Studies of forced-convection heat and mass transfer of fluttering realistic leaf models

The forced-convection mass transfer - and by analogy, heat transfer - of various realistic leaf models at Reynolds numbers 2 x 10³<Re<4 x 104 was studied with an electrochemical method. The results are compared with similar measurements on plates and with transfer coefficients calculated from the laminar boundary-layer theory. In this way the validity of the commonly-used analytical expressions which represent the leaf by a rigid plate and neglect the effects of leaf curvature, fluttering, surface roughness and fluid turbulence, can be tested.The measurements show that for fluttering single leaves, the convective mass-transfer coefficients must be expected to be higher by a factor of 1.4 ± 0.1 than the ones calculated for rigid plates of equal size and shape. For a leaf in a crop, the increase might be as high as a factor of 2. The high transfer coefficients measured for elements of cedar foliage are also discussed.     

Simultaneous determinations of the sensible and latent heat transfer coefficients for tree leaves

The heat and mass transfer coefficients for exchange across the fluid dynamic boundary layer over tree leaves were simultaneously determined in a controlled environment chamber. The mass transfer coefficients were calculated from measured values of evaporation, air specific humidity and a value of leaf specific humidity at leaf temperature. The heat transfer coefficients were calculated from measured values of air temperature, leaf temperature and an estimate of the sensible heat flux density calculated as the measured net radiation at the leaf surfaces minus the latent heat flux density. The experiments described in this paper indicate that the equations based on laminar boundary-layer theory can give reasonable estimates of the transfer coefficients of real tree leaves for the velocities most commonly experienced in plant canopies, if they are adjusted by a constant multiplier greater than one. Calculations of local mass transfer coefficients based on temperature measurements at three locations at different distances from the leading edge of the leaves, indicate that the deviation from theory is probably the result of transition to turbulent boundary-layer flow at some distance from the leading edge.     

Boundary-layer resistances of artificial leaves in turbulent air II: Leaves inclined to the mean flow

The effect of turbulence on boundary-layer resistances to heat and water vapour transfer from leaves inclined to the mean airflow has been studied using heated square plates in a wind tunnel. Heat and water vapour transfer coefficients increased with streamwise turbulence intensity for all angles of inclination of the plates to the mean flow, and the increase was dependent on the ratio of the longitudinal integral length scale to the plate dimension. This dependence on the turbulence length scale probably results from a resonant interaction between the boundary layer on the plate and the turbulence in the approaching mean flow.The paper also presents results of experiments with heated plates having serrated leading edges and/or a transverse ridge on the surface, conducted in an attempt to understand the aerodynamic importance of morphological irregularities on the leaf surface. The irregularities studied here disturbed the boundary layer on the plate, and greatly increased heat transfer when the angle of inclination of the plates to the mean wind was small, but had little effect when the angle of inclination exceeded 40 °.     

Measurements of Flows Over Isolated Valleys

Wind-tunnel measurements of the flow over an isolated valley both normal and at an angle (45°) to a simulated neutrally stable atmospheric boundary layer are presented. Attention is concentrated on the nature of the flow within the valley itself. The work formed part of a wider study that included detailed field measurements around an African desert valley and some limited comparisons with that work are included. A scale of about 1:1000 was used for the laboratory work, in which an appropriate combination of hot wire and particle image velocimetry was employed. For a valley normal to the upwind flow, it is shown that the upstream influence of the valley extends to a distance of at least one half of the axial valley width upstream of the leading edge, whereas differences in mean flow and turbulence could be identified well beyond two valley widths from the downwind edge. Non-normal wind angles lead to significant along-valley flows within the valley and, even at two valley heights above the valley ridge level, there remains a significant spanwise flow component. Downwind turbulence levels are somewhat lower in this case, but are still considerably higher than in the undisturbed boundary layer. At both flow angles, there are significant recirculation regions within the valleys, starting from mean separation just beyond the leading edge, but the strong spanwise flow in the 45° case reduces the axial extent of the separated zone. The flow is shown to be in some ways analogous to flow over an isolated hill. Our results usefully enhance the field data and could be used to improve modelling of saltation processes in the field.     

Influence d'un brise-vent sur les pertes convectives et radiatives d'une serre

An experimental study of air flow near the walls of a greenhouse protected by a natural windbreak shows that a low speed reversed flow is produced between the two obstacles and relatively large wind speeds and gradients are located at the top of the greenhouse (Figure 1). Estimation of the convective heat fluxes from the different zones of the greenhouse cover to the surroundings shows that heat losses by convective processes are most important from the top of the greenhouse. This implies a need for good greenhouse roof insulation in order to save energy.On the other hand, estimation of the incoming thermal radiation over the greenhouse shows that the presence of the wind-break modifies the radiative exchanges. The hedges act as a radiative shelter. So, the heat losses of the greenhouse are reduced.This paper also shows that the adoption of an overall heat transfer coefficient for the determination of convective heat losses from the greenhouse is inaccurate, leading to an overestimation of the above losses when using such a coefficient.     

Heat transport coefficients for constant energy flux models of broad leaves

Experimental determinations of the local heat transfer by forced convection from model leaves heated by a constant energy flux were made in the laboratory under laminar and turbulent flow conditions.The results are expressed in a logarithmic dimensionless plot of the local Nusselt number, Nu _d , against the local Reynolds number, Re _d . For the laminar case, Nu _d was only a linear function of Re _d ^1/2 downwind from the leading edge regions, although this relationship departed from that predicted theoretically due to the finite size and thickness of the model. For the turbulent case, a simple relationship between Nu _d and Re _d was found over a wide range of Reynolds numbers. The enhancement of heat transfer in the turbulent case depends primarily on the scale of turbulence rather than on the turbulent intensity.Past workers have discussed their results in relation to a factor , defined as the ratio between the heat transfer predicted by the Polhausen equation, and that measured. The results suggest that is not a unique parameter and may not be useful in describing the overall turbulent transfer process.     

Assessment of Gradient-Based Similarity Functions in the Stable Boundary Layer Derived from a Large-Eddy Simulation

Most of our knowledge on forest-edge flows comes from numerical and wind-tunnel experiments where canopies are horizontally homogeneous. To investigate the impact of tree-scale heterogeneities (\({>}1\) m) on the edge-flow dynamics, the flow in an inhomogeneous forest edge on Falster island in Denmark is investigated using large-eddy simulation. The three-dimensional forest structure is prescribed in the model using high resolution helicopter-based lidar scans. After evaluating the simulation against wind measurements upwind and downwind of the forest leading edge, the flow dynamics are compared between the scanned forest and an equivalent homogeneous forest. The simulations reveal that forest inhomogeneities facilitate flow penetration into the canopy from the edge, inducing important dispersive fluxes in the edge region as a consequence of the flow spatial variability. Further downstream from the edge, the forest inhomogeneities accentuate the canopy-top turbulence and the skewness of the wind-velocity components while the momentum flux remains unchanged. This leads to a lower efficiency in the turbulent transport of momentum within the canopy. Dispersive fluxes are only significant in the upper canopy. Above the canopy, the mean flow is less affected by the forest inhomogeneities. The inhomogeneities induce an increase in the mean wind speed that was found to be equivalent to a decrease in the aerodynamic height of the canopy. Overall, these results highlight the importance of forest inhomogeneities when looking at canopy–atmosphere exchanges in forest-edge regions.     

On the coupling of canopy flow to ambient flow for a variety of vegetation types and densities

A canopy flow coupling parameter is defined from earlier canopy flow research to describe the degree of coupling of air flow in vegetation to ambient flow of the surface boundary layer. This ratio concept employs an exponential wind-height relationship in the canopy referenced to the logarithmic wind-height relationship of the ambient air in close proximity to the vegetation interface. Qualitatively, the coupling ratio decreases as the index of canopy flow increases. Numerical criteria are derived to quantify the coupling upwind of the canopy, at the leading edge, through the transition zone, through the zone of established flow, at the trailing edge, and downwind from the canopy domain. It was found that coupling was relatively independent of element density for the more dense arrays, but increased rapidly as densities became more sparsely arrayed. A high degree of coupling existed both upwind and downwind of well-defined domains, while a degeneration of coupling is clearly evident through the zone of established flow. A seasonal contrast in coupling was also discerned. Gravity and slope flows contributed to a higher degree of coupling.     

Heat Flux in the Coastal Zone

Various difficulties with application of Monin–Obukhov similarity theory are surveyed including the influence of growing waves, advection and internal boundary-layer development. These complications are normally important with offshore flow. The transfer coefficient for heat is computed from eddy correlation data taken at a mast two kilometres off the Danish coast in RASEX. For these coastal zone data, the thermal roughness length shows no well-defined relation to the momentum roughness length or roughness Reynolds number, in contrast to previous theories. The variation of the momentum roughness length is dominated by wave state. In contrast, the thermal roughness length shows significant dependence on wave state only for small values of wave age where the mixing is apparently enhanced by wave breaking. The development of thin internal boundary layers with offshore flow substantially reduces the heat transfer and thermal roughness length but has no obvious influence on momentum roughness length. A new formulation of the thermal roughness length based on the internal boundary-layer depth is calibrated to the RASEX data. For the very stable case, the turbulence is mainly detached from the surface and existing formulations do not apply.As an alternative to adjusting the thermal roughness length, the transfer coefficient is related directly to the stability and the internal boundary-layer depth. This avoids specification of roughness lengths resulting from the usual integration of the non-dimensional temperature function. The resulting stability function is simpler than previous ones and satisfies free convection similarity theory without introduction of the gustiness factor. The internal boundary layer also influences the moisture transfer coefficient.     

The effect of ekman suction on a flow over a shallow topography in the beta plane

The effect of bottom Ekman layer suction on a homogeneous, constant depth, eastwards, low Rossby number flow over a shallow bottom topography in the beta plane is studied. The governing vorticity equation is obtained by expanding the velocities in the continuity and momentum equations in powers of the Rossby number, ?, and matching the vertical velocity with the vertical velocity at the outer edge of the bottom Ekman layer obtained from the Ekman layer solution. The suction effect is then linearized using an Oseen approxiamation and the resulting linear model is solved using Fourier transforms with the requirement that the solution behave like a vortex near the origin which is equivalent to the effect of an isolated bump, i.e., a Green's function solution is obtained. An analytical solution is thus, obtained in integral form and then numerically integrated. The effect of Ekman suction is found to be a damping of the downstream Rossby waves in a distance of order $\text{2√2U/f}{}_0\text{E}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, an increased upstream influence, and a counterclockwise rotation of the closed streamline region about the origin. It is pointed out that the vortex solutions can be superimposed in order to obtain the solution for flow over topographies of finite horizontal text. This technique was used to compute the flow over a right circular cylinder. The results agree favorably with the experimental results of McCartney (1975).     

Model experiments on free-convection heat and mass transfer of leaves and plant elements

Effects of orientation, shape, and surface structure on the free convection mass transfer of plates, leaf- and plant-models were studied in an electrolytic system. The results were extrapolated to the transfer of heat and mass in air, in an effort to predict realistic boundary-layer transfer coefficients for leaves and plant-like surfaces. Flow visualization complemented the investigation.The results indicate that increases in transfer of 50% over that of a vertical plate are possible for non-vertical rough leaves, but that a 25% increase is a more reasonable estimate for an average plant. Evidence is also presented that more reliable caluclations of the transfer properties of pine needles are obtained if the needles are approximated by vertical cylinders, rather than by horizontal ones.     

Aerodynamic boundary-layer adjustment over a crop in neutral stability

An experimental study of the modification of the neutral wind profile as air flows to a rougher surface is presented. The analysis is based on wind profiles measured at four locations extending about 100 m downwind from the leading edge of a mature wheat crop. The form of the modified wind profile, and the rate of internal boundary-layer growth are analyzed in terms of a non-dimensional wind velocity. Friction velocities, based on wind-profile computations, are also examined at different points in the flow field. Boundary-layer growth was more rapid than expected, but could be approximated by a 4/5th power of the fetch if a roughness factor is included. It is suggested that simple height:fetch ratios, such as 1:100 be avoided, especially where large roughness-length changes are involved.     

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     

Observations of longitudinal roll vortices during arctic cold air outbreaks over open water

An evolving convective Arctic planetary boundary layer (PBL) containing longitudinal roll vortices (rolls) was observed with aircraft data during the 1983 Marginal Ice Zone Experiment and the 1984 Arctic Cyclone Experiment.The PBL is observed to grow rapidly as the very cold and dry air flows off the ice over the relatively warm water. There is very large sensible heat flux, a result of the large surface-air temperature differences. Coherent structures were identified in these PBL's by use of power, coherence squared and phase spectra of the data. A systematic method of separating the rolls from organized thermal plumes was devised, based on theoretical characteristics for roll circulations and the resulting modified mean wind profile. The rapid mixing by the rolls aids in the establishment of equilibrium and an observed adiabatic modified mean Ekman layer. Rolls that form in a thermally neutral atmosphere over ice have different characteristics than those that appear in the unstable stratification over water. The rolls become increasingly more convective in character with distance from the ice edge. They have aspect ratios (wavelength/PBL height) that decrease with distance from the ice edge in agreement with linear theory. This is in contrast to the cloud street wavelength to inversion height ratio which is observed to increase downwind from the ice edge.     

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

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

北京上甸子秋冬季大气气溶胶的散射特征

分析了北京上甸子秋冬季气溶胶散射系数的变化特征、散射系数与PM2.5质量浓度的关系, 结合气象资料分析了风场对气溶胶散射系数变化的影响。通过研究得出, 上甸子秋冬季气溶胶散射系数平均值和标准差分别为179.7 Mm-1和253.2 Mm-1；阴天条件下的散射系数明显高于晴天；散射系数与PM2.5质量浓度之间有较好的相关性, 其相关系数为0.93；此外, 由于上甸子特殊的地理位置, 风场对气溶胶散射系数的影响显著, 不同风向条件下气溶胶散射系数差别很大。     

The translation of turbulent wind energy to individual corn plant motion during senescense

Wind flow within inflexible plant canopies is turbulent and leads to an oscillatory motion of individual plants. A study was conducted to describe the motion of corn (Zea mays L.) stalks in the wind using a transfer function in the frequency domain to gain insight into the transfer of energy between the turbulent wind and the corn plant. Plant motion was measured and the wind moment was estimated on 23 plants during six windy days in October 1988, at West Lafayette, IN. Plant motion was theoretically described by a rigid rod. The results showed that lower stalk motion was generally well described by a second-order response model defined by a damping coefficient, natural frequency, and rotary stiffness.Published as Paper Number 12,541 of the Purdue University Agricultural Experiment Station.     

Heat transfer coefficients for leaves on orchard apple trees

The coefficient for heat transfer from apple tree leaves was measured from the energy balance of leaves which were prevented from transpiring by applying Vaseline (petroleum jelly). Vaseline had negligible effect on the absorption of short-wave radiation by the leaves. The Nusselt number (Nu) describing heat flux from a leaf in terms of its average temperature was related to Reynolds numbers (Re) in the range 10³ to 10⁴ by Nu = 0.46 Re^0.54 Pr^0.33, where Pr is the Prandtl number. This supports Landsberg and Powell's (1973) wind-tunnel results for transfer from leaves subject to mutual interference.     

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.     

Analysis of canopy index values for various canopy densities

Canopy wind profiles can often be represented by an exponential function such that wind-speeds in these vegetative canopies are a function of height and the attenuation coefficient of this wind profile relationship. To be more precise, canopy flow is a function of canopy density, element flexibility, and height. An index of canopy flow, therefore, can be defined as a conservative measure of the gross flow response to the presence of various types of roughness elements. For this study, windspeed profile data of two quite different canopy density experiments — field and wind tunnel - have been analyzed based on least-square fittings. The results indicate that the two sets of index values of canopy flow behave in a similar manner with maxima occurring for optimum densities of one-third the potential full array of roughness elements. These index values also differ by some 0.2, but are still compatible when one accounts for the respective levels of turbulence within these dissimilar canopies.