湍流频散对边界层风廓线的影响

应用包括湍流粘性和频散的新的Reynolds平均动量方程，分析了边界层的垂直风速廓线，发现包含湍流频散的地面层的风速廓线对经典的风廓线指数规律有一个对数规律的修改；而且在不稳定层结下比在稳定层结下，湍流的频散效应更为显；在中性条件下，指数规律退化为对数规律并且Karman常数被另外一个常数所代替，而这个新常数也可以通过相似理论来获得。     

Optimizing the Determination of Roughness Parameters for Model Urban Canopies

We present an objective optimization procedure to determine the roughness parameters for very rough boundary-layer flow over model urban canopies. For neutral stratification the mean velocity profile above a model urban canopy is described by the logarithmic law together with the set of roughness parameters of displacement height d, roughness length \(z_0\), and friction velocity \(u_*\). Traditionally, values of these roughness parameters are obtained by fitting the logarithmic law through (all) the data points comprising the velocity profile. The new procedure generates unique velocity profiles from subsets or combinations of the data points of the original velocity profile, after which all possible profiles are examined. Each of the generated profiles is fitted to the logarithmic law for a sequence of values of d, with the representative value of d obtained from the minima of the summed least-squares errors for all the generated profiles. The representative values of \(z_0\) and \(u_*\) are identified by the peak in the bivariate histogram of \(z_0\) and \(u_*\). The methodology has been verified against laboratory datasets of flow above model urban canopies.     

Simulations of Turbulent Flow Over Complex Terrain Using an Immersed-Boundary Method

We present an immersed-boundary method to simulate high-Reynolds-number turbulent flow over the complex terrain of Askervein and Bolund Hills under neutrally-stratified conditions. We reconstruct both the velocity and the eddy-viscosity fields in the terrain-normal direction to produce turbulent stresses as would be expected from the application of a surface-parametrization scheme based on Monin–Obukhov similarity theory. We find that it is essential to be consistent in the underlying assumptions for the velocity reconstruction and the eddy-viscosity relation to produce good results. To this end, we reconstruct the tangential component of the velocity field using a logarithmic velocity profile and adopt the mixing-length model in the near-surface turbulence model. We use a linear interpolation to reconstruct the normal component of the velocity to enforce the impermeability condition. Our approach works well for both the Askervein and Bolund Hills when the flow is attached to the surface, but shows slight disagreement in regions of flow recirculation, despite capturing the flow reversal.     

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.     

大气层结和海气交换作用影响的海面风剖面研究

风速剖面是各类工程结构抗风设计的关键参数。为了准确估算近海各类工程建筑结构承受的风荷载作用,通过在对数风剖面中引入大气稳定度函数和拖曳系数来刻画大气层结和海气交换作用对近海风速剖面的影响并建立相应的模型,最后利用强台风“黑格比”(0814号)的实测数据对模型进行了验证。研究结果表明:大气层结和海气交换作用对台风“黑格比”风速剖面有一定的影响,考虑大气层结和海气交换作用的风速剖面较对数剖面更能准确描述台风过程的风速剖面特征。      

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.     

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.     

Momentum extraction with saltation: Implications for experimental evaluation of wind profile parameters

In wind tunnel studies of aeolian transport, the number and position of pitot tubes are decided by the researcher, so that there are important variations in the computation ofU _* between studies. Velocity measurements seldom are made very close to mobile surfaces because the tubes become blocked by drifting sand grains. This practice is fortuitous as demonstrated by recent selfregulatory models of saltation which indicate that fluid and grain-borne shear stress vary substantially within the lowest 0.01 m and application of the logarithmic law is therefore unsound. This study reports detailed velocity measurements which further suggest that no single logarithmic expression, based on fixed values of κ and τ, adequately represents the full wind profile which includes the inner saltation cloud above 0.01 m and the outer grain-free region of the boundary layer. A much improved fit over the logarithmic wind profile model is achieved with a square root relation, although there is no known physical basis for this specific form of power model. Relatively shallow boundary-layer development in wind tunnels forces the velocity gradient above the region of momentum extraction to attain exceptionally large values, uncommon in natural settings.     

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.     

Zero-plane displacement and roughness length for tall vegetation,derived from a simple mass conservation hypothesis

A method for the determination of the zero-plane displacement, d, and roughness length, z ₀, for tall vegetation is described. A new relationship between d and z ₀ is developed by imposing the condition of mass conservation on the logarithmic wind profile. Further, d and z ₀ can be evaluated directly if independent measurements of friction velocity are available in addition to wind profile measurements. The proposed method takes into account the existence of a transition layer immediately above the vegetation where the logarithmic wind profile law is not valid. Only one level of wind speed measurements is necessary within the inertial sub-layer.The method is applied to wind profile and eddy correlation measurements taken in and above an 18.5 m pine forest to yield d = 12.7 m and z ₀ = 1.28 m. The choice of height for the upper level of measurement and problems with measuring canopy flow are discussed.Work carried out while on leave at the Institute of Hydrology.     

The logarithmic profile in wind erosion: An algebraic solution

This paper presents a simple algebraic approach to the interpretation of wind erosion data that allows for density variation close to the surface due to the presence of large amounts of saltating material. The effect explains nonlinearities in the logarithmic velocity profile near the surface and extends the profile into the saltating layer.     

Direct Numerical Simulation of Stable Channel Flow at Large Stability

We consider a model for the stable atmospheric boundary at large stability, i.e. near the limit where turbulence is no longer able to survive. The model is a plane horizontally homogeneous channel flow, which is driven by a constant pressure gradient and which has a no-slip wall at the bottom and a free-slip wall at the top. At the lower wall a constant negative temperature flux is imposed. First, we consider a direct numerical simulation of the same channel flow. The simulation is computed with the neutral channel flow as initial condition and computed as a function of time for various values of the stability parameter h/L, where h is the channel height and L is related to the Obukhov length. We find that a turbulent solution is only possible for h/L < 1.25 and for larger values turbulence decays. Next, we consider a theoretical model for this channel flow based on a simple gradient transfer closure. The resulting equations allow an exact solution for the case of a stationary flow. The velocity profile for this solution is almost linear as a function of height in most of the channel. In the limit of infinite Reynolds number, the temperature profile has a logarithmic singularity at the upper wall of the channel. For the cases where a turbulent flow is maintained in the numerical simulation, we find that the velocity and temperature profiles are in good agreement with the results of the theoretical model when the effects of the surface layer on the exchange coefficients are taken into account. Frans Nieuwstadt, a recently retired member of the BLM Editorial Board and a well-known member of the boundary-layer/turbulence community, died unexpectedly on 18 May 2005. An obituary will appear in a later issue of BLM.     

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 temperature profile and heat transfer law in a neutrally and stably stratified planetary boundary layer

A logarithmic + polynomial approximation is proposed for the vertical temperature profile in a neutrally or stably stratified planetary boundary layer (PBL) in conditions of quasi-stationarity. Using this approximation with the asymptotic logarithmic + linear law of the Monin-Obukhov similarity theory for the near-surface layer and with the Zilitinkevich formula for the PBL thickness allows one to derive an analytical expression for the function C in the heat transfer law, which permits simple parameterization of the thermal interaction between the atmosphere and the underlying medium in terms of external parameters, such as the geostrophic wind velocity and the temperature difference across the PBL.     

Boundary-layer trade-wind profile and stress on a tropical windward coast

Under persistent onshore trade-wind conditions, the wind profile was measured in the surface layer on a mud flat of the tidal stream of Estero de Data, Gulf of Guayaquil, Ecuador. It was found that the logarithmic wind relation fitted the observations very well and that the inferred shear velocity was a linear function of wind speed in the range of wind velocity studied.     

An extended Miles' theory for wave generation by wind

Miles' inviscid theory of surface wave generation by wind is (a) modified by replacing the logarithmic shear velocity profile with one which applies right down to the wave surface and which exhibits an explicit dependence on the roughness of the surface, and (b) extended to include the effects of the interaction of wave with air flow turbulence by considering the wave-modified mean flow as the mean of the actual turbulent air flow over water waves and using this in a mixing-length model.The surface pressure is shown to depend significantly on the flow conditions being aerodynamically smooth or rough. Its component in phase with the surface elevation is practically unaffected by the wave-turbulence interaction. However, such interaction tends to increase the rate of energy input ß from wind to waves travelling in the same direction, e.g., the increase is 2gk ² for aerodynamically rough flow, where gk is the Von Karman constant. It also provides damping of waves in an adverse wind which can be about 10% of the growth rate in a favourable wind.     

An improved method for integrating the Mixed Spectral Finite Difference (MSFD) model equations

In their Mixed Spectral Finite Difference (MSFD) model for flow over complex terrain, Beljaars et al. (1987) solve a set of coupled, second-order ordinary differential equations (ODEs) for the first-order perturbations to the logarithmic velocity profile caused by nonuniform surface roughness and topography. To solve this set of ODEs, they employ a Forward Euler Shooting Method. It is demonstrated here that the shooting method is computationally unstable for this problem. An absolutely stable finite-difference method based on a block tridiagonal LU factorization of the finite-difference matrix is presented. The advantages of the present algorithm over the method used by Beljaars et al. are demonstrated both by theoretical argument and numerical experiment.     

A nonstationary nocturnal drainage flow model

The evolution and structure of the steady state of an idealized nocturnal drainage flow over a large uniformly-sloping surface are studied using a nonstationary model with a height-dependent eddy diffusivity profile and a specified surface cooling rate. The predicted mean velocity and temperature profiles are compared with Prandtl's stationary analytical solutions based on the assumption of a constant eddy diffusivity in the drainage layer. The effects of important physical parameters, such as the slope angle, surface cooling, atmospheric stability, and surface roughness, on the steady drainage flow are investigated.Affiliated with Oak Ridge Associated Universities (ORAU).     

Mean horizontal wind profiles measured in the atmospheric boundary layer about a simulated block building

Instrumented wind towers are used to measure the three components of wind about a simulated block building. The mean horizontal wind profiles over the building are compared with wind profiles measured in the absence of the building and the wind speed deficit in the wake of the building is correlated.Horizontal mean wind speeds measured in the natural atmospheric boundary layer with and without the presence of a simulated building show excellent reproducibility and agreement with fundamental concepts of fluid mechanics. The data possess all the characteristic features reported from wind-tunnel studies of building flows. In the present study the turbulence intensity is of the order of 20% in the undisturbed flow whereas the free stream turbulence intensity of wind-tunnel studies is generally not more than 5%. The effect of smaller averaging periods and the structure of the turbulence will be reported at a later time.The velocity profiles measured in the undisturbed flow zones support the representation of a neutrally stable atmospheric boundary layer with a logarithmic wind profile.