annual variation of surface roughness obtained from wind profile measurements

Summary Profile measurements of wind and temperature have been performed at the Agricultural University of Norway on a routine basis since 1997. 10-min. averages are stored in a database together with other relevant meteorological parameters. The database can be used to determine the seasonal variation of surface aerodynamic roughness, showing the growth of grass between cutting during the growing season, the effect of snowfall and the melting of snow etc. However, careful screening of the data must be conducted before reliable estimates can be made. The main objective of this study is to establish simple practical rules for filtering out unreliable datasets for the evaluation of the surface roughness parameter z₀, and to present its annual variation. The resulting values for the summer period agree well with values found in the literature for homogenous grass covered surfaces. In the transition periods during autumn and spring, and during wintertime in mild weather conditions, the surface is generally non-homogenous with a mixture of snow patches, ponds of melting water and shrubs of withered grass. The results show that the mechanical interaction between a non-homogeneous land surface and the boundary layer flow can be described by one roughness parameter, with a numeric value somewhere in between the ideal values for the different surface characteristics. Another use of the database is to investigate drainage flow and the relationship between drainage flow, prevailing wind direction and the mean vertical velocity of the air. Most micrometeorological studies of the fluxes of heat and water vapour in the surface layer, assume the mean vertical velocity to be zero, focusing on eddy fluxes and thereby excluding any transport in the mean flow. In certain situations, this may lead to serious errors. This work shows that convergence of horizontal flow leads to an upward movement of air, which is enhanced if the prevailing direction of the wind opposes the outflow of the cold drainage winds from the area.     

Cross‐shore variations of near‐surface wind velocity and atmospheric turbulence at the land‐sea boundary during CASP

Abstract

Airborne measurements of mean wind velocity and turbulence in the atmospheric boundary layer under wintertime conditions of cold offshore advection suggest that at a height of 50 m the mean wind speed increases with offshore distance by roughly 20% over a horizontal scale of order 10 km. Similarly, the vertical gust velocity and turbulent kinetic energy decay on scales of order 3.5 km by factors of 1.5 and 3.2, respectively. The scale of cross‐shore variations in the vertical fluxes of heat and downwind momentum is also 10 km, and the momentum flux is found to be roughly constant to 300 m, whereas the heat flux decreases with height. The stability parameter, z/L (where z = 50 m and L is the local Monin‐Obukhov length), is generally small over land but may reach order one over the warm ocean. The magnitude and horizontal length scales associated with the offshore variations in wind speed and turbulence are reasonably consistent with model results for a simple roughness change, but a more sophisticated model is required to interpret the combined effects of surface roughness and heat flux contrasts between land and sea.

Comparisons between aircraft and profile‐adjusted surface measurements of wind speed indicate that Doppler biases of 1–2 m s^?1 in the aircraft data caused by surface motions must be accounted for. In addition, the wind direction measurements of the Minimet anemometer buoy deployed in CASP are found to be in error by 25 ± 5°, possibly due to a misalignment of the anemometer vane. The vertical fluxes of heat and momentum show reasonably good agreement with surface estimates based on the Minimet data.     

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.     

Turbulence characteristics along several towers

Observations from several towers are used to show how measurements of wind and temperature near the surface can be used to estimate the variances of the horizontal velocity and the dissipation rate up to the top of the towers, provided the roughness length is known. The roughness length usually varies with wind direction, and the traditional methods of estimating it tend to lead to over-estimates.Analysis of cross spectra between velocity components at different levels shows that Davenport's Geometrical Similarity is satisfied. Coherence falls off exponentially with the ratio of height interval to wavelength, and the decay parameter depends on Richardson number near the surface. Coherences at different sites show no significant differences in neutral air. The lateral velocity components have larger coherence and more time delay between levels than the horizontal components at all sites.Time delay and coherence are also discussed in other Cartesian directions, and it is suggested that these quantities, having relatively simple properties, can be used as building blocks for an empirical three-dimensional model of turbulence.Contribution No. 6951     

Field And Wind-Tunnel Studies Of Aerodynamic Roughness Length

The aerodynamic roughness length (z₀) values of three Gobi desert surfaces were obtained by measurement of the boundary-layer wind profile in the field. To clarify the factors affecting the Gobi surface aerodynamic roughness length, a wind-tunnel experiment was conducted. The wind-tunnel simulation shows that z₀ values increase with increasingsize and coverage of roughness elements. Especially, the shape and height of roughnesselements are more important than other factors in affecting roughness length. The roughness length increases with decreasing values of the geometric parameter (the ratio of element horizontal surface area to height, ) of roughness elements. But at a higher free stream velocity, the height is more important than the shape in affecting roughness length.     

A model of internal boundary-layer development

A slab model of the boundary layer was used to study the dynamics of the internal boundary layer associated with changes in surface temperature. The usual numerical procedure involving finite differences was avoided by solving the governing equations in a Lagrangian framework. The results of the modelling study showed that mixed-layer growth was enhanced by: (a) an increase in surface roughness; (b) an increase in the surface temperature change; and (c) a decrease in the horizontal velocity. It was found that the vertical velocity induced by variations in the horizontal velocity could play an important role in controlling the expansion of the mixed layer.The second part of the study involved the formulation of a model by simplifying the governing equations. The analytical solution obtained from the model compared favourably with the results of the numerical model. Furthermore, the analytical expression for the mixed-layer height was virtually identical to that presented by Raynor et al. (1974) to fit their observational data.     

Flow over high roughness elements

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

Interaction Between Waves and Turbulence Within the Nocturnal Boundary Layer

Boundary-Layer Meteorology - Within the roughness sublayer (RSL) of dense urban canopies composed of uniformly distributed cuboids, the time and planar-averaged mean velocity profile exhibits an...     

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.