Two-Point Correlation Analysis Of Neutrally Stratified Flow Within And Above A Forest From Large-Eddy Simulation

Two-point space-time correlations ofvelocities, a passive scalar and static pressure arecalculated using the resolvable flow fields computedby large-eddy simulation (LES) of neutrally stratifiedflow within and above a sparse forest. Zero-time-lagspatial auto-correlation contours in thestreamwise-vertical cross-section for longitudinal andlateral velocities and for a scalar are tilted fromthe vertical in the downstream direction, as istypical in near-wall sheared flow. On the other hand,auto-correlations of vertical velocity and of staticpressure are vertically coherent. Zero-time-lagspatial auto-correlations in the spanwise-verticalcross-section show no distinct tilt, and those forboth longitudinal and vertical velocities demonstratedistinct negative side lobes in the middle forest andabove, while longitudinal velocity in the subcrowntrunk space is laterally in-phase. Static pressureperturbations appear to be spatially coherent in thespanwise direction at all heights, especially insidethe forest. Near the forest floor, longitudinalvelocity is found to be in-phase with static pressureperturbation and to be closely linked to theinstantaneous streamwise pressure gradient, supportinga previous proposal that longitudinal velocity in thisregion is dominantly modulated by the pressurepatterns associated with the coherent sweep/ejectionevents. Near treetop height, a lack of linkage betweenthe pressure gradient and the local time derivative ofthe longitudinal velocity supports the hypothesis ofadvection dominating turbulent flow.The major phase characteristics of the two-pointcorrelations essentially remained the same from fourLES runs with different domain size and/or gridresolution. A larger LES domain yielded betteragreement with field observations in a real forest onboth the magnitudes of the correlations and thesingle-point integral time scales. A finer gridresolution in the LES led to a faster rate of decreaseof correlation with increasing separation in space ortime, as did the higher frequency fluctuations in theturbulent records from field measurements. Convectivevelocities estimated from the lagged two-pointauto-correlations of the calculated flow fields werecompared with similar calculations from wind-tunnelstudies. At the canopy top, estimates from thecorrelation analyses agree with the translationvelocity estimated from instantaneous snapshots of ascalar microfront using both LES and field data. Thistranslation velocity is somewhat higher than the localmean wind speed. Convective velocities estimated fromlagged correlations increase with height above thecanopy. It is suggested that an appropriate filteringprocedure may be necessary to reduce the effects ofsmall-scale random turbulence, as was reported in astudy over an orchard canopy. The mean longitudinalvelocity near the treetops is found to be moreappropriate than the local mean longitudinal velocityat each height to link single-point integral timescales with directly calculated spatial integralstreamwise length scales.     

Large-eddy Simulation of Turbulent Flow Across a Forest Edge. Part I: Flow Statistics

The statistics of turbulent flow across a forest edge have been examined using large-eddy simulation, and results compared with field and wind-tunnel observations. The moorland-to-forest transition is characterized by flow deceleration in the streamwise direction, upward distortion of the mean flow, formation of a high pressure zone immediately in front of the edge, suppression of the standard deviations and covariance of velocity components, and enhancement of velocity skewnesses. For the selected forest density, it is observed that the maximum distortion angle is about 8 degrees from the horizontal. Instead of approaching a downwind equilibrium state in a monotonic manner, turbulence (standard deviations and covariances of velocity components) and mean streamwise velocity undershoot in the transition zone behind the edge. Evolution of flow statistics clearly reveals the growth of an internal boundary layer, and the establishment of an equilibrium layer downwind of the edge. It is evident that lower-order moments generally adjust more quickly over the new rough surface than do higher-order moments. We also show that the streamwise velocity standard deviation at canopy height starts its recovery over the rough surface sooner than does the vertical velocity standard deviation, but completes full adjustment later than the latter. Despite the limited domain size upstream of the edge, large-eddy simulation has successfully reproduced turbulent statistics in good agreement with field and wind-tunnel measurements.     

Edge Flow and Canopy Structure: A Large-Eddy Simulation Study

Sharp heterogeneities in forest structure, such as edges, are often responsible for wind damage. In order to better understand the behaviour of turbulent flow through canopy edges, large-eddy simulations (LES) have been performed at very fine scale (2 m) within and above heterogeneous vegetation canopies. A modified version of the Advanced Regional Prediction System (ARPS), previously validated in homogeneous conditions against field and wind-tunnel measurements, has been used for this purpose. Here it is validated in a simple forest-clearing-forest configuration. The model is shown to be able to reproduce accurately the main features observed in turbulent edge flow, especially the “enhanced gust zone” (EGZ) present around the canopy top at a few canopy heights downwind from the edge, and the turbulent region that develops further downstream. The EGZ is characterized by a peak in streamwise velocity skewness, which reflects the presence of intense intermittent wind gusts. A sensitivity study of the edge flow to the forest morphology shows that with increasing canopy density the flow adjusts faster and turbulent features such as the EGZ become more marked. When the canopy is characterized by a sparse trunk space the length of the adjustment region increases significantly due to the formation of a sub-canopy wind jet from the leading edge. It is shown that the position and magnitude of the EGZ are related to the mean upward motion formed around canopy top behind the leading edge, caused by the deceleration in the sub-canopy. Indeed, this mean upward motion advects low turbulence levels from the bottom of the canopy; this emphasises the passage of sudden strong wind gusts from the clearing, thereby increasing the skewness in streamwise velocity as compared with locations further downstream where ambient turbulence is stronger.     

Large-eddy Simulation of Turbulent Flow across a Forest Edge. Part II: Momentum and Turbulent Kinetic Energy Budgets

Momentum and turbulent kinetic energy (TKE) budgets across a forest edge have been investigated using large-eddy simulation (LES). Edge effects are observed in the rapid variation of a number of budget terms across this vegetation transition. The enhanced drag force at the forest edge is largely balanced by the pressure gradient force and by streamwise advection of upstream momentum, while vertical turbulent diffusion is relatively insignificant. For variance and TKE budgets, the most important processes at the forest edge are production due to the convergence (or divergence) of the mean flow, streamwise advection, pressure diffusion and enhanced dissipation by canopy drag. Turbulent diffusion, pressure redistribution and vertical shear production, which are characteristic processes in homogeneous canopy flow, are less important at the forest transition. We demonstrate that, in the equilibrated canopy flow, a substantial amount of TKE produced in the streamwise direction by the vertical shear of the mean flow is redistributed in the vertical direction by pressure fluctuations. This redistribution process occurs in the upper canopy layers. Part of the TKE in the vertical velocity component is transferred by turbulent and pressure diffusion to the lower canopy levels, where pressure redistribution takes place again and feeds TKE back to the streamwise direction. In this TKE cycle, the primary source terms are vertical shear production for streamwise velocity variance and pressure redistribution for vertical velocity variance. The evolution of these primary source terms downwind of the forest edge largely controls the adjustment rates of velocity variances.     

Large-Eddy Simulation of Flow and Pollutant Dispersion in High-Aspect-Ratio Urban Street Canyons with Wall Model

A large-eddy simulation (LES) with a one-equation subgrid-scale (SGS) model was developed to investigate the flow field and pollutant dispersion inside street canyons of high aspect ratio (AR). A 1/7th power-law wall model was implemented near rigid walls to mitigate the demanding near-wall resolution requirements in LES. This LES model had been extensively validated against experimental results for street canyons of AR = 1 and 2 before it was applied to the cases of AR = 3 and 5. A ground-level passive pollutant line source, located in the middle of the street, was used to simulate vehicular emissions. Three and five vertically aligned primary recirculations were developed in the street canyons of AR 3 and 5, respectively. The ground-level mean wind speed was less than 0.5% of the free stream value, which makes it difficult for the pollutant to be transported upward for removal. High pollutant concentration and variance were found near the buildings where the air flow is upwards. It was found that the velocity fluctuation, pollutant concentration and variance were all closely related to the interactions between the primary recirculations and/or the free surface layer. Several quantities, which are non-linear functions of AR, were introduced to quantify the air quality in street canyons of different configurations.     

The Effects of Vegetation Density on Coherent Turbulent Structures within the Canopy Sublayer: A Large-Eddy Simulation Study

Large-eddy simulation has become an important tool for the study of the atmospheric boundary layer. However, since large-eddy simulation does not simulate small scales, which do interact to some degree with large scales, and does not explicitly resolve the viscous sublayer, it is reasonable to ask if these limitations affect significantly the ability of large-eddy simulation to simulate large-scale coherent structures. This issue is investigated here through the analysis of simulated coherent structures with the proper orthogonal decomposition technique. We compare large-eddy simulation of the atmospheric boundary layer with direct numerical simulation of channel flow. Despite the differences of the two flow types it is expected that the atmospheric boundary layer should exhibit similar structures as those in the channel flow, since these large-scale coherent structures arise from the same primary instability generated by the interaction of the mean flow with the wall surface in both flows. It is shown here that several important similarities are present in the two simulations: (i) coherent structures in the spanwise-vertical plane consist of a strong ejection between a pair of counter-rotating vortices; (ii) each vortex in the pair is inclined from the wall in the spanwise direction with a tilt angle of approximately 45°; (iii) the vortex pair curves up in the streamwise direction. Overall, this comparison adds further confidence in the ability of large-eddy simulation to produce large-scale structures even when wall models are used. Truncated reconstruction of instantaneous turbulent fields is carried out, testing the ability of the proper orthogonal decomposition technique to approximate the original turbulent field with only a few of the most important eigenmodes. It is observed that the proper orthogonal decomposition reconstructs the turbulent kinetic energy more efficiently than the vorticity.     

Three-Dimensional Scalar Microfront Systems in a Large-Eddy Simulation of Vegetation Canopy Flow

Large-eddy simulation is used to reproduce neutrallystratified airflow inside and immediately above a vegetation canopy. A passive scalaris released from the canopy and the evolution of scalar concentration above the canopyis studied. The most significant characteristic of the scalar concentration is the repeatedformation and dissipation of scalar microfronts, a phenomenon that has been observedin nature. These scalar microfronts consist of downstream-tilted regions of highscalar concentration gradients. Computer visualization tools and a conditional samplingand compositing technique are utilized to analyze these microfronts. Peaks in positivepressure perturbation exceeding an experimental threshold are found to be effectiveindicators of scalar microfronts. Convergence of the streamwise velocity componentand divergence of the cross-stream velocity component are observed in the immediatevicinity of scalar microfronts, which helps explain their relatively longlifetimes. Many of these three-dimensional features have been observedin previous field studies of canopy flow.     

Application of a Large-Eddy Simulation Database to Optimisation of First-Order Closures for Neutral and Stably Stratified Boundary Layers

Large-eddy simulation (LES) is a well-established numerical technique, resolving the most energetic turbulent fluctuations in the planetary boundary layer. By averaging these fluctuations, high-quality profiles of mean quantities and turbulence statistics can be obtained in experiments with well-defined initial and boundary conditions. Hence, LES data can be beneficial for assessment and optimisation of turbulence closure schemes. A database of 80 LES runs (DATABASE64) for neutral and stably stratified planetary boundary layers (PBLs) is applied in this study to optimize first-order turbulence closure (FOC). Approximations for the mixing length scale and stability correction functions have been made to minimise a relative root-mean-square error over the entire database. New stability functions have correct asymptotes describing regimes of strong and weak mixing found in theoretical approaches, atmospheric observations and LES. The correct asymptotes exclude the need for a critical Richardson number in the FOC formulation. Further, we analysed the FOC quality as functions of the integral PBL stability and the vertical model resolution. We show that the FOC is never perfect because the turbulence in the upper half of the PBL is not generated by the local vertical gradients. Accordingly, the parameterised and LES-based fluxes decorrelate in the upper PBL. With this imperfection in mind, we show that there is no systematic quality deterioration of the FOC in the strongly stable PBL provided that the vertical model resolution is better than 10 levels within the PBL. In agreement with previous studies, we found that the quality improves slowly with the vertical resolution refinement, though it is generally wise not to overstretch the mesh in the lowest 500 m of the atmosphere where the observed, simulated and theoretically predicted stably stratified PBL is mostly located. The submission to a special issue of the “Boundary-Layer Meteorology” devoted to the NATO advanced research workshop “Atmospheric Boundary Layers: Modelling and Applications for Environmental Security”.     

Variations of Precipitation Structure and Microwave Tbs During the Evolution of a Hailstorm from TRMM Observations

In this paper, a hailstorm occurring on 9 May 1999 in Huanghuai region was studied by using the combined data from the precipitation radar (PR), microwave image (TMI), and visible infrared scanner (VIRS) on the Tropical Rainfall Measuring Mission (TRMM) satellite. According to the 3-orbit observations of 5-h duration from the TRMM satellite, the variation characteristics of the precipitation structures as well as cloud top temperature and microwave signals of the precipitating cloud were comprehensively analyzed during the evolution of hailstorm. The results show that the precipitation is obviously converted from early hail cloud with strong convection into the later storm cloud with weak convection. For hail cloud, there exists some strong convective cells, and the heavy solid precipitation is shown at the middle-top levels so that the contribution of rainfall amount above the freezing-layer to the column precipitation amount is rather larger than that within the melting-layer. However, for storm cloud, the convective cells are surrounded by the large area of stratiform precipitation, and the precipitation thickness gradually decreases, and the rainfall above the freezing-layer obviously reduces and the contribution of rainfall amount within the melting-layer rapidly increases. Therefore, the larger ratio of rainfall amount above the freezing layer to column precipitation amount is, the more convective the cloud is; reversely, the larger proportion of rainfall below the melting layer is, the more stable the stratiform cloud is. The different changing trends of microwave signals at different precipitation stages show that it is better to consider the structures and stages of precipitating cloud to choose the optimal microwave channels to retrieve surface rainfall.