Turbulence in waving wheat

Measurements of mean and fluctuating velocities, surface pressure and stalk waving have been made in a uniform wheat canopy. Features of the vertical profiles of mean turbulence quantities are discussed in the context of the resonant waving of wheat stalks. The discrete and prominent peaks in the velocity spectra measured in and above the canopy are then analyzed in the light of the organized travelling wave-type structure or ‘honami’, observed in such crops on windy days. Prominent peaks in the spectra are identified with the arrival of gusts, the stalk-waving frequency, and the frequency of oscillations in canopy height. Two possible mechanisms are proposed to account for the observed height dependence of the peak frequencies, directly associated with stalk waving.     

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

We analyse single-point velocity statistics obtained in a wind tunnel within and above a model of a waving wheat crop, consisting of nylon stalks 47 mm high and 0.25 mm wide in a square array with frontal area index 0.47. The variability of turbulence measurements in the wind tunnel is illustrated by using a set of 71 vertical traverses made in different locations, all in the horizontally-homogeneous (above-canopy) part of the boundary layer. Ensemble-averaged profiles of the statistical moments up to the fourth order and profiles of Eulerian length scales are presented and discussed. They are consistent with other similar experiments and reveal the existence of large-scale turbulent coherent structures in the flow. The drag coefficient in this canopy as well as in other reported experiments is shown to exhibit a characteristic height-dependency, for which we propose an interpretation. The velocity spectra are analysed in detail; within and just above the canopy, a scaling based on fixed length and velocity scales (canopy height and mean horizontal wind speed at canopy top) is proposed. Examination of the turbulent kinetic energy and shear stress budgets confirms the role of turbulent transport in the region around the canopy top, and indicates that pressure transport may be significant in both cases. The results obtained here show that near the top of the canopy, the turbulence properties are more reminiscent of a plane mixing layer than a wall boundary layer.     

A simple mathematical model of airflow in waving plant canopies

A simple mathematical model is proposed, which combines the effects of mean wind speed, plant spacing and the drag coefficients of individual plants to calculate the fluctuating airflow within a waving crop canopy. The model is non-linear and is only amenable to analytical treatment when linearized; however, the full non-linear version can be solved on an analogue computer.The linear and non-linear results show unexpectedly good agreement, and the success of the linearization allows clear conclusions to be drawn about the relationship between the elasticity, geometry and mean wind speed through a stand of plants and the fluctuating components of airflow and stalk motion.Finally, the analytical results are in qualitative agreement with wind-tunnel results from two model canopies with different characteristics.     

An Observational Study of Wind-Induced Waving of Plants

The motions of individual plants and the turbulence statistics of surface winds measured near the top of a canopy are obtained over a wheat field and a rush field. Two typical cases of motions of individual plants are presented. The displacements of the ear of wheat (the plant height is 1.0 m) showed a natural oscillation in wind speeds of 1.6 m s⁻¹ measured at a height of 30 cm over a wheat canopy, while displacements of the stem of a rush plant were closely related to the fluctuations of surface winds in wind speeds of 1.7 m s⁻¹ measured at the top of the rush plant. The power spectra of displacements of a rush plant seem to support the negative seven-third power hypothesis proposed by Inoue. The frequency responses of displacements of plants to fluctuations of the instantaneous momentum flux are also presented.     

An observational study of wind-induced waving of plants

The motions of individual plants and the turbulence statistics of surface winds measured near the top of a canopy are obtained over a wheat field and a rush field. Two typical cases of motions of individual plants are presented. The displacements of the ear of wheat (the plant height is 1.0 m) showed a natural oscillation in wind speeds of 1.6 m s^–1 measured at a height of 30 cm over a wheat canopy, while displacements of the stem of a rush plant were closely related to the fluctuations of surface winds in wind speeds of 1.7 m s^–1 measured at the top of the rush plant. The power spectra of displacements of a rush plant seem to support the negative seven-third power hypothesis proposed by Inoue. The frequency responses of displacements of plants to fluctuations of the instantaneous momentum flux are also presented.     

Mean and Turbulent Flow Statistics in a Trellised Agricultural Canopy

Flow physics is investigated in a two-dimensional trellised agricultural canopy to examine that architecture’s unique signature on turbulent transport. Analysis of meteorological data from an Oregon vineyard demonstrates that the canopy strongly influences the flow by channelling the mean flow into the vine-row direction regardless of the above-canopy wind direction. Additionally, other flow statistics in the canopy sub-layer show a dependance on the difference between the above-canopy wind direction and the vine-row direction. This includes an increase in the canopy displacement height and a decrease in the canopy-top shear length scale as the above-canopy flow rotates from row-parallel towards row-orthogonal. Distinct wind-direction-based variations are also observed in the components of the stress tensor, turbulent kinetic energy budget, and the energy spectra. Although spectral results suggest that sonic anemometry is insufficient for resolving all of the important scales of motion within the canopy, the energy spectra peaks still exhibit dependencies on the canopy and the wind direction. These variations demonstrate that the trellised-canopy’s effect on the flow during periods when the flow is row-aligned is similar to that seen by sparse canopies, and during periods when the flow is row-orthogonal, the effect is similar to that seen by dense canopies.     

A spectral and lag-correlation analysis of turbulence in a deciduous forest canopy

The processes influencing turbulence in a deciduous forest and the relevant length and time scales are investigated with spectral and cross-correlation analysis. Wind velocity power spectra were computed from three-dimensional wind velocity measurements made at six levels inside the plant canopy and at one level above the canopy. Velocity spectra measured within the plant canopy differ from those measured in the surface boundary layer. Noted features associated with the within-canopy turbulence spectra are: (a) power spectra measured in the canopy crown peak at higher wavenumbers than do those measured in the subcanopy trunkspace and above the canopy; (b) peak spectral values collapse to a relatively universal value when scaled according to a non-dimensional frequency comprised of the product of the natural frequency and the Eulerian time scale for vertical velocity; (c) at wavenumbers exceeding the spectral peak, the slopes of the power spectra are more negative than those observed in the surface boundary layer; (d) Eulerian length scales decrease with depth into the canopy crown, then increase with further depth into the canopy; (e) turbulent events below crown closure are more correlated with turbulent events above the canopy than are those occurring in the canopy crown; and (f) Taylor's frozen eddy hypothesis is not valid in a plant canopy. Interactions between plant elements and the mean wind and turbulence alter the processes that produce, transport and remove turbulent kinetic energy and account for the noted observations.     

Turbulence Statistics Measurements in a Northern Hardwood Forest

Tower-based turbulence measurements were collected in and over a mixed hardwood forest at the University of Michigan BiologicalStation (UMBS) UMBSflux site in the northern summerof 2000. Velocity and temperature fluctuations were measured at five levels within the canopy (up to the canopy height, H = 21.4 m), using one- and three-dimensional sonic anemometers and fine-wire thermocouples. Six additional thermocouples were distributed over the canopy-layer depth. Three-dimensional velocities and sonic temperatures were also measured above the canopy at 1.6H and at 2.15H on the AmeriFlux tower located at the UMBSflux site. Vertical profiles of buoyancy flux, mean horizontal velocity, Reynolds stress, and standard deviation and skewness of velocity components were calculated. The analysis of these measurements aims at a multi-layer parameterization framework of turbulence statistics forimplementation in Lagrangian stochastic models. Turbulence profiles and power spectra above the canopy were analyzed in the context of Monin-Obukhov similarity theory (MOST) and Kolmogorov theory, as determined by stability at the top level (2.15H), to assess the extent to which surface scaling is valid as the canopy top is approached. Velocity spectra were computed to explore the potential of estimating the viscous dissipation rate, and results show that the high frequency range of the spectra above the canopy exhibits the roll-off predicted by Kolmogorov theory. Similarly, velocity standard deviations above the canopy converge to MOST predicted values toward the top level, and spectral peaks shift with stability, as expected. Within the canopy, both turbulence statistics profiles and spectral distributions follow the general known characteristics inside forests.     

A Linear Analysis of the Interaction Between the Atmosphere and an Underlying Compliant Plant Canopy

We summarise the results of a theoretical investigation of the interaction between the lower atmosphere and a compliant plant canopy. In this investigation, plant collisions were modelled as simple spring or dashpot interactions between adjacent plants. Linearised canopy models show that dashpot collisions and spring collisions are effective at reducing the amplitude of a canopy’s response to wind forcing, and may thus serve to stabilise plants against lodging and windthrow. Both types of collisions can also induce shifts in the stand resonance frequency and may thus serve to stabilise stands even further by shifting the canopy resonance frequency away from the most energetic frequencies in the atmospheric power spectrum. We also include a linear analysis of the shear layer instability over a waving canopy, and show that canopy drag has a strong effect on the instability. However, stem stiffness and inter-plant collisions have only minor effects on the wavenumber, growth rate, and frequency of the most unstable wave.     

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 Taylor's 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 Taylor's 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.     

A case study of temperature fluctuations within and above a wheat field before and after sunset

Temperature fluctuations in the stable air layer before and after sunset were measured at 4 heights within and above a wheat field. Large positive temperature fluctuations were frequently observed within the plant canopy. The standard deviations, skewness factors and flatness factors of temperature fluctuations within the canopy showed peculiar time variations, having remarkable positive skewness factors. The occurrence of large positive temperature fluctuations was probably related to the difference of temperature gradients below and above the observation height, i.e., these fluctuations frequently occurred when the temperature gradient above the observation height was greater than that below the observation height. Furthermore, the vertical mixing associated with the penetration of downdrafts from the air layer above the canopy was requisite for the occurrence of the phenomenon.     

Coherent eddies and temperature structure functions for three contrasting surfaces. Part I: Ramp model with finite microfront time

Air temperature time series within and above canopies reveal ramp patternsassociated with coherent eddies that are responsible for most of thevertical transport of sensible heat. Van Atta used a simple step-changeramp model to analyse the coherent part of air temperature structurefunctions. However, his ocean data, and our own measurements for aDouglas-fir forest, straw mulch, and bare soil, reveal that even withoutlinearization his model cannot account for the observed decrease of thecubic structure function for small time lag. We found that a ramp model inwhich the rapid change at the end of the ramp occurs in a finite microfronttime can describe this decrease very well, and predict at least relativemagnitudes of microfront times between different surfaces. Averagerecurrence time for ramps, determined by analysis of the cubic structurefunction with the new ramp model, agreed well with values determined usingthe Mexican Hat wavelet transform, except at lower levels within theforest. Ramp frequency above the forest and mulch scaled very well withwind speed at the canopy top divided by canopy height. Within the forest,ramp frequency did not vary systematically with height. This is inaccordance with the idea that large-scale canopy turbulence is mostlygenerated by instability of the mean canopy wind profile, similar to aplane mixing layer. The straw mulch and bare soil experiments uniquelyextend measurements of temperature structure functions and ramp frequencyto the smallest scales possible in the field.     

A Flume Experiment on the Adjustment of the Mean and Turbulent Statistics to a Transition from Short to Tall Sparse Canopies

Water-flume experiments are conducted to study the structure of turbulent flow within and above a sparse model canopy consisting of two rigid canopies of different heights. This difference in height specifies a two-dimensional step change from a rough to a rougher surface, as opposed to a smooth-to-rough transition. Despite the fact that the flow is in transition from a rough to a rougher surface, the thickness of the internal boundary layer scales as x ^4/5, consistent with smooth-to-rough boundary layer adjustment studies, where x is the downstream distance from the step change. However, the analogy with smooth-to-rough transitions no longer holds when the flow inside the canopy and near the canopy top is considered. Results show that the step change in surface roughness significantly increases turbulence intensities and shear stress. In particular, there is an adjustment of the mean horizontal velocity and shear stress as the flow passes over the rougher canopy, so that their vertical profiles adjust to give maximum values at the top of this canopy. We also observe that the magnitude and shape of the inflection in the mean horizontal velocity profile is significantly affected by the transition. The horizontal and vertical turbulence spectra compare well with Kolmogorov’s theory, although a small deviation at high frequencies is observed in the horizontal spectrum within the canopy. Here, for relatively low leaf area index, shear is found to be a more effective mechanism for momentum transfer through the canopy structure than vortex shedding.     

On the flow structure and turbulence during sweep and ejection events in a wind-tunnel model canopy

Particle image velocimetry (PIV) data obtained in a wind-tunnel model of a canopy boundary layer is used to examine the characteristics of mean flow and turbulence. The vector spacing varies between 1.7 and 2.5 times the Kolmogorov scales. Conditional sampling based on quadrants, i.e. based on the signs of velocity fluctuations, reveals fundamental differences in flow structure, especially between sweep and ejection events, which dominate the flow. During sweeps, the downward flow generates a narrow, highly turbulent, shear layer containing multiple small-scale vortices just below canopy height. During ejections, the upward flow expands this shear layer and the associated small-scale flow structures to a broad region located above the canopy. Consequently, during sweeps the turbulent kinetic energy (TKE), Reynolds stresses, as well as production and dissipation rates, have distinct narrow peaks just below canopy height, whereas during ejections these variables have broad maxima well above the canopy. Three methods to estimate the dissipation rate are compared, including spectral fits, measured subgrid-scale (SGS) energy fluxes at different scales, and direct measurements of slightly underresolved instantaneous velocity gradients. The SGS energy flux is 40–60% of the gradient-based (direct) estimates for filter sizes inside the inertial range, while decreasing with scale, as expected, within the dissipation range. The spectral fits are within 5–30% of the direct estimates. The spectral fits exceed the direct estimates near canopy height, but are lower well above and below canopy height. The dissipation rate below canopy height increases with velocity magnitude, i.e. it has the highest values during sweep and quadrant 1 events, and is significantly lower during ejection and quadrant 3 events. Well above the canopy, ejections are the most dissipative. Turbulent transport during sweep events acts as a source below the narrow shear layer within the canopy and as a sink above it. Transport during ejection events is a source only well above the canopy. The residual term in the TKE transport equation, representing mostly the effect of pressure–velocity correlations, is substantial only within the canopy, and is dominated by sweeps.     

Microscale pressure fluctuations in a mature deciduous forest

Static pressure fluctuations in the microscale range were measured in a mature deciduous forest. Pressure measurements were taken at the ground and above the canopy, and mean profile data of windspeed were collected from above the canopy to near the forest floor. Time series, spectra, and cross-correlations were calculated under different canopy conditions, and relationships between surface pressure fluctuations and mean windspeeds were determined. High-frequency pressure fluctuations that occur over aerodynamically smoother surfaces do not occur at the forest floor. These surface fluctuations are advected by the wind above the canopy, not that within the trunk space. The shapes of the pressure spectra are affected by changes in windspeed. Comparisons of spectra above and below the canopy also show some effect of the canopy itself on the shape of the pressure spectra.     

Scaling Laws in Canopy Flows: A Wind-Tunnel Analysis

An analysis of velocity statistics and spectra measured above a wind-tunnel forest model is reported. Several measurement stations downstream of the forest edge have been investigated and it is observed that, while the mean velocity profile adjusts quickly to the new canopy boundary condition, the turbulence lags behind and shows a continuous penetration towards the free stream along the canopy model. The statistical profiles illustrate this growth and do not collapse when plotted as a function of the vertical coordinate. However, when the statistics are plotted as function of the local mean velocity (normalized with a characteristic velocity scale), they do collapse, independently of the streamwise position and freestream velocity. A new scaling for the spectra of all three velocity components is proposed based on the velocity variance and integral time scale. This normalization improves the collapse of the spectra compared to existing scalings adopted in atmospheric measurements, and allows the determination of a universal function that provides the velocity spectrum. Furthermore, a comparison of the proposed scaling laws for two different canopy densities is shown, demonstrating that the vertical velocity variance is the most sensible statistical quantity to the characteristics of the canopy roughness.     

Wind-Flow Dynamics Over a Vineyard

Wind-flow dynamics has been extensively studied over horizontally uniform canopies, but agricultural plantations structured in rows such as vineyards have received less attention. Here, the wind flow over a vineyard is studied in neutral stratification from both large-eddy simulation (LES) and in situ measurements. The impact of row structure on the wind dynamics is investigated over a range of wind directions from cross-row to down-row, and a typical range of row aspect ratio (row separation/height ratio). It is shown that the mean flow over a vineyard is similar to that observed in uniform canopies, especially for wind directions from cross-row to diagonal. For down-row winds, the mean flow exhibits noticeable spatial variability across each elementary row-gap pattern, as the wind is channeled in the inter-row. This spatial variability increases with the aspect ratio. With down-row winds the turbulent structures are also more intermittent and generate larger turbulent kinetic energy and momentum flux. The displacement height and roughness length of the vineyard vary with the aspect ratio in a way similar to their variation with canopy density in uniform canopies. Both parameters take smaller values in down-row wind flow, for which the canopy appears more open. The analysis of velocity spectra and autocorrelation functions shows that vineyard canopies share similar features to uniform canopies in terms of turbulent coherent structures, with only minor changes with wind direction.     

Variances and spectra of vertical velocity just above the surface layer

Variances and spectra of vertical velocity at 75 m and 225 m obtained by aircraft have been analyzed. Given effective roughness lengths for the different terrain types, nomograms for the standard deviations were constructed as functions of wind speed and lapse rate, guided by theoretical considerations.Normalized spectra agree well with analogous spectra obtained elsewhere, and with requirements of similarity theory; however, over mountainous terrain, low-frequency spectra peaks appear, the frequency of which appears to be independent of height.     

Stability Dependence of Canopy Flows over a Flat Larch Forest

The dependence on atmospheric stability of flow characteristics adjacent to a very rough surface was investigated in a larch forest in Japan. Micrometeorological measurements of three-dimensional wind velocity and air temperature were taken at two heights above the forest, namely 1.7 and 1.2 times the mean canopy height h. Under near-neutral and stable conditions, the observed turbulence statistics suggest that the flow was likely to be that of the atmospheric surface layer (ASL) at 1.7h, and of the roughness sublayer (RSL) at 1.2h. However, in turbulence spectra, canopy-induced large coherent motions appeared clearly at both heights. Even under strongly stable conditions, the large-scale motions were retained at 1.2h, whereas they were overwhelmed by small-scale motions at 1.7h. This phenomenon was probably due to the enhanced contribution of the ASL turbulence associated with nocturnal decay of the RSL depth, because the small-scale motions appeared at frequencies close to the peak frequencies of well-known ASL spectra. This result supports the relatively recent concept that canopy flow is a superimposition of coherent motions and the ASL turbulence. The large-scale motions were retained in temperature spectra over a wider region of stability compared to streamwise wind spectra, suggesting that a canopy effect extended higher up for temperature than wind. The streamwise spacing of dominant eddies according to the plane mixing-layer analogy was only valid in a narrow range at near neutral, and it was stabilised at nearly half its value under stable conditions.     

Statistics of atmospheric turbulence within and above a corn canopy

Two three-dimensional split-film anemometers were used to measure turbulence statistics within and above a corn canopy. Normalised profiles of mean windspeed, root-mean-square velocity, momentum flux, and heat flux were constructed from half-hourly averages by dividing within-canopy measurements by the simultaneous canopy-top measurement. With the exception of the heat flux, these profiles showed consistent shape from day to day. Time series of the three velocity components were recorded on magnetic tape and subsequently analysed to obtain Eulerian time and length scales and the power spectrum of each component at several heights. The timescale was found to have a local minimum value at the top of the canopy. However the length scale L _wformed from the timescale and the root-mean-square vertical velocity varied with height as L _w 0.1 z. The power-spectra were non-dimensionalised to facilitate comparison of spectra at different heights and times. All spectra had -5/3 regions spanning at least two decades in frequency.