On the parameterization of the roughness length for the air-sea interface in free convection

The roughness length at the air-sea interface during free convection (z_0fc) is mainly related to the convective velocity (w_*) rather than the friction velocity (u_*). The parameterization of z_0fc with w _* ² /g as proposed by Abdella and DAlessio in 2003 is evaluated. It is shown that their proposed formula is consistent with field measurements. In order to avoid self-correlation by using u_*, a new parameterization of w_* with wind speed (U_z) at height z and stability parameter (z/L, where L is the buoyancy length) is proposed. This new formula for w_* is in agreement with an independent field result.     

Parameterization of the roughness length over the sea in forced and free convection

In the condition of free convection, the Charnock relation is inadequate. In this paper we extend the Charnock relation to include the effect of free convection on the roughness length. As a result, the singularity in the Monin–Obukhov similarity theory can be avoided. This paper shows two approaches to derive the roughness length formula in the forced and free convections. The first approach is based on the mixing length theory and the use of the observational data of the vertical velocity variance. We introduce a new vertical velocity scale based on the vertical velocity variance; this velocity variance is well behaved in the atmospheric boundary layer and easy to obtain from field experiments. The second approach is based on the theoretical framework of Sykes et al. (Q R Met Soc, 119: 409–421). From that framework, we develop a theory to obtain the roughness length formula. The results of these two approaches are in agreement with each other. In the past, a multiplication factor associated with free convection was considered to be a constant. This paper shows that this multiplication factor is, in fact, also dependent on the depth of the mixing height. In previous studies, experimental works were often conducted without taking into account the depth of the mixing height. Not taking into account the mixing height in the estimation of the roughness length in free convection would result in an inaccurate estimate of the roughness length and hence the drag coefficient. An erratum to this article can be found at     

Numerical Simulation of Interaction of the Heavy Gas Cloud with the Atmospheric Surface Layer

The numerical time-dependent three-dimensional model [Kovalets, I.V. and Maderich, V.S.: 2001, Int. J. Fluid Mech. Res. 30, 410–429] of the heavy gas dispersion in the atmospheric boundary layer has been improved by parameterizing momentum and heat fluxes on the surface of Earth using Monin–Obukhov similarity theory. Three parameterizations of heat exchange with the surface of Earth were considered: (A) formula of Yaglom A.M. and Kader B.A. [1974, J. Fluid Mech. 62, 601–623] for forced convection, (B) interpolation formula for mixed convection and (C) similarity relationship for mixed convection [Kader, B.A. and Yaglom, A.M.: 1990, J. Fluid Mech. 212, 637–662]. Two case studies were considered. In the first study based on experiment of Zhu et al., J. Hazard Mater 62, 161–186], the interaction of an isothermal heavy gas plume with an atmospheric surface layer was simulated. It was found that stable stratification in the cloud essentially suppresses the turbulence in the plume, reducing the turbulent momentum flux by a factor of down to 1/5 in comparison with the undisturbed value. This reduction essentially influences velocities in the atmospheric boundary layer above the cloud, increasing the mean velocity by a factor of up to 1.3 in comparison with the undisturbed value. A simulation of cold heavy gas dispersion was carried out in the second case based on field experiment BURRO 8. It was shown that both forced and free convections under moderate wind speeds significantly influence the plume. The relative rms and bias errors of prediction the plume’s height were σ_H ≈ 30% and ɛ_H = − 10%, respectively, for parameterization B, while for A and C the errors were σ_H ≈ 80% and ɛ_H ≈ − 65%. It is therefore advised to use the simple parameterization B in dense gas dispersion models.     

Experimental Study of the Criteria of Flow Laminarization in Two-Dimensional Dense Gas Plumes

Laminarization of flow in a two-dimensional dense gas plume was experimentally investigated in this study. The plume was created by releasing CO₂ through a ground-level line source into a simulated turbulent boundary layer over an aerodynamically rough surface in a meteorological wind tunnel. The bulk Richardson number (Ri_*), based on negative plume buoyancy, plume thickness, and friction velocity, was varied over a wide range so that the effects of stable stratification on plume laminarization could be observed. A variety of ambient wind speeds as well as three different sizes of roughness arrays were used so that possible effects of roughness Reynolds number (Re_*) on plume laminarization could also be identified. Both flow visualization methods and quantitative measurements of velocity and intermittency of turbulence were used to provide quantitative assessments of plume laminarization.Flow visualization provided an overall picture of how the plume was affected by the negative buoyancy. With increasing Ri_*, both the plume depth and the vertical mixing were significantly suppressed, while upstream propagation of the plume from the source was enhanced. The most important feature of the flow revealed by visualization was the laminarization of flow in the lower part of the plume, which appeared to be closely related to both Ri_* and Re_*.Measurements within the simulated dense gas plumes revealed the influence of the stable stratification on mean velocity and turbulence intensity profiles. Both the mean velocity and turbulence intensity were significantly reduced near the surface; and these reductions systematically depended on Ri_*. The roughness Reynolds number also had considerable influence on the mean flow and turbulence structure of the dense gas plumes.An intermittency analysis technique was developed and applied to the digitized instantaneous velocity signals. It not only confirmed the general flow picture within the dense plume indicated by the flow visualization, but also clearly demonstrated the changes of flow regime with variations in Ri_* and Re_*. Most importantly, based on this intermittency analysis, simple criteria for characterizing different flow regimes are formulated; these may be useful in predicting when plume laminarization might occur.     

An Approach for the Aggregation of Aerodynamic Surface Parameters in Calculating the Turbulent Fluxes over Heterogeneous Surfaces in Atmospheric Models

Experimental evidence indicates that there is a significant departure of the wind profile above the underlying surface consisting of patches of solid and liquid parts, and plant communities with different morphological from that predicted by the logarithmic relationship, which gives the values larger than those observed. This situation can seriously affect the transfer of momentum, heat and water vapor from the surface fluxes into the atmosphere.The object of this paper is to generalize the calculation of the exchange of momentum between the atmosphere and a very heterogeneous surface, find a general equation for the wind speed profile in a roughness sublayer under neutral conditions, and, then, derive aggregated roughness length and displacement height over the grid cell. The suggested expression for the wind profile is compared with some earlier approaches, using a common parameterization of aerodynamic parameters over the grid cell, and the observations obtained at an experimental site in Philadelphia, PA.     

Design and Testing of a Turbulence Probe for Harsh Flows

The force of wind on the ground created by turbulent eddies is commonly used to describe the horizontal flux of material during wind erosion. Here we present the Murdoch Turbulence Probe, an instrument for use in both clean and eroding flows which uses pressure differences to measure the three components of wind velocity. Correlation techniques calculate the forces near the ground and turbulence statistics in nearly real time, including turbulent velocity fluctuations from less than 0.1 Hz to 200 Hz, mean flow velocities, Reynolds stresses as well as the integral length and time scales. In the portable wind-tunnel used by Agriculture Western Australia, turbulence statistics were recorded over stable surfaces and in blowing sand from the initiation of erosion up to the time the sand supply was exhausted. Estimates of the friction velocity derived from the turbulence probe were compared with estimates obtained from the wind speed profile measured with a rake of pitot and static tubes. The Murdoch Turbulence Probe appears to work well in sandblasting conditions. Relative turbulence intensities ranged from 0.11 to 0.2 and are in close agreement with values in the literature. The ratio of the turbulence to the friction velocity (3 to 3.2) is at the high end of the reported range. The Reynolds stress measurements agree closely with predictions of the threshold friction velocities of the sand and estimates from the wind speed profile with a von Kármán constant of about 0.3, lower than the commonly accepted value of 0.4. We suggest that the wind-tunnel profile represents the `outer layer' of the boundary-layer that may best be described by a `Wake Law' or `Defect Law'. At about 54 mm above the surface, the friction velocity decreases from 0.64 m/s to 0.39 m/s and the mean velocity increases from 9.6 m/s to 11.6 m/s as the supply of sand is depleted. In addition to the friction velocity, other scales may be necessary to characterise the overriding effect of the wind and in extending wind-tunnel results to the field.     

Wind Characteristics of Mesquite Streets in the Northern Chihuahuan Desert, New Mexico, USA

Past research has shown that the most important areas for active sand movement in the northern part of the Chihuahuan Desert are mesquite-dominated desert ecosystems possessing sandy soil texture. The most active sand movement in the mesquite-dominated ecosystems has been shown to take place on elongated bare soil patches referred to as “streets”. Aerodynamic properties of mesquite streets eroded by wind should be included in explaining how mesquite streets are more emissive sand sources than surrounding desert land. To understand the effects of wind properties, we measured them at two flat mesquite sites having highly similar soil textures but very different configurations of mesquite. The differences in wind properties at the two sites were caused by differences of size, orientation, and porosity of the mesquite, along with the presence of mesquite coppice dunes (sand dunes stabilized by mesquites growing in the dune and on its surface) found only at one of the two sites. Wind direction, u_* (friction velocity), z₀ (aerodynamic roughness height) and D (zero plane displacement height) were estimated for 15-m tower and 3-m mast data. These aerodynamic data allowed us to distinguish five categories with differing potentials for sediment transport. Sediment transport for the five categories varied from unrestricted, free transport to virtually no transport caused by vegetation protection from wind forces. In addition, “steering” of winds below the level of the tops of mesquite bushes and coppice dunes allowed longer parallel wind durations and increased wind erosion for streets that aligned roughly SW–NE. U.S. Government right to retain a non-exclusive royalty-free licence in and to any copyright is acknowledged.     

初论地表粗糙度

粗糙度是流体力学引进的一个重要参数,是现代地球表面各种物质流运动研究中不可或缺的一个重要概念。它在定床流动中曾获得巨大的成功,但在动床及所谓零位移较大的粗糙面上,表现出其局限性。文章在系统阐述了空气动力学意义上粗糙度概念的由来及其物理意义;在总结某些学科领域中粗糙度的应用成果基础上,发现对于定床,地表粗糙具有地表阻力系数特性,它比地表物体群落平均高度小一个量级;而对于动床,粗糙度则更具有阻力系数的特性,它与超出临界摩阻之值成正比;至于植被地表的粗糙度则近似于定床,但它要从零平面位移高度算起。因此,地表粗糙度概念的进一步完善应从地表阻力系数和实验研究入手,并加强自然界和室内实验室的观测和实验以获得相应系数的变化规律,最终解决粗糙度本身和流体力学相关的理论和实践问题。     

Observations of the cross-wind velocity variance in the stable boundary layer

Nine tower datasets over grassland, brush rangeland, snow covered plain, the ocean, three different pine forests, an aspen forest and an urban site, are used to document the scale-dependence of the cross-wind velocity variance in the stable boundary layer. The turbulence velocity variance scales with the surface momentum flux, as reported in previous studies. Such scaling removes the stability dependence of the variance at a given site, and also removes most of the differences between sites. The scaling is more effective with use of a record-dependent averaging time for defining the turbulent fluctuations. The variable averaging time is the timescale associated with the gap region in the heat flux multiresolution cospectra. On scales larger than turbulence and less than a few hours (mesoscale), variations in the cross-wind velocity variance at a given site are not related to local variables such as the friction velocity. Possible exceptions include suppression of turbulence and mesoscale motions in well-defined drainage flows and enhancement of turbulence and mesoscale motions in stronger winds downstream of a ridge. Larger mesoscale variance is associated with complex terrain and forested sites compared to the more homogeneous sites in flat terrain with short or no vegetation. These differences between sites are related to the absence of a gap region in the velocity spectra at the complex terrain and forested sites. The observed probability distribution functions of the total variance and the mesoscale variance are documented for different averaging times, stability classes and site characteristics.     

Compound channel flow with a longitudinal transition in hydraulic roughness over the floodplains

Flows in a compound open-channel (two-stage geometry with a main channel and adjacent floodplains) with a longitudinal transition in roughness over the floodplains are experimentally investigated in an 18 m long and 3 m wide flume. Transitions from submerged dense vegetation (meadow) to emergent rigid vegetation (wood) and vice versa are modelled using plastic grass and vertical wooden cylinders. For a given roughness transition, the upstream discharge distribution between main channel and floodplain (called subsections) is also varied, keeping the total flow rate constant. The flows with a roughness transition are compared to flows with a uniformly distributed roughness over the whole length of the flume. Besides the influence of the downstream boundary condition, the longitudinal profiles of water depth are controlled by the upstream discharge distribution. The latter also strongly influences the magnitude of the lateral net mass exchanges between subsections, especially upstream from the roughness transition. Irrespective of flow conditions, the inflection point in the mean velocity profile across the mixing layer is always observed at the interface between subsections. The longitudinal velocity at the main channel/floodplain interface, denoted \(U_{int}\), appeared to be a key parameter for characterising the flows. First, the mean velocity profiles across the mixing layer, normalised using \(U_{int}\), are superimposed irrespective of downstream position, flow depth, floodplain roughness type and lateral mass transfers. However, the profiles of turbulence quantities do not coincide, indicating that the flows are not fully self-similar and that the eddy viscosity assumption is not valid in this case. Second, the depth-averaged turbulent intensities and Reynolds stresses, when scaled by the depth-averaged velocity \(U_{d,int}\) exhibit two plateau values, each related to a roughness type, meadow or wood. Lastly, the same results hold when scaling by \(U_{d,int}\) the depth-averaged lateral flux of momentum due to secondary currents. Turbulence production and magnitude of secondary currents are increased by the presence of emergent rigid elements over the floodplains. The autocorrelation functions show that the length of the coherent structures scales with the mixing layer width for all flow cases. It is suggested that coherent structures tend to a state where the magnitude of velocity fluctuations (of both horizontal vortices and secondary currents) and the spatial extension of the structures are in equilibrium.     

A Computational Fluid Dynamics Approach for Urban Area Transport and Dispersion Modeling

A simulation tool has been developed to model the wind fields, turbulence fields, and the dispersion of Chemical, Biological, Radiological and Nuclear (CBRN) substances in urban areas on the building to city blocks scale. A Computational Fluid Dynamics (CFD) approach has been taken that naturally accounts for critical flow and dispersion processes in urban areas, such as channeling, lofting, vertical mixing and turbulence, by solving the steady-state, Reynolds-Averaged Navier–Stokes (RANS) equations. Rapid generation of high quality cityscape volume meshes is attained by a unique voxel-based model generator that directly interfaces with common Geographic Information Systems (GIS) file formats. The flow and turbulence fields are obtained by solving the steady-state RANS equations using a collocated, pressure-based approach formulated for unstructured and polyhedral mesh elements. Turbulence modeling is based upon the Renormalization Group variant of the k–ε model (k–ε RNG). Neutrally buoyant simulations are made by prescribing velocity boundary condition profiles found by a power–law relationship, while turbulence quantities boundary conditions are defined by a prescribed mixing length in conjunction with the assumption of turbulence equilibrium. Dispersion fields are computed by solving an unsteady transport equation of a dilute gas, formulated in a Eulerian framework, using the velocity and turbulence fields found from the steady-state RANS solution. In this paper the model is explained and detailed comparisons of predicted to experimentally obtained velocity, turbulence and dispersion fields are made to neutrally stable wind tunnel and hydraulic flume experiments.     

Canopy-wake dynamics and wind sheltering effects on Earth surface fluxes

The atmospheric boundary layer adjustment at the abrupt transition from a canopy (forest) to a flat surface (land or water) is investigated in a wind tunnel experiment. Detailed measurements examining the effect of canopy turbulence on flow separation, reduced surface shear stress and wake recovery are compared to data for the classical case of a solid backward-facing step. Results provide new insights into the interpretation for flux estimation by eddy-covariance and flux gradient methods and for the assessment of surface boundary conditions in turbulence models of the atmospheric boundary layer in complex landscapes and over water bodies affected by canopy wakes. The wind tunnel results indicate that the wake of a forest canopy strongly affects surface momentum flux within a distance of 35–100 times the step or canopy height, and mean turbulence quantities require distances of at least 100 times the canopy height to adjust to the new surface. The near-surface mixing length in the wake exhibits characteristic length scales of canopy flows at the canopy edge, of the flow separation in the near wake and adjusts to surface layer scaling in the far wake. Components of the momentum budget are examined individually to determine the impact of the canopy wake. The results demonstrate why a constant flux layer does not form until far downwind in the wake. An empirical model for surface shear stress distribution from a forest canopy to a clearing or lake is proposed.     

Characteristics of flow structure of free-surface flow in a partly obstructed open channel with vegetation patch

Free-surface flows over patchy vegetation are common in aquatic environments. In this study, the hydrodynamics of free-surface flow in a rectangular channel with a bed of rigid vegetation-like cylinders occupying half of the channel bed was investigated and interpreted by means of laboratory experiments and numerical simulations. The channel configurations have low width-to-depth aspect ratio (1.235 and 2.153). Experimental results show that the adjustment length for the flow to be fully developed through the vegetation patch in the present study is shorter than observed for large-aspect-ratio channels in other studies. Outside the lateral edge of the vegetation patch, negative velocity gradient (\(\partial \overline{u}/\partial z < 0\)) and a local velocity maximum are observed in the vertical profile of the longitudinal velocity in the near-bed region, corresponding to the negative Reynolds stress (\(- \overline{{u^{\prime}w^{\prime}}} < 0\)) at the same location. Assuming coherent vortices to be the dominant factor influencing the mean flow field, an improved Spalart–Allmaras turbulence model is developed. The model improvement is based on an enhanced turbulence length scale accounting for coherent vortices due to the effect of the porous vegetation canopy and channel bed. This particular flow characteristic is more profound in the case of high vegetation density due to the stronger momentum exchange of horizontal coherent vortices. Numerical simulations confirmed the local maximum velocity and negative gradient in the velocity profile due to the presence of vegetation and bed friction. This in turn supports the physical interpretation of the flow processes in the partly obstructed channel with vegetation patch. In addition, the vertical profile of the longitudinal velocity can also be explained by the vertical behavior of the horizontal coherent vortices based on a theoretical argument.     

Simulation of exchange flow between open water and floating vegetation using a modified RNG <Emphasis Type="Italic">k</Emphasis>-<Emphasis Type="Italic">ε</Emphasis> turbulence model

The paper focuses on the numerical simulation of the exchange flow between open water and floating vegetation, which plays an important role in maintaining the ecological balance by transporting nutrient matter. The simulation was conducted using a new solver developed upon OpenFOAM. A modified RNG k-ε turbulence model, which is expected to model both the high- and low-Reynolds number flows correctly, was used to determine the eddy viscosity. Several particular terms were added into the momentum equations and turbulence model equations to model the effects of vegetation and buoyancy. Among these terms, the term for the effect of vegetation in the ε-equation was re-modelled. The model was validated by properly predicting the profiles of mean velocity and turbulent kinetic energy for flows through suspended canopies. The density flow between open and vegetated water was simulated with the same conditions as those of the experiment conducted by Zhang and Nepf. The predicted results agreed well with the experimental data and provided more detailed information of such exchange flow. The convection between the root layer and the layer beneath the roots, which was not observed in the experiment, was observed in the numerical simulation.     

Interaction between flow, transport and vegetation spatial structure

This paper summarizes recent advances in vegetation hydrodynamics and uses the new concepts to explore not only how vegetation impacts flow and transport, but also how flow feedbacks can influence vegetation spatial structure. Sparse and dense submerged canopies are defined based on the relative contribution of turbulent stress and canopy drag to the momentum balance. In sparse canopies turbulent stress remains elevated within the canopy and suspended sediment concentration is comparable to that in unvegetated regions. In dense canopies turbulent stress is reduced by canopy drag and suspended sediment concentration is also reduced. Further, for dense canopies, the length-scale of turbulence penetration into the canopy, δ _e , is shown to predict both the roughness height and the displacement height of the overflow profile. In a second case study, the relation between flow speed and spatial structure of a seagrass meadow gives insight into the stability of different spatial structures, defined by the area fraction covered by vegetation. In the last case study, a momentum balance suggests that in natural channels the total resistance is set predominantly by the area fraction occupied by vegetation, called the blockage factor, with little direct dependence on the specific canopy morphology.     

Relationship between the Aerodynamic Roughness Length and the Roughness Density in Cases of Low Roughness Density*

This paper presents measurements of roughness length performed in a wind tunnel for low roughness density. The experiments were performed with both compact and porous obstacles (clusters), in order to simulate the behavior of sparsely vegetated surfaces. The experimental results have been used to investigate the relationship between the ratio z₀/h and the roughness density, and the influence of an obstacle's porosity on this relationship. The experiments performed for four configurations of compact obstacles provide measurements of roughness length z₀ for roughness densities between 10^–3 and 10^–2 which are in good agreement with the only data set available until now for this range of low roughness densities. The results obtained with artificial porous obstacles suggests that the aerodynamic behavior of such roughness elements can be represented by the relationship established for compact obstacles, provided a porosity index has been used to determine the efficient roughness density (the fraction of the silhouette area actually sheltered by solid elements) rather than counting the porous object as solid. However, the experiments have been performed with relatively low porosity indices (maximum =25%) for which the porosity has a negligible influence. In this range of porosity index, representing the aerodynamic behavior of porous obstacles using the relationship established for compact obstacles, should not lead to a significant error. However, the influence of the porosity may be important for porosity indices larger than 30%.     

Some characteristics of the urban boundary layer above Rome, Italy, and applicability of Monin–Obukhov similarity

Air temperature and wind speed profiles measured during one year by means of a SODAR-RASS system located within a large park were examined for the urban boundary layer (UBL) over Rome, Italy. These data, combined with velocity and temperature measurements performed near the ground were used to analyze the vertical structure of the boundary layer and to estimate some turbulence parameters characterizing the surface layer. About 52,000 vertical profiles of wind speed and temperature were used for the analysis, allowing investigation for a large variety of stability conditions. First, friction velocity and Obukhov length were examined, showing clearly their dependence on the time of day and season. Second, the applicability of the Monin–Obukhov (MO) similarity theory—developed over rural terrain—was tested up to 200?m above ground level. For the wind speed profiles, the performance of the MO similarity degrades with both increasing height and stability, with maximum errors that are on the order of 300?% at 200?m for the most stable case. In contrast, for the air temperature the error always remains below 50?%.     

Near-boundary velocity and turbulence in depth-varying stream flows

This research examined the temporal distribution of turbulent structure near a streambank toe through the progression of a flood wave in West Run (Morgantown, WV, USA). Three-dimensional velocities and water depths were measured through a 17-h flood event. Turbulence characteristics were examined: Reynolds stresses, turbulent kinetic energy, and turbulence intensities. On average, near-boundary velocity during the rising stage was less than the falling stage, likely due to the measurement location and local roughness. The velocity vectors shifted from towards bed before the flood wave to toward the streambank during progression of the flood wave. Turbulent kinetic energy increased with increasing water depth during the rising stage. Reynolds stress, τ_xz, increased with increasing water depth during the rising stage, but the majority of the stresses were negative through the storm event. Reynolds stress, τ_xy, was positive throughout the event and did not vary with depth. This work is among the first to evaluate turbulence during depth-varying flows in the field.     

Turbulence structure and coherent vortices in open-channel flows with wind-induced water waves

When wind-induced water waves appear over the free-surface flows such as natural rivers and artificial channels, large amounts of oxygen gas and heat are transported toward the river bed through the interface between water and wind layers. In contrast, a bed region is a kind of turbulent boundary layer, in which turbulence generation and its transport is promoted by the production of bed shear stress. In particular, coherent hairpin vortices, together with strong ejection events toward the outer part of the layer, promote mass and momentum exchanges between the inner and outer layers. It is inferred that such a near-bed turbulence may be influenced significantly by these air–water interfacial fluctuations accompanied with free-surface velocity shear and wind-induced water waves. However, these wind effects on the wall-turbulence structure are less understood. To address these exciting and challenging topics, we conducted particle imagery velocimetry (PIV) measurements in open-channel flows combined with air flows, and furthermore the present measured data allows us to investigate the effects of air–water interactions on turbulence structure through the whole depth region.