Roughness Length Zo Research Articles

Investigating the Aerodynamic Surface Roughness Length over Baghdad City Utilizing Remote Sensing and GIS Techniques

This study calculated the surface roughness length (Zo), zero-displacement length (Zd) and height of the roughness elements (ZH) using GIS applications. The practical benefit of this study is to classify the development of Baghdad, choose the appropriate places for installing wind turbines, improve urban planning, find rates of turbulence, pollution and others. The surface roughness length (Zo) of Baghdad city was estimated based on the data of the wind speed obtained from an automatic weather station installed at Al-Mustansiriyah University, the data of the satellite images digital elevation model (DEM), and the digital surface model (DSM), utilizing Remote Sensing Techniques. The study area was divided into 15 municipalities (Rasheed, Mansour, Shulaa, Karrada, Shaab, Adhamiyah, Sadre 2, Sadre 1, Rusafa, Alghadeer, Baghdad Aljadeedah, Karkh, Kadhumiya, Green zone, and Dora). The results indicated that the variations in Zo depend strongly on zero-displacement length (Zd) and the roughness element height (ZH) and wind speed. The research results demonstrated that Baghdad Aljadeedah has the largest (Zo) with 0.43 m and Rasheed has the lowest value of (Zo) with 0.19 m.; the average (Zo) of Baghdad city was 0.32 m.

Temporal changes in small scale snowpack surface roughness length for sublimation estimates in hydrological modelling

Snowpack aerodynamic surface roughness length (zo) is a critical variable in estimating heat transfers to and from a snow surface and thus sublimation rates. This variable has been shown to be site specific. To illustrate a temporal variation in zo, laboratory experiments were performed using a small evaporation pan sitting on a load cell with a constant wind flow over the snow surface. Comparing multi-layer meteorological data above the pan to sublimation measured from mass change showed a decrease in the snowpack surface roughness length as the snow metamorphosed. The sensitivity of snowpack zo changes over time in modeling of sublimation was examined using hourly meteorological data for the winter of 2000-2001 at Syracuse, New York and Leadville Colorado for several scenarios, including increasing or decreasing zo after a snowfall event, considering directionality of zo as a function of the wind direction, and a ratio of latent heat to momentum roughness lengths. The base case used a constant zo of 0.01 metres. The modeled differences were a function of the values of zo, which varied with the frequency of occurrence of fresh snow and the distribution of wind from various directions. The temporal and spatial variability in surface roughness is crucial in computing the energy and mass balance of a snowpack.

Some Measurements of Surface Drag in Urban-Type Boundary Layers at Various Wind Angles

Using experimental data obtained in naturally grown boundary layers over a generic urban-type roughness (height h) it is shown that the surface drag is strongly dependent on the flow direction with respect to the roughness orientation. The variations with wind direction are accompanied by corresponding changes in the parameters contained in the usual logarithmic description of the flow in the near-wall inertial layer, \({U/u_\tau=\frac{1}{\kappa}\ln[(z-d)/z_{\rm o}]}\), principally the roughness length zo, which can vary by a factor of around three. The maximum surface drag (and roughness length) occur when the flow direction is at an angle around 45° to the faces of the cubical roughness elements, consistent with the known fact that the drag of an isolated cube in a thick boundary layer is much larger at that orientation than for flow directions normal to the faces. An accurate electronic balance was used to determine the surface drag (and hence friction velocity uτ) and pressure-tapped roughness elements allowed estimation of the zero plane displacement d. It is shown that the best logarithmic-law fits then generally require values of the von Karman ‘constant’ κ significantly lower than its classical value of around 0.41. For a factor of six increase in the Reynolds number (from \({U_{\rm ref}h/\nu\approx 3,500}\)), Reynolds number effects are shown to be very weak and, coupled with the form drag and total drag data, the results thus suggest that frictional contributions to the total surface drag are relatively small.

Effects of Land Use and Meteorological Conditions on Local and Regional Momentum Transport and Roughness for Midwestern Cropping Systems

Abstract Eddy covariance measurements of wind speed u and shear velocity u* from tower- and aircraft-based systems collected over rapidly developing corn- (Zea mays L.) and soybean [Glycine max (L.) Merr.] fields were used in determining the local and regional (effective) surface roughness length zo and 〈zo〉, respectively. For corn, canopy height increased from ∼1 to 2 m and the leaf area index changed from ∼1 to 4 during the study period, while for soybean, canopy height increased from ∼0.1 to 0.5 m and the leaf area index increased from ∼0.5 to 2. A procedure for the aggregation of local roughness values from the different land cover types based on blending-height concepts yielded effective surface roughness values that were from ∼1/2 to 1/4 of the magnitude estimated with the aircraft data. This indicated additional kinematic stress caused by form drag from isolated obstacles (i.e., trees, houses, and farm buildings), and the interaction of adjacent corn- and soybean fields were probably important factors influencing the effective surface roughness length for this landscape. The comparison of u* measurements from the towers versus the aircraft indicated that u* from aircraft was 20%–30% higher, on average, and that u* over corn was 10%–30% higher than over soybean, depending on stability. These results provide further evidence for the likely sources of additional kinematic stress. Although there was an increase in zo and 〈zo〉 over time as the crops rapidly developed, particularly for corn, there was a more significant trend of increasing roughness length with decreasing wind speed at wind speed thresholds of around 5 m s−1 for the aircraft and 3 m s−1 for the tower measurements. Other studies have recently reported such a trend. The impact on computed sensible heat flux H using 〈zo〉 derived from the aggregation of zo from the different land cover types, using the blending-height scheme, and that estimated from the aircraft observations, was evaluated using a calibrated single-source/bulk resistance approach with surface–air temperature differences from the aircraft observations. An underestimate of 〈zo〉 by 50% and 75% resulted in a bias in the H estimates of approximately 10% and 15%, respectively. This is a relatively minor error when considering that the root-mean-square error (rmse) value between single-source estimates and the aircraft observations of H was 15 W m−2 using the aircraft-derived 〈zo〉, and only increased to approximately 20 and 25 W m−2 using the 1/2 and 1/4 〈zo〉 values, as estimated from the blending-height scheme. The magnitude of the excess resistance relative to the aerodynamic resistance to heat transfer was a major contributing factor in minimizing the error in heat flux calculations resulting from these underestimations of 〈zo〉.

Some observations of the effects of micro-organisms growing on the bed of an open channel on the turbulence properties

In this paper we report the results of an experimental study of periphyton–flow interactions conducted in a specially designed outdoor hydraulic flume. ‘Periphyton’ is a collective term for the micro-organisms which grow on stream beds, and includes algae, bacteria, and fungi, with algae usually the dominant and most conspicuous component. The main goals of the study are to identify potential effects of periphyton–flow interactions as well as the potential mechanisms of mass transfer in the near-bed region, which could influence periphyton growth and losses. The main results of the study may be summarized as follows.A linear velocity distribution in the interfacial sublayer (i.e. below the roughness tops), and a logarithmic distribution above the roughness tops appeared to be reasonable approximations for both flow types, with and without periphyton on the bed. However, the appearance of periphyton on a rough bed shifts the origin of the bed upwards, increases the roughness length zo by 16–21%, and reduces the ratio of the mean velocity at the level of roughness tops to the shear velocity by ≈30%. In general, below the roughness tops the periphyton suppresses the mean velocities, the turbulent stresses, turbulence intensities, and vertical turbulent fluxes of the turbulent energy and turbulent shear stresses.It was found that in flows without periphyton large-scale eddies successfully penetrate the interfacial sublayer. However, tufts of periphyton on the tops of the roughness elements significantly weaken the penetration processes leading to spatial de-correlation in the velocity field within the interfacial sublayer. The appearance of periphyton on the bed does not change appreciably the velocity spectra above the roughness tops but reduces the total spectral energy and generates a wide spectral peak in the interfacial sublayer. Most probably, this peak is formed by penetration of sweep events into the interfacial sublayer, ‘filtered’ by the periphyton tufts. Thus, sweep events may be the main mechanism responsible for the delivery of nutrients from the outer region to the biologically active interfacial sublayer. The potential effects of flow properties on the periphyton community are also discussed.

Friction velocityu⋆ and roughness length zo of atmospheric surface boundary layer in sparse-tree land

Sparse-tree land is one of the typical lands and can be considered as one typical rough surface in boundary layer meteorology. Many lands can be classified into the kind surface in the view of scale and distribution feature of the roughness elements such as agroforest, scatter planted or growing trees, savanna and so on. The structure of surface boundary layer in sparse-tree land is analyzed and the parameters, friction velocityu⋆and roughness length zo are deduced based on energy balance law and other physical hypothesis. The models agree well with data of wind tunnel experiments and field measurements.

The effect of sediment concentration on bedload roughness

Bedload roughness is the roughness produced by sediment transported near the bed. While it is well established that the magnitude of this roughness is proportional to the thickness of the moving sediment layer, the effect of sediment concentration remains largely unknown. This paper presents the results of a flume experiment that was designed to investigate the effect of sediment concentration on bedload roughness. The experiment consisted of creating flow conditions where bedload transport is supply-limited and injecting gravel size particles (D50=7·4 mm) at the upstream end of the flume in order to produce bedload transport. While keeping flow conditions constant, sediment concentration was varied by successively increasing the injection rate of gravel in the flow. For each injection rate, flow velocity profiles were measured in order to evaluate changes of mean flow velocity U, shear velocity u*, roughness length zo and resistance to flow f. The results indicate that low sediment concentration affects mainly the near bed portion of the flow where it causes a reduction of mean flow velocity and an increase of shear velocity and roughness length. For larger sediment concentration, the whole flow velocity profile becomes affected by bedload roughness but the importance of this effect always remain larger near the bed. As sediment concentration is augmented, mean flow velocity is consistently reduced but shear velocity and roughness length increase until a plateau is reached where these two variables become constant. Copyright © 1999 John Wiley & Sons, Ltd.

Estimates of bottom roughness length and bottom shear stress in South San Francisco Bay, California

A field investigation of the hydrodynamics and the resuspension and transport of particulate matter in a bottom boundary layer was carried out in South San Francisco Bay (South Bay), California, during March‐April 1995. Using broadband acoustic Doppler current profilers, detailed measurements of turbulent mean velocity distribution within 1.5 m above bed have been obtained. A global method of data analysis was used for estimating bottom roughness length zo and bottom shear stress (or friction velocities u*). Field data have been examined by dividing the time series of velocity profiles into 24‐hour periods and independently analyzing the velocity profile time series by flooding and ebbing periods. The global method of solution gives consistent properties of bottom roughness length zo and bottom shear stress values (or friction velocities u*) in South Bay. Estimated mean values of zo and u* for flooding and ebbing cycles are different. The differences in mean zo and u* are shown to be caused by tidal current flood‐ebb inequality, rather than the flooding or ebbing of tidal currents. The bed shear stress correlates well with a reference velocity; the slope of the correlation defines a drag coefficient. Forty‐three days of field data in South Bay show two regimes of zo (and drag coefficient) as a function of a reference velocity. When the mean velocity is >25–30 cm s−1, the ln zo (and thus the drag coefficient) is inversely proportional to the reference velocity. The cause for the reduction of roughness length is hypothesized as sediment erosion due to intensifying tidal currents thereby reducing bed roughness. When the mean velocity is <25–30 cm s−1, the correlation between zo and the reference velocity is less clear. A plausible explanation of scattered values of zo under this condition may be sediment deposition. Measured sediment data were inadequate to support this hypothesis, but the proposed hypothesis warrants further field investigation.

A New Method for Estimating Roughness Parameters and Evaluating the Quality of Observations

A new method for estimating the roughness parameters (displacement height d, momentum roughness length zo, and friction velocity u∗), under adiabatic conditions, is introduced in this paper. The goals of this method are to obtain an unambiguous best fit for the roughness parameters and, perhaps, to reduce the present large uncertainties in these estimations via screening of the wind profile observations using a standard quality-of-fit measure. There are a number of advantages to this new method. Not only does it produce better fits (less error between predicted and observed values) than the two most commonly used methods but it also does so more effectively when the observations are of high quality. The standard wind profile equation is rewritten in a manner that allows linear least squares analysis to be performed unambiguously to determine the best fit values for dand zo for any given u∗. The u∗ is scanned to find the true best fit for all three parameters. The quality of fit, Q, of the parameters to the wind profile observations is also found. This quality of fit test is used beyond the normal test for adiabaticity to screen out the low-quality observations. Using only high-quality observations to estimate the roughness parameters should reduce the uncertainties. The purposes of this paper are to introduce the method, to illustrate how it improves the fit, and to make it known that a fortran program that performs this analysis is available by contacting the author for the World Wide Web address.

The scintillation method tested over a dry vineyard area

Measurements of a scintillometer device mounted at 4 m above a dry vineyard area in La Mancha, Spain, are used to obtain an average sensible heat flux densityH. Averaging is over a rectangular area determined by the distance between the scintillometer light source and receptor (875 m) and some upwind distance governed by the horizontal wind speed perpendicular to that line. Using similarity relations obtained from La Crau, a good correspondence betweenH measured with the scintillometer and an eddy-correlation device in the centre of a vineyard is obtained. The friction velocityu * was either measured directly using a sonic anemometer or obtained indirectly from two wind speeds and known values of the roughness length zo and displacementd. The free convection formulation underestimates the sensible heat flux by about 30%. This is due to a significant contribution of mechanically generated turbulence to the total turbulent transport, which was caused by relatively strong winds and rough terrain.

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 δ up to 0.15H and wavelength λ 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 lengthzo=10−4H. 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 δ/H. The turbulence variances increase mainly in the lower half of the mixed layer forU/w*>2.

Secondary circulations in the bottom boundary layer over sedimentary furrows

Secondary circulation is known to be an important feature of many atmospheric and laboratory boundary layers. The presence of streamwise, helical, counterrotating vortices is documented here for the first time in the bottom boundary layer of a large natural body of water. Simultaneous vertical profiles of velocity and temperature were recorded on either side of a sedimentary furrow on the floor of Lake Superior (depth = 100 m) in November 1985. Flow roughness length zo was estimated to be 0.3 cm. Friction velocity u* and turbulent boundary layer thickness LW were estimated for each profile allowing for stratification effects. Typically, LW ≈ 10 m. Thermal stratification near the lake bed was an important constraint to boundary layer development; bottom mixed layers were absent in most cases. Mean flow toward the furrow at lower levels within the boundary layer (z/LW<0.37) and mean flow away from the furrow at higher levels (0.37 < z/LW < 1.65) were observed for near‐bottom speeds greater than 6 cm/s when mean flow direction was within 25° of the furrow direction. This implies helical vortex pair circulations with upward motion over the furrow, consistent with earlier hypotheses. Cross‐stream (secondary) flows were typically 5% of the free stream (primary flow) speed. Streamwise vorticity in the range 1.5 m ≤ z ≤ 5 m was estimated to be 2.1×10−3 s−1.

Turbulent shear flows over low hills

A general analysis is developed for turbulent shear flows over two- and three-dimensional hills with low-slopes which allows for a wide range of upwind velocity profiles, such as those caused by wakes of upwind hills, roughness changes, or changes in stratification. In this paper the atmosphere is assumed to be neutrally stable and the half-lengths of the hills, L, are large compared with their heights, H, which are very large compared with the roughness length zo. The general structure of the solution is defined by dividing the flow into two regions, each of which is divided into two sublayers: an inviscid outer region composed of an upper layer in which there is potential flow when the atmosphere is neutrally stable, and a middle layer in which the wind shear dominates; and an inner region of thickness l ≤ L in which the effects of perturbation shear stresses are confined. The latter region is divided into two: a shear stress layer where the shear stresses, although weak, determine that the maximum of the perturbation velocity is located in this layer; and an inner surface layer of thickness ls where the shear stress gradient varies rapidly and the perturbation velocity tends to zero. The details of the middle layer are given here for different kinds of upwind profiles, including logarithmic, ‘power law’ and linear profiles. It is shown that the analysis can be extended to allow for nonlinear inertial effects in the middle layer. Analytical solutions are derived for the inner region as asymptotic expansions in δ = [ln(l/zo)]−1, which is assumed to be small, and this shows that ls ∼ zo(l/zo)1/2. The results of the analytical model are compared with our own and with previously published numerical computations of the full equations (applying the same assumptions used for calculating the turbulent shear stresses as used in the analytical work), which have largely been validated against full-scale measurements. These results confirm that the relative increase of surface stress is significantly greater than the increase of wind speed near the surface except when there is no upwind shear (as for example in a logarithmic boundary layer when the roughness length tends to zero). Finally, the paper shows that the outer regions of laminar (or constant eddy viscosity) and of turbulent flows over hills are broadly similar, but that the effects of the flow in the inner region on the outer regions are much smaller in the latter case.

Turbulent shear flows over low hills

AbstractA general analysis is developed for turbulent shear flows over two‐ and three‐dimensional hills with low‐slopes which allows for a wide range of upwind velocity profiles, such as those caused by wakes of upwind hills, roughness changes, or changes in stratification. In this paper the atmosphere is assumed to be neutrally stable and the half‐lengths of the hills, L, are large compared with their heights, H, which are very large compared with the roughness length zo. The general structure of the solution is defined by dividing the flow into two regions, each of which is divided into two sublayers: an inviscid outer region composed of an upper layer in which there is potential flow when the atmosphere is neutrally stable, and a middle layer in which the wind shear dominates; and an inner region of thickness l ≤ L in which the effects of perturbation shear stresses are confined. The latter region is divided into two: a shear stress layer where the shear stresses, although weak, determine that the maximum of the perturbation velocity is located in this layer; and an inner surface layer of thickness ls where the shear stress gradient varies rapidly and the perturbation velocity tends to zero. The details of the middle layer are given here for different kinds of upwind profiles, including logarithmic, ‘power law’ and linear profiles. It is shown that the analysis can be extended to allow for nonlinear inertial effects in the middle layer. Analytical solutions are derived for the inner region as asymptotic expansions in δ = [ln(l/zo)]−1, which is assumed to be small, and this shows that ls ∼ zo(l/zo)1/2.The results of the analytical model are compared with our own and with previously published numerical computations of the full equations (applying the same assumptions used for calculating the turbulent shear stresses as used in the analytical work), which have largely been validated against full‐scale measurements. These results confirm that the relative increase of surface stress is significantly greater than the increase of wind speed near the surface except when there is no upwind shear (as for example in a logarithmic boundary layer when the roughness length tends to zero).Finally, the paper shows that the outer regions of laminar (or constant eddy viscosity) and of turbulent flows over hills are broadly similar, but that the effects of the flow in the inner region on the outer regions are much smaller in the latter case.

The formation of areally-averaged roughness lengths

It is argued that the best area average of the roughness length zo in heterogeneous terrain is that which, if it applied in homogeneous terrain, would produce the correct spatial average value of the surface stress. A heuristic argument is presented to show that this effective value of z0, zeff0, can be obtained by averaging drag coefficients based on a ‘blending’ height. The blending height of about L/200, where L is the horizontal scale of the roughness variations, is the characteristic height at which the flow changes from equilibrium with the local surface to independence of horizontal position. These calculations are compared with numerical simulations of planetary boundary layer flow over variations in roughness length and show good agreement. The values of surface stress which result are always greater than those which would be deduced by assuming a local flow equilibrium through the whole depth of the boundary layer. For variations of z0 on short length scales, zeff0 approaches the largest values of z0 within the averaging area.

The formation of areally‐averaged roughness lengths

AbstractIt is argued that the best area average of the roughness length zo in heterogeneous terrain is that which, if it applied in homogeneous terrain, would produce the correct spatial average value of the surface stress. A heuristic argument is presented to show that this effective value of z0, zeff0, can be obtained by averaging drag coefficients based on a ‘blending’ height. The blending height of about L/200, where L is the horizontal scale of the roughness variations, is the characteristic height at which the flow changes from equilibrium with the local surface to independence of horizontal position. These calculations are compared with numerical simulations of planetary boundary layer flow over variations in roughness length and show good agreement. The values of surface stress which result are always greater than those which would be deduced by assuming a local flow equilibrium through the whole depth of the boundary layer. For variations of z0 on short length scales, zeff0 approaches the largest values of z0 within the averaging area.

WIND OF AN AIR LAYER CHARACTERIZED BY VEGETATIONS

The purpose of the present paper is to clarify the behaviour of the roughness length zo and the zero-plane displacement d against friction velocity and to explain the vertical wind profile within a canopy using introduced theoretical relationships between physical quantities. Measurements were carried out at the heat and water balances observation field in the Environmental Research Center of the University of Tsukuba, Ibaraki, Japan. The field surface was covered by pasture grass (rye grass, Secale Cereale) with a height of 0.46m. The observations under the near neutral condition show that mean values of zo and d increase with the growth of plant height h. The relations are expressed by z0=0.065 h and d=0.401 h respectively. The value of z0/(h-d)=0.109 is smaller than those found by many other canopies, for instance, 0.44 over wheat field, 0.26 over needle-leaned tree, 0.24 over bean field and 0.12 over corn field (Hayashi and Kotoda, 1980). It is noteworthy that the pasture canopy contributes less effectively to aerodynamical roughness than the other canopies. Tall, flexible vegetations are more deformed with the increase of wind speed. Therefore, z0 and d change in accordance with wind speed at a fully rough surface. Then z0 increases slightly with the increase of the friction velocity u* as follows (Fig. 6): z0=0.044 u*+0.018 On the other hand d diminishes with the increase of friction velocity as follows (Fig. 7): d=-0.361 u*+0.288 This is attributed to the phenomena that the wind penetrates more into the canopy as the speed increases and that the aerodynamical surface, a level of no downward momentum flux, becomes lower. Under such conditions, tall vegetations are exposed more to the wind, and the canopy changes its aerodynamical roughness. For the flat surface, the friction velocity u* is in direct proportion to the wind speed uh. But for the pasture field, the friction velocity settles down at a value of u*=0.370m/s and deviates from the linear relation between u and u* in the range of uh_??_2.0m/s. The main cause for the deviation of the value of u* is considered to be the difference in the shape of the canopy under such windy conditions (Fig. 8). The relation between the momentum diffusivity KM and the friction velocity is expressed essentially by two straight lines as follows (Fig. 9): KM=0.093 u* (u* 0.3m/s) We can also recognize that the drag coefficient is independent of the friction velocity and the mean value of the drag coefficient CD is 3.07×10-2 at z=0.46 m, although the deviation is not small (Fig. 10). For the purpose of verification of the theoretical relationships between the physical quantities within the canopy, a numerical solution of the wind profile is done and compared with the results of the field observation. Under near neutral condition the wind profile over the pasture canopy is represented by a logarithmic law. But in the canopy layer, the following relations are given: τ=ρKMdu/dz KM=βζ0muh(1-ra) where ζ0 is the normalized roughness length, i.e. ζ0=z0/h, /h, τ the shearing stress, p the air density, Cd the drag coefficient of canopy element, a the leaf area density, and α, β and m are nondimensional constants, and r is the newly defined luxuriant length.

Air flow over a two-dimensional hill: studies of velocity speed-up, roughness effects and turbulence

Wind tunnel measurements have been made of the streamwise mean and turbulent velocities over a rough, bell-shaped, two-dimensional hill, with height h and maximum slope 0.26, placed in a neutrally stable boundary layer of thickness 10 h and roughness length zo = 0.02 h. Close agreement is found between the mean velocity and predictions obtained from Taylor's (1977) computational model and Jackson and Hunt's (1975) analytical linearized model, for locations at or upwind of the hill top but not in the wake. Examination of the models shows that the shear stresses are only important in an inner region close to the hill surface, so that, as suggested by Jackson and Hunt (1975), the perturbation to the mean flow outside this region is essentially inviscid. the theory shows that over very rough surfaces, such as wooded or urban terrain, the height of this inner region can be of the same order as the height of the roughness elements (so that in our experiments no measurements could be made in this region). In a second experiment flow over a smooth hill on a rough surface was studied. the additional increase of wind speed over the hill top can be estimated by assuming a linear superposition of the velocity changes produced by the changes in elevation and in surface roughness (in this case rough to smooth). In the lee of a hill, however, the change in roughness significantly alters the flow with flow separation being suppressed and here a linear superposition is not appropriate. Finally we consider why observed changes in turbulence structure close to the surface differ from those well above the surface. Calculations of these changes based on the simple theoretical arguments of equilibrium shear layers and rapidly distorted turbulent flows agree well with turbulence measurements in wind tunnels and in the field.

Air flow over a two‐dimensional hill: Studies of velocity speed‐up, roughness effects and turbulence

AbstractWind tunnel measurements have been made of the streamwise mean and turbulent velocities over a rough, bell‐shaped, two‐dimensional hill, with height h and maximum slope 0.26, placed in a neutrally stable boundary layer of thickness 10 h and roughness length zo = 0.02 h. Close agreement is found between the mean velocity and predictions obtained from Taylor's (1977) computational model and Jackson and Hunt's (1975) analytical linearized model, for locations at or upwind of the hill top but not in the wake. Examination of the models shows that the shear stresses are only important in an inner region close to the hill surface, so that, as suggested by Jackson and Hunt (1975), the perturbation to the mean flow outside this region is essentially inviscid. the theory shows that over very rough surfaces, such as wooded or urban terrain, the height of this inner region can be of the same order as the height of the roughness elements (so that in our experiments no measurements could be made in this region).In a second experiment flow over a smooth hill on a rough surface was studied. the additional increase of wind speed over the hill top can be estimated by assuming a linear superposition of the velocity changes produced by the changes in elevation and in surface roughness (in this case rough to smooth). In the lee of a hill, however, the change in roughness significantly alters the flow with flow separation being suppressed and here a linear superposition is not appropriate.Finally we consider why observed changes in turbulence structure close to the surface differ from those well above the surface. Calculations of these changes based on the simple theoretical arguments of equilibrium shear layers and rapidly distorted turbulent flows agree well with turbulence measurements in wind tunnels and in the field.

A numerical investigation of variations in the drag coefficient for air flow above water waves

Numerical predictions of the drag coefficient for air flow above a train of monochromatic water waves are presented. The air is assumed to be neutrally stratified, and the water surface aerodynamically rough, characterized by a local small-scale roughness length Zo associated primarily with capillary waves. Details of the numerical model are described in an earlier paper. The variation of the drag coefficient with wave slope and with the ratio of wave phase speed to friction velocity is analysed. The applicability of the results to the sea is discussed in relation to the many observations of the drag coefficient.