Turbulent kinetic energy budgets in a model canopy: comparisons between LES and wind-tunnel experiments

A comparative study of turbulence in a wind-tunnel model canopy is performed, using Large eddy simulation (LES) and experimental data from PIV and hot-wire anemometry measurements. The model canopy is composed of thin cylindrical stalks. In the LES, these are represented using a plant-scale approach, while the scale-dependent Lagrangian dynamic model is used as subgrid-scale model. LES predictions of turbulence statistics and energy spectra are found to be in good agreement with the experimental data. Turbulent kinetic energy (TKE) budgets from the LES simulation are analyzed to provide more information absent in the measurements. Results confirm that sloshing motions at the low levels of the canopy are mainly driven by pressure fluctuations. A difference between the energy flux obtained from the energy spectrum and the SGS dissipation rate is observed, consistent with a spectral bypass mechanism in which the real spectral flux due to cascade is smaller than that implied by the energy-spectrum level, due to direct drain by the canopy.     

Simulation of Ekman Boundary Layers by Large Eddy Model with Dynamic Mixed Subfilter Closure

Theoretical analysis of boundary layer turbulence has suggested a feasibility of sufficiently accurate turbulence resolving simulations at relatively coarse meshes. However, large eddy simulation (LES) codes, which employ traditional eddy-viscosity turbulence closures, fail to provide adequate turbulence statistics at coarse meshes especially within a surface layer. Manual tuning of parameters in these turbulence closures may correct low order turbulence statistics but severely harms spectra of turbulence kinetic energy (TKE). For more than decade, engineering LES codes successfully employ dynamic turbulence closures. A dynamic Smagorinsky turbulence closure (DSM) has been already tried in environmental LES. The DSM is able to provide adequate turbulence statistics at coarse meshes but it is not completely consistent with the LES equations. This paper investigates applicability of an advanced dynamic mixed turbulence closure (DMM) to simulations of Ekman boundary layers of high Reynolds number flows. The DMM differs from the DSM by explicit calculation of the Leonard term in the turbulence stress tensor. The Horizontal Array Turbulence Study (HATS) field program has revealed that the Leonard term is indeed an important component of the real turbulence stress tensor. This paper presents validation of a new LES code LESNIC. The study shows that the LES code with the DMM provides rather accurate low order turbulence statistics and the TKE spectra at very coarse meshes. These coarse LES maintain more energetic small scale fluctuations of velocity especially within the surface layer. This is critically important for success of simulations. Accurate representation of higher order turbulence statistics, however, requires essentially better LES resolution. The study also shows that LES of the Ekman boundary layer cannot be directly compared with conventionally neutral atmospheric boundary layers. The depth of the boundary layer is an important scaling parameter for turbulence statistics.     

LES validation of urban flow,part I: flow statistics and frequency distributions

Essential prerequisites for a thorough model evaluation are the availability of problem-specific, quality-controlled reference data and the use of model-specific comparison methods. The work presented here is motivated by the striking lack of proportion between the increasing use of large-eddy simulation (LES) as a standard technique in micro-meteorology and wind engineering and the level of scrutiny that is commonly applied to assess the quality of results obtained. We propose and apply an in-depth, multi-level validation concept that is specifically targeted at the time-dependency of mechanically induced shear-layer turbulence. Near-surface isothermal turbulent flow in a densely built-up city serves as the test scenario for the approach. High-resolution LES data are evaluated based on a comprehensive database of boundary-layer wind-tunnel measurements. From an exploratory data analysis of mean flow and turbulence statistics, a high level of agreement between simulation and experiment is apparent. Inspecting frequency distributions of the underlying instantaneous data proves to be necessary for a more rigorous assessment of the overall prediction quality. From velocity histograms local accuracy limitations due to a comparatively coarse building representation as well as particular strengths of the model to capture complex urban flow features with sufficient accuracy are readily determined. However, the analysis shows that further crucial information about the physical validity of the LES needs to be obtained through the comparison of eddy statistics, which is focused on in part II. Compared with methods that rely on single figures of merit, the multi-level validation strategy presented here supports conclusions about the simulation quality and the model’s fitness for its intended range of application through a deeper understanding of the unsteady structure of the flow.     

LES validation of urban flow,part II: eddy statistics and flow structures

Time-dependent three-dimensional numerical simulations such as large-eddy simulation (LES) play an important role in fundamental research and practical applications in meteorology and wind engineering. Whether these simulations provide a sufficiently accurate picture of the time-dependent structure of the flow, however, is often not determined in enough detail. We propose an application-specific validation procedure for LES that focuses on the time dependent nature of mechanically induced shear-layer turbulence to derive information about strengths and limitations of the model. The validation procedure is tested for LES of turbulent flow in a complex city, for which reference data from wind-tunnel experiments are available. An initial comparison of mean flow statistics and frequency distributions was presented in part I. Part II focuses on comparing eddy statistics and flow structures. Analyses of integral time scales and auto-spectral energy densities show that the tested LES reproduces the temporal characteristics of energy-dominant and flux-carrying eddies accurately. Quadrant analysis of the vertical turbulent momentum flux reveals strong similarities between instantaneous ejection-sweep patterns in the LES and the laboratory flow, also showing comparable occurrence statistics of rare but strong flux events. A further comparison of wavelet-coefficient frequency distributions and associated high-order statistics reveals a strong agreement of location-dependent intermittency patterns induced by resolved eddies in the energy-production range. The validation concept enables wide-ranging conclusions to be drawn about the skill of turbulence-resolving simulations than the traditional approach of comparing only mean flow and turbulence statistics. Based on the accuracy levels determined, it can be stated that the tested LES is sufficiently accurate for its purpose of generating realistic urban wind fields that can be used to drive simpler dispersion models.     

Flow structure and turbulence characteristics downstream of a spanwise suspended linear array

Laboratory experiments are conducted to quantify the mean flow structure and turbulence properties downstream of a spanwise suspended linear array in a uniform ambient water flow using Particle Tracking Velocimetry. Eighteen experimental scenarios, with four depth ratios (array depth to water column depth) of 0.35, 0.52, 0.78, and 0.95 and bulk Reynolds number (length scale is the array depth) from 11,600 to 68,170, are investigated. Three sub-layers form downstream of the array: (1) an internal wake zone, where the time-averaged velocity decreases with increasing distance downstream, (2) a shear layer which increases in vertical extent with increasing distance downstream of the array, and the rate of the increase is independent of the bulk Reynolds number or the depth ratio, and (3) an external wake layer with enhanced velocity under the array. The location of the shear layer is dependent on the depth ratio. The spatially averaged and normalized TKE of the wake has a short production region, followed by a decay region which is comparable to grid turbulence decay and is dependent on the depth ratio. The results suggest that the shear layer increases the transfer of horizontal momentum into the internal wake zone from the fluid outside of the array and that the turbulence in the internal wake zone can be modeled similarly to that of grid turbulence.     

Mass exchange in a shallow channel flow with a series of groynes: LES study and comparison with laboratory and field experiments

The exchange of dissolved matter between a straight open channel and a series of shallow embayments present at one of its sides is investigated using large eddy simulation (LES). The direct link between the mechanism of mass exchange and the dynamics of coherent structures is demonstrated. It is shown that for the geometrical configuration considered in the present study, the mass exchange process is very non-uniform over the depth in the vicinity of the channel–embayment interface. Most of the contaminant is ejected from the embayments close to the free surface. The amount of contaminant re-entrained into the embayments situated downstream of the one in which contaminant was introduced is quantified. The mass exchange coefficient predicted by LES does not vary significantly with the embayment rank and is in very good agreement with the one predicted by the model proposed by Weitbrecht et al. (J Hydraul Eng 134(2):173–183, 2008) based on the value of a dimensionless morphometric groyne-field parameter. Field experiments were purposely performed in a natural stream with embayments whose length over width ratios were close to the ratio in the LES study. The concentration fields predicted by LES are compared with video-records of colored dye used to visualize the mass exchange in the field experiment. It is shown that, for both LES and the field experiment, the dominant passage frequency of the eddies inside the interfacial mixing layer is well predicted by the analytical model of Sukhodolov and Sukhodolova (in: Cowen et al (eds) Hydraulic measurements & experimental methods. Proceedings of international conference, Lake Placid, USA, pp 172–177, 2007). The model is then used to scale the time in the LES animations and field video-records showing the temporal evolution of the concentration field. The results of the comparison indicate several similarities in the mixing process, despite the differences in the bathymetry and the large difference in the Reynolds number between LES and the field experiment. This proves the usefulness of performing detailed LES and laboratory studies in well-controlled environments to understand mass-exchange processes around river groyne fields.     

Front velocity and structure of bottom gravity currents with a low volume of release propagating in a porous medium

The paper reports results of large eddy simulations of lock exchange compositional gravity currents with a low volume of release advancing in a horizontal, long channel. The channel contains an array of spanwise-oriented square cylinders. The cylinders are uniformly distributed within the whole channel. The flow past the individual cylinders is resolved by the numerical simulation. The paper discusses how the structure and evolution of the current change with the main geometrical parameters of the flow (e.g., solid volume fraction, ratio between the initial height of the region containing lock fluid and the channel depth, ratio between the initial length and height of the region containing lock fluid) and the Reynolds number. Though in all cases with a sufficiently large solid volume fraction the current transitions to a drag-dominated regime, the value of the power law coefficient, α, describing the front position’s variation with time (x _f  ~ t ^α , where t is the time measured from the removal of the lock gate) is different between full depth cases and partial depth cases. The paper also discusses how large eddy simulation (LES) results compare with findings based on shallow-water equations. In particular, LES results show that the values of α are not always equal to values predicted by shallow water theory for the limiting cases where the current height is comparable, or much smaller, than the channel depth.     

Performance analysis of WRF and LES in describing the evolution and structure of the planetary boundary layer

We implemented the Weather Research and Forecast (WRF) model and WRF Large-Eddy Simulation (WRF–LES), focusing on calculations for the planetary boundary layer (PBL), and compared the results against a data set of a well-documented campaign, in the Houston–Galveston area, Texas, in summer 2006. A methodology using WRF in a mesoscale and LES was implemented to assess the performance of the model in simulating the evolution and structure of the PBL over Houston during the Vertical Mixing Experiment. Also, the WRF model in a real case mode was examined to explore potential differences between the results of each simulation approach. We analyzed both WRF results for key meteorological parameters like wind speed, wind direction and potential temperature, and compared the model results against the observations. The reasonably good agreement of LES results forced with observed surface fluxes provides confidence that LES describes turbulence quantities such as turbulent kinetic energy correctly and warrants further turbulence structure analysis. The LES results indicate a weak but noticeable nighttime turbulent kinetic energy which was produced by wind shear in Houston’s planetary boundary layer and which may likely be related to intermittent turbulence. This is supported by observations made at the University of Houston Moody Tower air quality station when intermittent peaks of carbon monoxide occurred in the evening, although the variability in wind conditions was very little.     

Numerical simulation of water mixing and renewals in the Barcelona harbour area: the winter season

In the present paper, we use numerical simulation to investigate currents, mixing and water renewal in Barcelona harbour under typical conditions of wind forcing for the winter season. This site is of particular importance due to the interplay between touristic and commercial activities, requiring detailed and high-definition studies of water quality within the harbour. We use Large Eddy Simulation (LES) which directly resolves the anisotropic and energetic large scales of motion and parametrizes the small, dissipative, ones. Small-scale turbulence is modelled by the anisotropic Smagorinsky model (ASM) to be employed in presence of large cell anisotropy. The complexity of the harbour is modelled using a combination of curvilinear, structured, non-staggered grid and the immersed boundary method. Boundary conditions for wind and currents at the inlets of the port are obtained from in-situ measurements. Analysis of the numerical results is carried out based on both instantaneous and time-averaged velocity fields. First- and second-order statistics, such as turbulent kinetic energy and horizontal and vertical eddy viscosities, are calculated and their spatial distribution is discussed. The study shows the presence of intense current in the narrow and elongated part of the harbour together with sub-surface along-shore elongated rolling structures (with a time scale of a few hours), and they contribute to the vertical water mixing. Time-averaged velocity field reveals intense upwelling and downwelling zones along the walls of the harbour. The analysis of second-order statistics shows strong inhomogeneity of turbulent kinetic energy and horizontal and vertical eddy viscosities in the horizontal plane, with larger values in the regions characterized by stronger currents. The water renewal within the port is quantified for particular sub-domain regions, showing that the complexity of the harbour is such that certain in-harbour basins have a water renewal of over five days, including the yacht marina area. The LES solution compares favourably with available current-meter data. The LES solution is also compared with a RANS solution obtained in literature for the same site under the same forcing conditions, the comparison demonstrating a large sensitivity of properties to model resolution and frictional parametrization.     

A dispersion model for traffic produced turbulence in a two-way traffic scenario

Low wind speed conditions are often associated with poor air quality in urban areas, especially near roadways. Predictions of pollutant concentration under such conditions, i.e. low wind-speeds and near road locations, are, however, complicated by the role of traffic produced turbulence (TPT) on pollutant mixing and dilution. Existing dispersion models consider the effect of TPT on pollutant concentrations near roadways, accounting for parameters such as vehicle intensity, vehicle speeds, etc, but do not explicitly account for the contribution of two-way traffic interaction on the pollutant dispersion parameter. The turbulent kinetic energy (TKE) resulting from a two-way traffic condition will be higher than that with a one-way traffic pattern. Here, we obtain a simple formulation for TKE under a two-way traffic pattern from the balance of production and dissipation of turbulence. Considering the vorticity generated by the two-way traffic and determining the equivalent drag coefficient, an expression for TKE due to the two-way traffic interaction was obtained for three different traffic density regimes: light, intermediate, and heavy. The model predictions are validated by comparison with published data from a field study. An improved parameterization of the TPT considering the two-way traffic interaction effect is seen to significantly improve predictions of near roadway pollutant concentrations.     

Numerical simulation and optimization study of the wind flow through a porous fence

Three turbulence closure models (RNG k-ε, SST k-ω and RSM) were used to investigate the flow characteristics around a two-dimensional isolated porous fence. The comparison between the numerical results and the experimental measurements indicated that RSM model shows a better performance than the other two models. The aim of this paper is to accurately and efficiently determine the optimum porosity that attain the best shelter effect of the wind fence in the near wake region (0–4h_b) and in the far wake region (4h_b–10h_b) respectively, where h_b is the height of the fence. The gradient algorithm was adopted as the optimization algorithm and the RSM model was used to model turbulent features of the flow. The shelter effect was parameterized by the peak velocity ratio involving velocity and turbulence. The objective was to reduce the peak velocity ratio in the near or far wake region by changing the design variable porosity (?) of the fence, which ranged between 2 and 60%. The results revealed that a porosity of 10.2% was found as the optimum value giving rise to the best shelter effect in the near wake region, and ? = 22.1% was determined in the case of the far wake region. In addition, based on the proposed optimization method, it is found that the recirculating bubble behind the fence can only be detected when ? < 29.9%.     

Large-eddy simulation of turbulent flow and dispersion over a complex urban street canyon

Turbulent flow and dispersion characteristics over a complex urban street canyon are investigated by large-eddy simulation using a modified version of the Fire Dynamics Simulator. Two kinds of subgrid scale (SGS) models, the constant coefficient Smagorinsky model and the Vreman model, are assessed. Turbulent statistics, particularly turbulent stresses and wake patterns, are compared between the two SGS models for three different wind directions. We found that while the role of the SGS model is small on average, the local or instantaneous contribution to total stress near the surface or edge of the buildings is not negligible. By yielding a smaller eddy viscosity near solid surfaces, the Vreman model appears to be more appropriate for the simulation of a flow in a complex urban street canyon. Depending on wind direction, wind fields, turbulence statistics, and dispersion patterns show very different characteristics. Particularly, tall buildings near the street canyon predominantly generate turbulence, leading to homogenization of the mean flow inside the street canyon. Furthermore, the release position of pollutants sensitively determines subsequent dispersion characteristics.     

LES validation of lock-exchange density currents interacting with an emergent bluff obstacle

Environmental Fluid Mechanics - We address the capability of large eddy simulation (LES) to predict the physics of density currents interacting with bluff obstacles. Most density currents of...     

Large eddy simulation of flow and scalar transport in a vegetated channel

Predicting flow and mass transport in vegetated regions has a broad range of applications in ecology and engineering practice. This paper presents large eddy simulation (LES) of turbulent flow and scalar transport within a fully developed open-channel with submerged vegetation. To properly represent the scalar transport, an additional diffusivity was introduced within the canopy to account for the contribution of stem wakes, which were not resolved by the LES, to turbulent diffusion. The LES produced good agreement with the velocity and concentration fields measured in a flume experiment. The simulation revealed a secondary flow distributed symmetrically about the channel centerline, which differed significantly from the circulation in a bare channel. The secondary circulation accelerated the vertical spread of the plume both within and above the canopy layer. Quadrant analysis was used to identify the form and shape of canopy-scale turbulent structures within and above the vegetation canopy. Within the canopy, sweep events contributed more to momentum transfer than ejection events, whereas the opposite occurred above the canopy. The coherent structures were similar to those observed in terrestrial canopies, but smaller in scale due to the constraint of the water surface.     

Single-column model and large eddy simulation of the evening transition in the planetary boundary layer

In the present study, the well-known case of day 33 of the Wangara experiment is resimulated using the Weather Research and Forecasting (WRF) model in an idealized single-column mode to assess the performance of a frequently used planetary boundary layer (PBL) scheme, the Yonsei University PBL scheme. These results are compared with two large eddy simulations for the same case study imposing different surface fluxes: one using previous surface fluxes calculated for the Wangara experiment and a second one using output from the WRF model. Finally, an alternative set of eddy diffusivity equations was tested to represent the transition characteristics of a sunset period, which led to a gradual decrease of the eddy diffusivity, and replaces the instantaneous collapse of traditional diagnostics for eddy diffusivities. More appreciable changes were observed in air temperature and wind speed (up to 0.5 K, and 0.6 m s^?1, respectively), whereas the changes in specific humidity were modest (up to 0.003 g kg^?1). Although the representation of the convective decay in the standard parameterization did not show noticeable improvements in the simulation of state variables for the selected Wangara case study day, small changes in the eddy diffusivity over consecutive hours throughout the night can impact the simulation of distribution of trace gases in air quality models. So, this work points out the relevance of simulating the turbulent decay during sunset, which could help air quality forecast models to better represent the distribution of pollutants storage in the residual layer during the entire night.     

The effects of littoral zone vegetation on turbulent mixing in lakes

Micro-scale thermal profile data were acquired in four lakes in northwest England and southeast Australia that ranged from a small, sheltered pond with a surface area of about 1 ha to more open lakes with surface areas of several square kilometres. These lakes provided a range of topographic and climatic contexts, basin morphologies and dominant macrophyte species. The data were acquired using two SCAMP profilers, one deployed in the open water and the other mounted on a field traverse deployed within the vegetated littoral zone. From these profile data, turbulence parameters were calculated. The results show the variation in the influence of vegetation on turbulence in the four lakes, which depends on the combination of wind stress, solar radiative forcing and macrophyte mechanical properties. In the sheltered pond, the vegetation alters the light climate within the water, thus reducing stratification and allowing weak, thermally-driven mixing. In the larger lakes, however, the primary action of the vegetation is to prevent surface-generated TKE from penetrating the water column, although this effect becomes less important as the plant separation increases. A simple mechanistic model, calibrated against the field data, suggests that the macrophyte mechanical properties are most important in determining the turbulent kinetic energy (TKE) profile. Increasing the number of turbulence-generating plants reduces the transport of surface-generated TKE into the deeper water, consistent with the field observations. The model suggests that solar forcing, as measured by the temperature gradient between the surface and bottom waters, is of less importance since the TKE profile is similar in runs with different gradients. Perhaps most surprisingly, the value of the surface-wind stress used in the model is not important, within the limitations of the model, as it does not change the TKE profile, except in a thin surface layer.     

Measurements and modeling of open-channel flows with finite semi-rigid vegetation patches

The hydrodynamics of flows through a finite length semi-rigid vegetation patch (VP) were investigated experimentally and numerically. Detailed measurements have been carried out to determine the spatial variation of velocity and turbulence profiles within the VP. The measurement results show that an intrusion region exists in which the peak Reynolds stress remains near the bed. The velocity profile is invariant within the downstream part of the VP while the Reynolds stress profile requires a longer distance to attain the spatially invariant state. Higher vegetation density leads to a shorter adjustment length of the transition region, and a higher turbulence level within the VP. The vegetation density used in the present study permits the passing through of water and causes the peak Reynolds stress and turbulence kinetic energy each the maximum at the downstream end of the patch. A 3D Reynolds-averaged Navier–Stokes model incorporating the Spalart–Allmaras turbulence closure was employed subsequently to replicate the flow development within the VP. The model reproduced transitional flow characteristics well and the results are in good agreement with the experimental data. Additional numerical experiments show that the adjustment length can be scaled by the water depth, mean velocity and maximum shear stress. Empirical equations of the adjustment lengths for mean velocity and Reynolds stress were derived with coefficients quantified from the numerical simulation results.     

Large-Eddy Simulations of the Atmospheric Boundary Layer Using a New Subgrid-Scale Model – II. Weakly and moderately stable cases

A series of simulations under weakly to moderately stable boundary layers (SBLs) have been performed using the proposed subgrid-scale (SGS) model implemented into the Terminal Area Simulation System (TASS). The proposed SGS model incorporates some aspects of the two-part eddy viscosity SGS model of Sullivan et al. (1994) and further refinements which include the dependence of SGS mixing length on stratification, two-part separation of the SGS eddy diffusivity of heat, and more realistic empirical forms of Monin–Obukhov similarity functions. The potential temperature profiles from simulations clearly show a three-layer structure: a stable surface layer of strong gradients, a middle layer of small gradients, and an inversion layer on the top. The wind speed profiles show the formation of low level jet (LLJ). However, the sub-layer structures under moderately SBLs differ from those under weakly SBLs. Both the momentum and heat fluxes decrease almost linearly in the lower part of the SBL. The near surface values of the normalized turbulent kinetic energy (TKE/u _* ²) in all simulations are about 4 which is much less than the typical value of 5.5 under the neutral condition. The decay of turbulence first occurs in the area with large values of Richardson number (R _i<0.2). Generally, instantaneous values of the TKE and R _i at the various grid points are negatively correlated, but there is not a unique relationship between the two parameters.     

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.