Turbulent transfer in a barley canopy

As a first step towards estimating the vertical flux of CO₂ in the canopy of a barley crop, the eddy diffusivity for turbulent transfer was estimated by two independent techniques: the energy balance method which needs measurement of net radiation, temperature and humidity throughout the canopy; and a flux method which needs measurements of individual leaf photosynthesis together with in-canopy CO₂ gradients and the soil CO₂ flux.At the top of the canopy the two sets of diffusivity measurements agreed with each other and with an aerodynamic estimate of the diffusivity. In the lower part of the canopy, however, large systematic differences occurred between the two estimates. Hence fluxes of CO₂ and flux divergences calculated from diffusivity profiles may be seriously in error.The basic assumptions and approximations embodied in the two sets of calculations are reviewed. Horizontal inhomogeneity in the crop is the most likely source of error. Lack of uniformity may be responsible for horizontal fluxes of heat, water vapour and CO₂ large enough to invalidate the one-dimensional approximation inherent in the micrometeorological methods used.In the current state of the art, inserting leaves in transparent chambers in a gas flow system or dosing them with ¹⁴CO₂ appear to be the most reliable methods of estimating photosynthetic rates layer by layer in a canopy. These techniques will be compared in a future paper in the series.     

Turbulent transport within and above a maize canopy

Hot-wire anemometers were used to measure air temperature and the three velocity components of the wind within and above a maize canopy. From digitized anemometer outputs, correlation coefficients for vertical heat flux and turbulent momentum transfer were calculated. A comparison of these coefficients with profiles of mean wind speed and mean temperature indicates that the main features of the turbulence may be explained in terms of the usual mixing-length theory. Instantaneous records of heat and momentum flux, however, indicate the existence of other competing turbulent mechanisms due to the unsteady, non-equilibrium nature of the turbulent flow. Regimes of flow dominated by mechanical and/or thermal mixing are indicated. Spectral results show that high shear and turbulent intensity levels as well as the presence of the maize leaves and stalks as vortex-shedding surfaces complicate the energy transfer mechanism. An energy balance between radiation and convection reveals that the energy budget is primarily a balance between solar radiation and the flux of latent heat.Contribution of the Sibley School of Mechanical and Aerospace Engineering, Cornell University, in cooperation with the Agricultural Research Service, U.S. Department of Agriculture, Ithaca, N.Y., U.S.A. and the Cornell University Agricultural Experiment Station. Department of Agronomy Series No. 1116.Sibley School of Mechanical and Aerospace Engineering, Cornell University; U.S. Department of Agriculture, Gainesville, Florida Section for Estuary and Fjord Studies, River and Harbour Laboratory, Technical University of Norway, Trondheim, Norway; State Univ. of New York at Buffalo; and U.S. Department of Agriculture and Cornell University; respectively.     

A new nonlinear analytical model for canopy flow over a forested hill

A new nonlinear analytical model for canopy flow over gentle hills is presented. This model is established based on the assumption that three major forces (pressure gradient, Reynolds stress gradient, and nonlinear canopy drag) within canopy are in balance for gentle hills under neutral conditions. The momentum governing equation is closed by the velocity-squared law. This new model has many advantages over the model developed by Finnigan and Belcher (Quart J Roy Meteorol Soc 130: 1–29 2004, hereafter referred to as FB04) in predicting canopy wind velocity profiles in forested hills in that: (1) predictions from the new model are more realistic because surface drag effects can be taken into account by boundary conditions, while surface drag effects cannot be accounted for in the algebraic equation used in the lower canopy layer in the FB04 model; (2) the mixing length theory is not necessarily used because it leads to a theoretical inconsistency that a constant mixing length assumption leads to a nonconstant mixing length prediction as in the FB04 model; and (3) the effects of height-dependent leaf area density (a(z)) and drag coefficient (C _d ) on wind velocity can be predicted, while both a(z) and C _d must be treated as constants in FB04 model. The nonlinear algebraic equation for momentum transfer in the lower part of canopy used in FB04 model is height independent, actually serving as a bottom boundary condition for the linear differential momentum equation in the upper canopy layer. The predicting ability of the FB04 model is largely restricted by using the height-independent algebraic equation in the bottom canopy layer. This study has demonstrated the success of using the velocity-squared law as a closure scheme for momentum transfer in forested hills in comparison with the mixing length theory used in FB04 model thus enhancing the predicting ability of canopy flows, keeping the theory consistent and simple, and shining a new light into land-surface parameterization schemes in numerical weather and climate models.     

Stratified flow over non-uniform surfaces: Turbulent energy model

A turbulent energy model is developed to simulate the response of a neutrally stratified atmospheric boundary layer to sudden changes in surface roughness. A mechanism of turbulent energy transfer is proposed, based upon the results of numerical experiments, that explains the distribution of shear stress and hence the distribution of velocity profiles in the atmospheric surface layer. Two length scales associated with the turbulent energy equation are obtained from experimental data and the law of the wall. Turbulent energy is also predicted.The predicted growth of the internal boundary layer is slower than that obtained from mixing-length models. Also, the predicted surface shear stress obtained from the turbulent energy model is in better agreement with field data than that obtained from mixing-length models.     

Turbulent flow over a wavy boundary

The linearized, two-dimensional flow of an incompressible fully turbulent fluid over a sinusoidal boundary is solved using the method of matched asymptotic expansions in the limit of vanishing skin-friction.A phenomenological turbulence model due to Saffman (1970, 1974) is utilized to incorporate the effects of the wavy boundary on the turbulence structure.Arbitrary lowest-order wave speed is allowed in order to consider both the stationary wavy wall, and the water wave moving with arbitrary positive or negative velocity.Good agreement is found with measured tangential velocity profiles and surface normal stress coefficients. The phase shift of the surface normal stress exhibits correct qualitative behavior with both positive and negative wave speeds, although predicted values are low.     

Organized structures in developing turbulent flow within and above a plant canopy,using a Large Eddy Simulation

A Large Eddy Simulation (LES) model representing the air flow within and above a plant canopy layer has been completed. Using this model, the organized structures of turbulent flow in the early developmental stages of a crop are simulated and discussed in detail.The effect of the drag due to vegetation is expressed by a term added to the three-dimensional Navier-Stokes equation averaged over the grid scale. For the formulation of sub-grid turbulence processes, the equations for the time-dependent SGS (Sub-Grid-Scale) turbulence energy equation is used, which includes the effects of dissipation (both by viscosity and leaf drag), shear production and diffusion.The organized structure of turbulent flow at the air-plant interface, obtained numerically by the model, yields its contribution to momentum transfer. The three-dimensional large eddy structures, which are composed of spanwise vortices (rolls) and streamwise vortices (ribs), are simulated near the air-plant interface. They are induced by the shear instability at inflection points of the velocity profile. The structure clearly has a life cycle. The instantaneous image of the structure is similar to those observed in the field observations of Gaoet al. (1989) and in the laboratory flume experiments of Ikeda and Ota (1992). These organized structures also account for the well known fact that the sweep motion of turbulence dominates momentum transport within and just above a plant canopy, and the motion of ejection prevails in the higher regions.     

Nighttime free convection characteristics within a plant canopy

An intensive measurement campaign within and above a maize row canopy was carried out to investigate flow characteristics within this vegetation. Attention was given to finding adequate scaling parameters of the within-canopy windspeed and air temperature profiles under above-canopy stable stratification.During clear and calm nights the within-canopy condition differs considerably from the abovecanopy state. In contrast to the daytime, the windspeed and temperature profiles do not scale with the above-canopy friction velocity,u ^* , and the scaling temperature,T ^* , respectively. A free convection flow regime is generated, forced by the soil heat flux at the canopy floor and by cooling at the top of the canopy. However, the windspeed and temperature profiles appear to scale well with the free convective velocity scale,w ^* , and the free convective temperature scale,T ^f , respectively. The free convective state within the canopy agrees well with the free convection criterion Gr>16Re²(u ^* ), where Gr is the Grashof number and Re(u ^* ) the Reynolds number, a criterion often used in technical flow problems. Also it is shown that under within-canopy free convection, there is a unique relation between the Grashof number, Gr, and the Reynolds number if the latter is based on the free convective velocity scale.Under within-canopy free convective conditions, it appears that within the canopy the fluxes of heat and water vapour can be estimated well with the relatively simple variance technique. Under these conditions, the Grashof, or Rayleigh number, represents a measure for the kinetic energy of the turbulence within the canopy.     

A note on vertical coherence of streamwise turbulence inside and above a model plant canopy

Measurements of longitudinal turbulent velocity were made at pairs of levels inside and above a model plant canopy in the wind tunnel. It was found that above approximately the zero-plane displacement level, the coherence and phase results were similar in many respects to atmospheric data, but that deviations from this behaviour appeared deeper in the model canopy.     

Experiments on scalar dispersion within a model plant canopy part I: The turbulence structure

This is the first of a series of three papers describing experiments on the dispersion of trace heat from elevated line and plane sources within a model plant canopy in a wind tunnel. Here we consider the wind field and turbulence structure. The model canopy consisted of bluff elements 60 mm high and 10 mm wide in a diamond array with frontal area index 0.23; streamwise and vertical velocity components were measured with a special three-hot-wire anemometer designed for optimum performance in flows of high turbulence intensity. We found that:

1. The momentum flux due to spatial correlations between time-averaged streamwise and vertical velocity components (the dispersive flux) was negligible, at heights near and above the top of the canopy.
2. In the turbulent energy budget, turbulent transport was a major loss (of about one-third of local production) near the top of the canopy, and was the principal gain mechanism lower down. Wake production was greater than shear production throughout the canopy. Pressure transport just above the canopy, inferred by difference, appeared to be a gain in approximate balance with the turbulent transport loss.
3. In the shear stress budget, wake production was negligible. The role of turbulent transport was equivalent to that in the turbulent energy budget, though smaller.
4. Velocity spectra above and within the canopy showed the dominance of large eddies occupying much of the boundary layer and moving downstream with a height-independent convection velocity. Within the canopy, much of the vertical but relatively little of the streamwise variance occurred at frequencies characteristic of wake turbulence.
5. Quadrant analysis of the shear stress showed only a slight excess of sweeps over ejections near the top of the canopy, in contrast with previous studies. This is a result of improved measurement techniques; it suggests some reappraisal of inferences previously drawn from quadrant analysis.

     

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.     

Experiments on scalar dispersion within a model plant canopy part II: An elevated plane source

This paper describes a wind-tunnel experiment on the dispersion of trace heat from an effectively planar source within a model plant canopy, the source height being h _s = 0.80 h _c , where h _c is the canopy height. A sensor assembly consisting of three coplanar hot wires and one cold wire was used to make simultaneous measurements of the temperature and the streamwise and vertical velocity components. It was found that:

1. The thermal layer consisted of two parts with different length scales, an inner sublayer (scaling with h _s and h _c ) which quickly reached streamwise equilibrium downstream of the leading edge of the source, and an outer sublayer which was self-preserving with a length scale proportional to the depth of the thermal layer.
2. Below 2h _c , the vertical eddy diffusivity for heat from the plane source (K _HP ) was substantially less than the far-field limit of the corresponding diffusivity for heat from a lateral line source at the same height as the plane source. This shows that dispersion from plane or other distributed sources in canopies is influenced, near the canopy, by turbulence ‘memory’ and must be considered as a superposition of both near-field and far-field processes. Hence, one-dimensional models for scalar transport from distributed sources in canopies are wrong in principle, irrespective of the order of closure.
3. In the budgets for temperature variance, and for the vertical and streamwise components of the turbulent heat flux, turbulent transport was a major loss between h _s and h _c and a principal gain mechanism below h _s , as also observed in the budgets for turbulent energy and shear stress.
4. Quadrant analysis of the vertical heat flux showed that sweeps and ejections contributed about equal amounts to the heat flux between h _s and h _c , though among the more intense events, sweeps were dominant. Below h _s , almost all the heat was transported by sweeps.

     

Mean canopy flow in an oak forest and estimation of the foliage profile by a numerical model

Summary The interaction of flow with the canopy structure is shown for an oak forest with hornbean trees (Carpinus betulus) as dense undergrowth using a large sample of 15 min mean profiles for the winter (without leaves) and the summer period (with leaves). The usefulness of the canopy flow index is analysed.To identify the processes involved in the momentum interaction a first-order closure model is interactively used. An approximation of the foliage area density from wind profile measurements is derived.With 7 Figures     

Turbulent kinetic energy budgets from a large-eddy simulation of airflow above and within a forest canopy

The output of a large-eddy simulation was used to study the terms ofthe turbulent kinetic energy (TKE) budget for the air layers above andwithin a forest. The computation created a three-dimensional,time-dependent simulation of the airflow, in which the lowest third ofthe domain was occupied by drag elements and heat sources to representthe forest. Shear production was a principal source of TKE in theupper canopy, diminishing gradually above tree-top height and moresharply with depth in the canopy. The transfer of energy to subgridscales (dissipation) was the main sink in the upper part of the domainbut diminished rapidly with depth in the canopy. Removal ofresolved-scale TKE due to canopy drag was extremely important,occurring primarily in the upper half of the forest where the foliagedensity was large. Turbulent transport showed a loss at the canopytop and a gain within the canopy. These general features have beenfound elsewhere but uncertainty remains concerning the effects ofpressure transport. In the present work, pressure was calculateddirectly, allowing us to compute the pressure diffusion term. Wellabove the canopy, pressure transport was smaller than, and opposite insign to, the turbulent transport term. Near the canopy top andbelow, pressure transport acted in concert with turbulent transport toexport TKE from the region immediately above and within the uppercrown, and to provide turbulent energy for the lower parts of theforest. In combination, the transport terms accounted for over half ofthe TKE loss near the canopy top, and in the lowest two-thirds of thecanopy the transport terms were the dominant source terms in thebudget. Moreover, the pressure transport was the largest source ofturbulent kinetic energy in the lowest levels of the canopy, beingparticularly strong under convective conditions. These resultsindicate that pressure transport is important in the plant canopyturbulent kinetic energy budget, especially in the lowest portion ofthe stand, where it acts as the major driving force for turbulentmotions.     

On the canopy flow index of a tropical forest

The usefulness of the canopy flow index concept is demonstrated for a two-story evergreen tropical forest. A sample of about 2500 wind profiles was utilized. It encompasses a large range of ambient wind conditions and spans the whole monsoon cycle in Southeast Asia.It was found that the use of two canopy flow indices (one for the upper and one for the lower canopy) would be necessary to simulate the average canopy flow. For the upper canopy, an average value of 4.04 was obtained; for the lower canopy an index of 1.77 was computed. The indices seem to be independent of the ambient wind speed (if 2 m s^-1 is exceeded), yet strongly dependent on wind direction.     

Experiments on scalar dispersion within a model plant canopy,part III: An elevated line source

An experiment is reported in which heat was released as a passive tracer from an elevated lateral line source within a model plant canopy, with h _s = 0.85 h _c (h _s and h _c being the source and canopy heights, respectively). A sensor assembly consisting of three coplanar hot wires and one cold wire was used to measure profiles of mean temperature % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiikamaana% aabaGaeqiUdehaaiaacMcaaaa!390C!\[(\overline \theta )\], temperature variance (Σ_θ ²), vertical and streamwise turbulent heat fluxes, and third moments of wind and temperature fluctuations. Conclusions were:

1. Despite the very heterogeneous flow within the canopy, the observed dispersive heat flux (due to spatial correlation between time-averaged temperature and vertical velocity) was small. However, there is evidence from the plume centroid (which was lower than h _s at the source) of systematic recirculating motions within the canopy.
2. The ratio % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeq4Wdm3aaS% baaSqaaiabeI7aXjaab2gacaqGHbGaaeiEaaqabaGccaGGVaWaa0aa% aeaacqaH4oqCaaWaaSbaaSqaaiaab2gacaqGHbGaaeiEaaqabaaaaa!41DF!\[\sigma _{\theta {\text{max}}} /\overline \theta _{{\text{max}}} \] (of maximum values on vertical profiles) decreased from 1 near the source to an asymptotic value of 0.4 far downstream, in good agreement with previous experimental and theoretical work for concentration fluctuations in the surface layer well above the canopy.
3. The eddy diffusivity for heat from the line source (K _HL ) increased, downstream of the source, to a nearly constant ‘far-field’ vertical profile. Within the canopy, the far-field K _HL was an order of magnitude larger than K _HP , the equivalent diffusivity for a plane source; well above the canopy, the two were equal. The time scale defined by (far-field K _HL )/(vertical velocity variance) was independent of height within the canopy.
4. Budgets for temperature variance, vertical heat flux and streamwise heat flux are remarkably similar to the equivalent budgets for an elevated line source in the surface layer well above the canopy, except in the lower part of the canopy in the far field, where vertical transport is much more important than in the surface layer.
5. A random flight simulation of the mean height and depth of the temperature plume was generally in good agreement with experiment. However, details of the temperature and streamwise turbulent heat flux profiles were not correct, suggesting that the model formulation needs to be improved.

     

Turbulent flow over a very rough,random surface

A knowledge of the nature of turbulent flow over very rough surfaces is important for an understanding of the environment of crops, forests, and cities. For this reason, a wind-tunnel investigation was carried out on the variations in mean velocity, Reynolds shear-stress, and other turbulence quantities in a deep turbulent flow over a rough surface having a fair degree of randomness in the shapes, sizes, and positions of its elements.There was a layer close to the surface with considerable variations in both mean velocity and shear-stress, and the horizontal scale over which the mean velocity varied was much larger than the average distance between roughness elements. Above this layer, whose depth was of the order of the spacing between roughness elements, shear stress was constant with height, and the velocity profile had a logarithmic form. The usefulness of both mean profile and eddy-correlation methods for estimating fluxes above very rough terrain is discussed in the light of these findings.     

A wind-profile index for canopy flow

Canopy wind profiles can often be represented by an exponential function. The associated attenuation index,a, is found to be proportional to [(Flexibility)(Leaf Area)(Density)]^1/3. Leastsquare values of the index have been calculated for wind profiles in about a dozen natural and artificial canopies which included oats, wheat, corn, rice, sunflowers, larch trees, citrus trees, Xmas trees, plastic strips, wooden pegs and bushel baskets. It is found that canopy flow is a function of canopy density, element flexibility, and height and that the behaviour of artificial canopy elements is compatible with that of natural vegetation. The same calculations also show that the attenuation coefficient: (a) is not a universal constant, (b) is however, rather limited in range (-0.3 to 3.0), (c) varies with stage of growth, and (d) increases as density and flexibility increase. A compilation ofa-values for several canopies reveals that lowa-values correspond to sparsely arrayed rigid elements while higha-values correspond to densely arrayed and flexible elements. Finally, lowa-values appear to be relatively independent of wind speed, while higha-values tend to increase as wind speeds increase.     

Wave-like wind fluctuations observed in the stable surface layer over a plant canopy

Observations of wind velocity and temperature fluctuations were made in the nocturnal surface inversion layer over a paddy field. A remarkable wave-like motion of about 8 min period was seen in horizontal wind speed and standard deviation of vertical wind velocity. In addition, fluctuations of horizontal wind speed and anticlockwise rotation of wind direction with a period of about 30 min were found by power spectral analysis. The phenomena persisted for more than 2 hours. Similar phenomena were also observed at a coastal site at a distance of about 10 km from the paddy field.     

Observation of organized structure in turbulent flow within and above a forest canopy

Ramp patterns of temperature and humidity occur coherently at several levels within and above a deciduous forest as shown by data gathered with up to seven triaxial sonic anemometer/thermometers and three Lyman-alpha hygrometers at an experimental site in Ontario, Canada. The ramps appear most clearly in the middle and upper portion of the forest. Time/height cross-sections of scalar contours and velocity vectors, developed from both single events and ensemble averages of several events, portray details of the flow structures associated with the scalar ramps. Near the top of the forest they are composed of a weak ejecting motion transporting warm and/or moist air out of the forest followed by strong sweeps of cool and/or dry air penetrating into the canopy. The sweep is separated from the ejecting air by a sharp scalar microfront. At approximately twice the height of the forest, ejections and sweeps are of about equal strength.In the middle and upper parts of the canopy, sweeps conduct a large proportion of the overall transfer between the forest and the lower atmosphere, with a lesser contribution from ejections. Ejections become equally important aloft. During one 30-min run, identified structures were responsible for more than 75% of the total fluxes of heat and momentum at mid-canopy height. Near the canopy top, the transition from ejection of slow moving fluid to sweep bringing fast moving air from above is very rapid but, at both higher and lower levels, brief periods of upward momentum transfer occur at or immediately before the microfront.