Roger H. Shaw

A Higher Order Closure Model for Canopy Flow

Abstract The equations of motion were used to develop a one-dimensional, nonbuoyant mathematical model of air flow within vegetative canopies. The model consists of equations for mean horizontal momentum, Reynolds stress, and for the three components of turbulent kinetic energy with closure achieved by parameterizing the higher order terms. This eliminates the need to model the Reynolds stress directly using an eddy viscosity. The closure schemes rely upon a prescribed length scale and have been used elsewhere in modeling the atmospheric boundary layer free of vegetation. The equations were solved numerically using specified boundary conditions. Using a profile of plant area density for a crop of corn (Zea mays L.) the model predicted mean wind velocity, Reynolds stress and turbulent intensities for the region from the soil surface to twice the canopy height that compare well with experimental measurements (Shaw et al., 1974a,b). The model is believed to overestimate the intensity of turbulence generated ...

Averaging procedures for flow within vegetation canopies

Most one-dimensional models of flow within vegetation canopies are based on horizontally averaged flow variables. This paper formalizes the horizontal averaging operation. Two averaging schemes are considered: pure horizontal averaging at a single instant, and time averaging followed by horizontal averaging. These schemes produce different forms for the mean and turbulent kinetic energy balances, and especially for the ‘wake production’ term describing the transfer of energy from large-scale motion to wake turbulence by form drag. The differences are primarily due to the appearance, in the covariances produced by the second scheme, of dispersive components arising from the spatial correlation of time-averaged flow variables. The two schemes are shown to coincide if these dispersive fluxes vanish.

LARGE-EDDY SIMULATION OF TURBULENT FLOW ABOVE AND WITHIN A FOREST

A large-eddy simulation has been performed of an atmospheric surface layer in which the lower third of the domain is occupied by a drag layer and heat sources to represent a forest. Subgridscale processes are treated using second-order closure techniques. Lateral boundaries are periodic, while the upper boundary is a frictionless fixed lid. Mean vertical profiles of wind velocity derived from the output are realistic in their shape and response to forest density. Similarly, vertical profiles of Reynolds stress, turbulent kinetic energy and velocity skewness match observations, at least in a qualitative sense. The limited vertical extent of the domain and the artificial upper boundary, however, cause some departures from measured turbulence profiles in real forests. Instantaneous turbulent velocity and scalar fields are presented which show some of the features obtained by tower instrumentation in the field and in wind tunnels, such as the vertical coherence of vertical velocity and the slope of structures revealed by temperature patterns.

A wind tunnel study of air flow in waving wheat: Two-point velocity statistics

Two-point, space-time correlations of streamwise and vertical velocity were obtained from a wind tunnel simulation of an atmospheric surface layer with an underlying model wheat canopy constructed of flexible nylon stalks. Velocity data extend from 1/6 canopy height to several canopy heights, with in excess of 2000 three-dimensional vector separations of the two x-wire probes. Isocorrelation contours over anx, z slice show the streamwise velocity autocorrelation to be roughly circular, such that vertical velocities at the same horizontal position but different heights are closely in phase. Cross-correlations between the two velocity components reflect this difference to some extent. Lateral displacements of the probes revealed side lobes with correlations of reversed sign but we cannot positively link this pattern to particular vorticular structures. Integral length scales obtained directly from the spatial correlations match similar scales deduced from single-point time series with Taylors hypothesis at 2 to 3 times the canopy height but greatly exceed such scales at lower levels, particularly within the wheat. We conclude that the reversed sign lateral lobes are important components of the correlation field and that an integral length scale for the lateral direction must be defined such that they are included. Convective velocities obtained from the time lag to optimally restore correlation lost by physical separation of the probes change only slowly with height and greatly exceed the mean wind velocity within and immediately above the canopy. Thus, mean wind velocity is not a suitable proxy for convective velocity in the application of Taylors hypothesis in this situation. The ratio of vertical to longitudinal convective velocity for the streawise velocity signal yields a downwind tilt angle of about 39° which is probably a better estimate of the slope of the dominant fluid motions than the tilt of the major axis of the isocorrellation contours mentioned previously.

Aerodynamic roughness of a plant canopy: A numerical experiment

A numerical model based on second-order closure principles was used to evaluate the response of the logarithmic wind profile parameters, the roughness length, z0 and the displacement height, d, to changes in the density and vertical structure of an underlying canopy of vegetation. The profile parameters were calculated by forcing the logarithmic wind equation to match the computed wind profile over three successive grid points used in the numerical model. Both z0 and d calculated in this manner were functions of height but the displacement height calculated from the wind profile at twice the canopy height was a good approximation to the center-of-pressure within the canopy over a wide range of densities. The displacement height increased monotonically with plant density and with the height of the center of gravity of the vegetation. The roughness length was a unimodal function of density, increasing with density in sparse canopies but decreasing with density in dense canopies. Vertical structure was important. The roughest canopies were those with a high center of gravity at low plant densities but those with a low center of gravity at high densities. At high densities, a single linear relationship between z0 and d was evident, irrespective of density or structure. Evidence based on the sensitivity of the profile parameters to an arbitrarily set length scale suggests that a second-order closure model is superior to the traditional gradient-diffusion model in the proximity of a plant canopy.

Leaf area measurements based on hemispheric photographs and leaf-litter collection in a deciduous forest during autumn leaf-fall

Abstract Predicted relationships between leaf area index ( LAI ) and gap frequency using the Poisson, binomial and Markov theoretical models of canopy geometry (Nilson, 1971) were used to estimate LAI from hemispherical photographs taken during the autumn leaf-fall period in a maple-aspen forest in southern Ontario, Canada. Both the binomial and Markov models require specification of a parameter to describe the clumpiness of the leaf distributions. For the binomial model, the parameter value given by Baldocchi et al. (1985) for an oak-hickory forest in Tennessee was used, while for the Markov model, a means for estimating the required parameter was developed based on conditional gap probabilities deduced from the hemispheric photographs. LAI estimates derived from the theoretical models were compared with values obtained from leaf-litter collection as the canopy went from fully leafed to leafless ( LAI range 0–∼5.1). Comparisons were obtained for 6 days over this period. Estimates from the models were based on photographs taken at the bottom of the canopy at nine locations within a 15 × 15-m plot. Analysis of photographs was performed using a video camera and a commercial image analyser. Poisson model-derived results were appreciably less than the LAI from leaf-litter collection for values of the latter greater than ∼2, while results from the binomial and the Markov models compared favourably with leaf-litter collection for LAI >2. The apparent failure of the Poisson model at the relatively larger LAI s was attributed to the expected clumpiness of leaf distributions in deciduous forests. For LAI s less than ∼1, the estimates from all models exceeded the leaf-litter collection values, reflecting the influence of tree branches on the gap frequencies recorded in the hemispheric photographs. An estimate of 0.5 was obtained for the woody element area index based on the mean collection LAI estimates. For the Markov model, this difference showed little trend with decreasing leaf area, but for the binomial model, the corresponding difference tended to increase as LAI decreased, probably reflecting a change in the true clumpiness parameter from the full canopy value as leaf area decreased. Estimates of leaf area density profiles were also obtained. These were derived from hemispheric field-of-view photographs taken at seven levels from a tower within the forest. Only the equivalent of one photograph at each level for any measurement day could be obtained, which increased the inherent uncertainty of the estimates relative to the entire canopy estimates, which were based on nine photographs. With a little subjective smoothing of the LAI profiles produced by application of the Markov model, physically consistent leaf area density profiles were produced which appeared reasonable based on the few measurements of such profiles that have been reported.

Structure of the Reynolds Stress in a Canopy Layer

Abstract The u, w velocity covariance above and within a plant canopy (Zea mays L) was examined using the technique of quadrant analysis to separate the momentum transport into events classified as sweep, ejection, and outward and inward interactions. A hyperbolic hole of variable size acted as an excluded region in the u, w domain to asses the relative importance of short-lived events of large magnitude. The results of the analysis were a reasonably close match to rough-wall wind tunnel studies but differed in some respects from a similar experiment performed elsewhere in a flexible wheat canopy. Generally, sweeps exceeded ejections in their contribution to the Reynolds stress, especially at mid-canopy, while the interaction events were of minor importance. Sweeps that were large in magnitude relative to the time-averaged stress were evident at all levels and were intermittent in character. Compared with the layers above, the effect of the canopy was to increase the dominance of sweeps over ejections and...

Influence of foliar density and thermal stability on profiles of Reynolds stress and turbulence intensity in a deciduous forest

Observations were made of turbulence in an extensive deciduous forest on level terrain using a vertical array of seven three-dimensional sonic anemometer/thermometers within and above the canopy. Data were collected through the period of leaf fall and over a range of thermal stabilities. A bulk canopy drag coefficient was nearly independent of the density of the forest but decreased greatly with the onset of nocturnal stability. The depth of penetration of momentum into the forest increased with leaf fall but, again, was greatly curtailed by stable conditions. Turbulent velocities decreased with increasing depth in the forest but relative turbulence intensities increased to mid-canopy levels. Leaf density influenced turbulence levels but not as strongly as did thermal stability. Thermal effects were adequately described by the single parameter h/L, where h is the canopy height and L is the Monin-Obukhov length. The longitudinal and vertical velocity correlation coefficient was larger in magnitude than expected in the upper layers of the forest but decreased to a small value in the lowest layers where the Reynolds stress was small. The ratio Σw/u*, where u* is the local friction velocity, reflected changes in the uw correlation, becoming smaller than usual in the upper canopy layers. It is believed that these effects result from the intermittent, spatially coherent structures that are responsible for a large fraction of the momentum flux to the forest.

Turbulence structure above a vegetation canopy

We compare the turbulence statistics of the canopy/roughness sublayer (RSL) and the inertial sublayer (ISL) above. In the RSL the turbulence is more coherent and more efficient at transporting momentum and scalars and in most ways resembles a turbulent mixing layer rather than a boundary layer. To understand these differences we analyse a large-eddy simulation of the flow above and within a vegetation canopy. The three-dimensional velocity and scalar structure of a characteristic eddy is educed by compositing, using local maxima of static pressure at the canopy top as a trigger. The characteristic eddy consists of an upstream head-down sweep-generating hairpin vortex superimposed on a downstream head-up ejection-generating hairpin. The conjunction of the sweep and ejection produces the pressure maximum between the hairpins, and this is also the location of a coherent scalar microfront. This eddy structure matches that observed in simulations of homogeneous-shear flows and channel flows by several workers and also fits with earlier field and wind-tunnel measurements in canopy flows. It is significantly different from the eddy structure educed over smooth walls by conditional sampling based only on ejections as a trigger. The characteristic eddy was also reconstructed by empirical orthogonal function (EOF) analysis, when only the dominant, sweep-generating head-down hairpin was recovered, prompting a re-evaluation of earlier results based on EOF analysis of wind-tunnel data. A phenomenological model is proposed to explain both the structure of the characteristic eddy and the key differences between turbulence in the canopy/RSL and the ISL above. This model suggests a new scaling length that can be used to collapse turbulence moments over vegetation canopies.

On coherent structures in turbulence above and within agricultural plant canopies

Abstract The existence of ramp structures in scalar fields such as air temperature has been reported in laboratory flows over smooth and rough walls, in the atmospheric boundary layer and in flows in and above forests. They have been recognized as the signature of coherent turbulent structures. The aim of this paper is to present some observations and analyses of these features in the agricultural environment. Evidence is given from samples of time traces recorded during experiments conducted in maize crops and orchards. Ramps of air temperature, surface temperature, humidity and CO 2 concentrations are shown to occur under stable, neutral and unstable conditions. Ramp structures are more apparent above short canopies than within them, in contrast to taller tree canopies where ramps are seen most clearly near the canopy top. Under stable conditions, they are sometimes found in association with trapped gravity waves. It is demonstrated that the frequency of occurrence of the coherent structures is related to a wind shear scale characteristic of the canopy flow.