Seasonal and diurnal variations of coherent structures over a deciduous forest

Coherent structures in turbulent flow above a midlatitude deciduous forest are identified using a wavelet analysis technique. Coupling between motions above the canopy (z/h=1.5, whereh is canopy height) and within the canopy (z/h=0.6) are studied using composite velocity and temperature fields constructed from 85 hours of data. Data are classified into winter and summer cases, for both convective and stable conditions. Vertical velocity fluctuations are in phase at both observation levels. Horizontal motions associated with the structures within the canopy lead those above the canopy, and linear analysis indicates that the horizontal motions deep in the canopy should lead the vertical motions by 90°. On average, coherent structures are responsible for only about 40% of overall turbulent heat and momentum fluxes, much less than previously reported. However, our large data set reveals that this flux fraction comes from a wide distribution that includes much higher fractions in its upper extremes. The separation distanceL _s between adjacent coherent structures, 6–10h, is comparable to that obtained in previous observations over short canopies and in the laboratory. Changes in separation between the summer and winter (leafless) conditions are consistent withL _s being determined by a local horizontal wind shear scale.     

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.     

Turbulence Over Urban-type Roughness: Deductions from Wind-tunnel Measurements

Turbulence data from experiments conducted over a staggered cube array, modelling a neutrally stable atmospheric boundary layer in an urban environment, are presented. The results support the contention that organised eddy structures in the near-wall region differ significantly from those in regular smooth-wall flows or in rough-wall boundary layers with much smaller h/δ ratios (where δ and h are the boundary-layer thickness and the height of the roughness elements, respectively). Attention is concentrated on spatial correlations, spectra (and thus the dominant length and time scales), maps of anisotropy invariants and quadrant analyses of the stress tensor. Results are obtained within both the roughness sublayer (i.e. the region above the roughness but within which the flow is spatially inhomogeneous) and the canopy region (i.e. below the height of the roughness elements) and discussion includes consideration of the turbulence kinetic energy balance at various heights.     

Regional roughness of the landes forest and surface shear stress under neutral conditions

Mean wind velocity profiles were measured by means of radio-windsondes over the Landes region in southwestern France, which consists primarily of pine forests with scattered villages and clearings with various crops. Analysis of neutral profiles indicated the existence of a logarithmic layer between approximately z – d ₀ = 67(±18)z ₀ and 128(+-32)z ₀ (z is the height above the ground, z ₀ the surface roughness and d ₀ the displacement height). The upper limit can also be given as z – d ₀ = 0.33 (±0.18)h, where h is the height of the bottom of the inversion. The profiles showed that the surface roughness of this terrain is around 1.2 m and the displacement height 6.0 m. Shear stresses derived from the profiles were in good agreement with those obtained just above the forest canopy at a nearby location with the eddy correlation method by a team from the Institute of Hydrology (Wallingford, England).     

The ejection-sweep cycle over bare and forested gentle hills: a laboratory experiment

Progress on practical problems such as quantifying gene flow and seed dispersal by wind or turbulent fluxes over nonflat terrain now demands fundamental understanding of how topography modulates the basic properties of turbulence. In particular, the modulation by hilly terrain of the ejection-sweep cycle, which is the main coherent motion responsible for much of the turbulent transport, remains a problem that has received surprisingly little theoretical and experimental attention. Here, we investigate how boundary conditions, including canopy and gentle topography, alter the properties of the ejection-sweep cycle and whether it is possible to quantify their combined impact using simplified models. Towards this goal, we conducted two new flume experiments that explore the higher-order turbulence statistics above a train of gentle hills. The first set of experiments was conducted over a bare surface while the second set of experiments was conducted over a modelled vegetated surface composed of densely arrayed rods. Using these data, the connections between the ejection-sweep cycle and the higher-order turbulence statistics across various positions above the hill surface were investigated. We showed that ejections dominate momentum transfer for both surface covers at the top of the inner layer. However, within the canopy and near the canopy top, sweeps dominate momentum transfer irrespective of the longitudinal position; ejections remain the dominant momentum transfer mode in the whole inner region over the bare surface. These findings were well reproduced using an incomplete cumulant expansion and the measured profiles of the second moments of the flow. This result was possible because the variability in the flux-transport terms, needed in the incomplete cumulant expansion, was shown to be well modelled using “local” gradient-diffusion principles. This result suggests that, in the inner layer, the higher-order turbulence statistics appear to be much more impacted by their relaxation history towards equilibrium rather than the advection-distortion history from the mean flow. Hence, we showed that it is possible to explore how various boundary conditions, including canopy and topography, alter the properties of the ejection-sweep cycle by quantifying their impact on the gradients of the second moments only. Implications for modelling turbulence using Reynolds-averaged Navier Stokes equations and plausible definitions for the canopy sublayer depth are briefly discussed.     

Aerodynamic Scaling for Estimating the Mean Height of Dense Canopies

We used an aerodynamic method to objectively determine a representative canopy height, using standard meteorological measurements. The canopy height may change if the tree height is used to represent the actual canopy, but little work to date has focused on creating a standard for determining the representative canopy height. Here we propose the ‘aerodynamic canopy height’ h _a as the most effective means of resolving the representative canopy height for all forests. We determined h _a by simple linear regression between zero-plane displacement d and roughness length z ₀, without the need for stand inventory data. The applicability of h _a was confirmed in five different forests, including a forest with a complex canopy structure. Comparison with stand inventory data showed that h _a was almost equivalent to the representative height of trees composing the crown surface if the forest had a simple structure, or to the representative height of taller trees composing the upper canopy in forests with a complex canopy structure. The linear relationship between d and z ₀ was explained by assuming that the logarithmic wind profile above the canopy and the exponential wind profile within the canopy were continuous and smooth at canopy height. This was supported by observations, which showed that h _a was essentially the same as the height defined by the inflection point of the vertical profile of wind speed. The applicability of h _a was also verified using data from several previous studies.     

The Impact of Landscape Fragmentation on Atmospheric Flow: A Wind-Tunnel Study

Landscape discontinuities such as forest edges play an important role in determining the characteristics of the atmospheric flow by generating increased turbulence and triggering the formation of coherent tree-scale structures. In a fragmented landscape, consisting of surfaces of different heights and roughness, the multiplicity of edges may lead to complex patterns of flow and turbulence that are potentially difficult to predict. Here, we investigate the effects of different levels of forest fragmentation on the airflow. Five gap spacings (of length approximately 5h, 10h, 15h, 20h, 30h, where h is the canopy height) between forest blocks of length 8.7h, as well as a reference case consisting of a continuous forest after a single edge, were investigated in a wind tunnel. The results reveal a consistent pattern downstream from the first edge of each simulated case, with the streamwise velocity component at tree top increasing and turbulent kinetic energy decreasing as gap size increases, but with overshoots in shear stress and turbulent kinetic energy observed at the forest edges. As the gap spacing increases, the flow appears to change monotonically from a flow over a single edge to a flow over isolated forest blocks. The apparent roughness of the different fragmented configurations also decreases with increasing gap size. No overall enhancement of turbulence is observed at any particular level of fragmentation.     

Coherent Turbulent Structures Across a Vegetation Discontinuity

The study of turbulent flow across a vegetation discontinuity is of significant interest as such landscape features are common, and as there is no available theory to describe this regime adequately. We have simulated the three-dimensional dynamics of the airflow across a discontinuity between a forest (with a leaf area index of 4) and a clearing surface using large-eddy simulation. The properties of the bulk flow, as well as the large-scale coherent turbulent structures across the forest-to-clearing transition and the clearing-to-forest transition, are systematically explored. The vertical transport of the bulk flow upstream of the leading edge gives rise to the enhanced gust zone around the canopy top, while the transport downstream of the trailing edge leads to the formation of a recirculation zone above the clearing surface. The large-scale coherent structures across the two transitions exhibit both similarities with and differences from those upstream of the corresponding transition. For example, the ejection motion is dominant over the sweep motion in most of the region 1?<?z/h < 2 (h is the canopy height) immediately downstream of the trailing edge, much as in the forested area upstream. Also, the streamwise vortex pair, which has previously been observed within the canopy sublayer and the atmospheric boundary layer, is consistently found across both transitions. However, the inflection observed both in the mean streamwise velocity, as well as in the vertical profiles of the coherent structures in the forested area, disappears gradually across the forest-to-clearing transition. The coherence of the turbulence, quantified by the percentage of the total turbulence kinetic energy that the coherent structures capture from the flow, decreases sharply immediately downstream of the trailing edge of the forest and increases downstream of the leading edge of the forest. The effects of the ratio of the forest/clearing lengths under a given streamwise periodicity on flow statistics and coherent turbulent structures are presented as well.     

Exploring the Effects of Microscale Structural Heterogeneity of Forest Canopies Using Large-Eddy Simulations

The Regional Atmospheric Modeling System (RAMS)-based Forest Large-Eddy Simulation (RAFLES), developed and evaluated here, is used to explore the effects of three-dimensional canopy heterogeneity, at the individual tree scale, on the statistical properties of turbulence most pertinent to mass and momentum transfer. In RAFLES, the canopy interacts with air by exerting a drag force, by restricting the open volume and apertures available for flow (i.e. finite porosity), and by acting as a heterogeneous source of heat and moisture. The first and second statistical moments of the velocity and flux profiles computed by RAFLES are compared with turbulent velocity and scalar flux measurements collected during spring and winter days. The observations were made at a meteorological tower situated within a southern hardwood canopy at the Duke Forest site, near Durham, North Carolina, U.S.A. Each of the days analyzed is characterized by distinct regimes of atmospheric stability and canopy foliage distribution conditions. RAFLES results agreed with the 30-min averaged flow statistics profiles measured at this single tower. Following this intercomparison, two case studies are numerically considered representing end-members of foliage and midday atmospheric stability conditions: one representing the winter season with strong winds above a sparse canopy and a slightly unstable boundary layer; the other representing the spring season with a dense canopy, calm conditions, and a strongly convective boundary layer. In each case, results from the control canopy, simulating the observed heterogeneous canopy structure at the Duke Forest hardwood stand, are compared with a test case that also includes heterogeneity commensurate in scale to tree-fall gaps. The effects of such tree-scale canopy heterogeneity on the flow are explored at three levels pertinent to biosphere-atmosphere exchange. The first level (zero-dimensional) considers the effects of such heterogeneity on the common representation of the canopy via length scales such as the zero-plane displacement, the aerodynamic roughness length, the surface-layer depth, and the eddy-penetration depth. The second level (one-dimensional) considers the normalized horizontally-averaged profiles of the first and second moments of the flow to assess how tree-scale heterogeneities disturb the entire planar-averaged profiles from their canonical (and well-studied planar-homogeneous) values inside the canopy and in the surface layer. The third level (three-dimensional) considers the effects of such tree-scale heterogeneities on the spatial variability of the ejection-sweep cycle and its propagation to momentum and mass fluxes. From these comparisons, it is shown that such microscale heterogeneity leads to increased spatial correlations between attributes of the ejection-sweep cycle and measures of canopy heterogeneity, resulting in correlated spatial heterogeneity in fluxes. This heterogeneity persisted up to four times the mean height of the canopy (h _c ) for some variables. Interestingly, this estimate is in agreement with the working definition of the thickness of the canopy roughness sublayer (2h _c –5h _c ).     

Heat and mass transfer to and from surfaces with dense vegetation or similar permeable roughness

A differential equation is obtained to describe the concentration of passive admixtures (water vapor, sensible heat, pollutants, CO₂, etc.) of turbulent flow inside a dense and uniform vegetational canopy. The profiles of eddy diffusivity, wind speed and shear stress are assumed to be exponential decay functions of depth below the top of the canopy. This equation is solved for the case of a vegetation with constant concentration of the admixture at the foliage surfaces. The solution is used to formulate bulk mass or heat transfer coefficients, which can be applied to practical problems involving surfaces covered with a vegetation or with similar porous or fibrous roughness elements. The results are shown to be consistent with experimental data presented by Chamberlain (1966), Garratt and Hicks (1973) and Garratt (1978). Calculations with the model illustrate that, as compared to its behavior over surfaces with bluff roughness elements, ln(z ₀/z _0c ) (wherez ₀ is the momentum roughness andz _0c , the scalar roughness) for permeable roughness elements is relatively insensitive tou _* and practically independent ofz ₀.     

Detecting Near-Surface Coherent Structure Characteristics Using Wavelet Transform with Different Meteorological Elements

In the present study, three wavelet basis functions (Mexican-hat, Morlet, and Wave) were used to analyze atmospheric turbulence data obtained from an eddy covariance system in order to determine effect of six meteorological elements (three-dimensional wind speed, temperature, and CO2 and H2O concentrations) on the time scale of coherent structures. First, we used the degree of correlation between original and reconstructed waveforms to test the three wavelets’ performance when determining the time scale of coherent structures. The Wave wavelet’s reconstructed coherent structure signal best matched the original signal; thus, it was used for further analysis of the time scale, number, and time cover of the meteorological elements. We found similar results for all elements, though there was some internal variation, suggesting that coherent structures are not inherently dependent on these elements. Our results provide a basis for proper coherent structure detection in atmospheric turbulence and improve the understanding of similarities and differences between coherent structure characteristics of different meteorological elements, which is helpful for further research into atmospheric turbulence and boundary layers.     

Characteristics of canopy turbulence over a deciduous forest on complex terrain

Canopy turbulence plays an important role in mass and energy exchanges at the canopy-atmosphere interface. Despite extensive studies on canopy turbulence over a flat terrain, less attention has been given to canopy turbulence in a complex terrain. The purpose of this study is to scrutinize characteristics of canopy turbulence in roughness sublayer over a hilly forest terrain. We investigated basic turbulence statistics, conditionally sampled statistics, and turbulence spectrum in terms of different atmospheric stabilities, wind direction and vertical structures of momentum fluxes. Similarly to canopy turbulence over a homogeneous terrain, turbulence statistics showed coherent structure. Both quadrant and spectrum analysis corroborated the role of intermittent and energetic eddies with length scale of the order of canopy height, regardless of wind direction except for shift of peak in vertical wind spectrum to relatively high frequency in the down-valley wind. However, the magnitude of the momentum correlation coefficient in a neutral condition was smaller than typical value over a flat terrain. Further scrutiny manifested that, in the up-valley flow, temperature skewness was larger and the contribution of ejection to both momentum and heat fluxes was larger compared to the downvalley flow, indicating that thermal instability and weaker wind shear in up-valley flow asymmetrically affect turbulent transport within the canopy.     

Vertical Structure of Selected Turbulence Characteristics above an Urban Canopy

Summary In this paper the results of an urban measurement campaign are presented. The experiment took place from July 1995 to February 1996 in Basel, Switzerland. A total of more than 2000 undisturbed 30-minute runs of simultaneous measurements of the fluctuations of the wind vector u′, v′, w′ and the sonic temperature θ _s ′ at three different heights (z=36, 50 and 76 m a.g.l.) are analysed with respect to the integral statistics and their spectral behaviour. Estimates of the zero plane displacement height d calculated by the temperature variance method yield a value of 22 m for the two lower levels, which corresponds to 0.92 h (the mean height of the roughness elements). At all three measurement heights the dimensionless standard deviation σ _w /u _* is systematically smaller than the Monin-Obukhov similarity function for the inertial sublayer, however, deviations are smaller compared to other urban turbulence studies. The σ_θ/θ_* values follow the inertial sublayer prediction very close for the two lowest levels, while at the uppermost level significant deviations are observed. Profiles of normalized velocity and temperature variances show a clear dependence on stability. The profile of friction velocity u _* is similar to the profiles reported in other urban studies with a maximum around z/h=2.1. Spectral characteristics of the wind components in general show a clear dependence on stability and dimensionless measurement height z/h with a shift of the spectral peak to lower frequencies as thermal stability changes from stable to unstable conditions and as z/h decreases. Velocity spectra follow the −2/3 slope in the inertial subrange region and the ratios of spectral energy densities S _w (f)/S _u (f) approach the value of 4/3 required for local isotropy in the inertial subrange. Velocity spectra and spectral peaks fit best to the well established surface layer spectra from Kaimal et al. (1972) at the uppermost level at z/h=3.2. Received September 26, 1997 Revised February 15, 1998     

Turbulence Statistics Above And Within Two Amazon Rain Forest Canopies

The turbulence structure in two Amazon rain forestswas characterised for a range of above-canopystability conditions, and the results compared withprevious studies in other forest canopies and recenttheory for the generation of turbulent eddies justabove forest canopies. Three-dimensional wind speedand temperature fluctuation data were collectedsimultaneously at up to five levels inside and abovetwo canopies of 30–40 m tall forests, during threeseparate periods. We analysed hourly statistics, jointprobability distributions, length scales, spatialcorrelations and coherence, as well as power spectraof vertical and horizontal wind speed.The daytime results show a sharp attenuation ofturbulence in the top third of the canopies, resultingin very little movement, and almost Gaussianprobability distributions of wind speeds, in the lowercanopy. This contrasts with strongly skewed andkurtotic distributions in the upper canopy. At night,attenuation was even stronger and skewness vanishedeven in the upper canopy. Power spectral peaks in thelower canopy are shifted to lower frequencies relativeto the upper canopy, and spatial correlations andcoherences were low throughout the canopy. Integrallength scales of vertical wind speed at the top of thecanopy were small, about 0.15 h compared to avalue of 0.28 h expected from the shear lengthscale at the canopy top, based on the hypothesis that theupper canopy air behaves as a plane mixing layer. Allthis suggests that, although exchange is not totallyinhibited, tropical rain forest canopies differ from other forests in that rapid, coherentdownward sweeps do not penetrate into the lowercanopy, and that length scales are suppressed. This isassociated with a persistent inversion of stability inthat region compared to above-canopy conditions. Theinversion is likely to be maintained by strong heatabsorption in the leaves concentrated near thecanopy top, with the generally weak turbulence beingunable to destroy the temperature gradients over thelarge canopy depth.     

Momentum Absorption in Rough-Wall Boundary Layers with Sparse Roughness Elements in Random and Clustered Distributions

A wind-tunnel experiment has been used to investigate momentum absorption by rough surfaces with sparse random and clustered distributions of roughness elements. An unusual (though longstanding) method was used to measure the boundary-layer depth δ and friction velocity u _* and thence to infer the functional relationship z ₀/h = f(λ) between the normalised roughness length z ₀/ h and the roughness density λ (where z ₀ is the roughness length and h the mean height of the roughness elements). The method for finding u _* is based on fitting the velocity defect in the outer layer to a functional form for the dimensionless velocity-defect profile in a canonical zero-pressure-gradient boundary layer. For the conditions investigated here, involving boundary layers over sparse roughness with strong local heterogeneity, this velocity-defect-law method is found to be more robust than several alternative methods for finding u _* (uw covariance, momentum integral and slope of the logarithmic velocity profile).The experimental results show that, (1) there is general agreement in the relationship z ₀/h = f(λ) between the present experiment with random arrays and other wind-tunnel experiments with regular arrays; (2) the main effect of clustering is to increase the scatter in the z ₀/h = f(λ) relationship, through increased local horizontal heterogeneity; (3) this scatter obscures any trend in the z ₀/h = f(λ) relationship in response to clustering; and (4) the agreement between the body of wind-tunnel data (taken as a whole) and field data is good, though with scatter for which it is likely that a major contribution stems from local horizontal heterogeneity in the field.     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

Intermittent wind close to the ground within a grass canopy

Wind speed was measured at a height of 1 cm above the ground and at several other heights in and above a canopy of tall fescue grass (Festuca arundinacea) using single hot-wire and triple hot-film anemometers. The plant area density in the canopy was concentrated close to the ground, with 75% of the plant area standing belowz=15 cm, wherez is height above the ground. The frequency distributions of horizontal wind speeds,s, were sharply skewed towards positive values at all measurement heights, but were most highly skewed near the ground where the coefficient of skewness ranged from 1.6 to 2.9. Above mid-canopy height, the frequency distribution ofs was described reasonably well by a Gumbel extreme value distribution. Average wind speed,S, decreased exponentially with depth into the canopy with an exponential scale length of abouth/2.8, whereh is the height of the canopy. Atz=1 cm, the value ofS was about 11% of the surface-layeru _*. The standard deviation of the fluctuations of the vertical and horizontal components of the wind speed also decreased exponentially with depth inside the canopy with a scale length of abouth/2.5.Inside the canopy, the Eulerian integral time scales for the vertical ( _w ) and horizontal ( _u ) components of wind speed were about 0.1 s and 1.0 s, respectively, and were approximately constant with height. Above the canopy, these time scales increased sharply and, atz=2.25h, _w and _u were approximately 1.0 and 3.0s, respectively. Turbulence length scales in the vertical and downwind directions, _u and _w ·U, respectively, were approximately 1 cm for heights between 1 to 10 cm above the ground inside the canopy, while atz=2.25h, they were about 55 cm and 277 cm. Relatively quiescent periods (lulls) in the air close to the ground were interrupted frequently by gusts. The frequency of occurrence of gusts appears to be correlated with the value of the local shear near the top of the canopy.     

Aerodynamic roughness of vegetated surfaces

Available experimental results indicate that as the density of roughness elements over a horizontally homogeneous surface is varied, the roughness length, z ₀, varies in a manner that exhibits a maximum at intermediate density values. In an attempt to explain this behaviour, the available analytical solutions for the wind profile inside dense homogeneous canopies were reviewed. The review indicated that the variation of z ₀ with density depends on the interrelationship between the leaf density, a, and the mixing length, l. In view of this finding, a numerical model was devised based on a simple rule for constructing mixing-length profiles in the canopy. The rule states that the actual value of l is the maximum possible under the two constraints: l l _i and ¦dl/dz¦ k, where k is the von Karman constant and the intrinsic mixing length, l _i, is a function of the local internal structure of the canopy. The model which ensures a smooth transition from dense to thin canopy, was used to reproduce the observed maximum of z ₀. The model is also capable of handling vertically non-homogeneous canopies.     

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.