Scalar Concentration Profiles Research Articles

A random field approach to the Lagrangian modeling of turbulent transport in vegetated canopies

We present an application of a Lagrangian Stochastic Model (LSM) to turbulent dispersion over complex terrain, where turbulent coherent structures are known to play a crucial role. We investigate the case of a vegetated canopy by using semi-empirical parameterizations of turbulence profiles in the region inside and above a canopy layer. The LSM is based on a 4-dimensional Fokker-Planck (4DFP) equation, which extends the standard Thomson87 Lagrangian approach. The 4DFP model is derived by means of a Random Field description of the turbulent velocity field. The main advantage of this approach is that not only the experimental Eulerian one-point statistics, but also the Eulerian two-point two-time covariance structure can be included explicitly in the LSM. At variance with the standard Thomson87 approach, the 4DFP model allows to consider explicit parameterizations of the turbulent coherent structures as it explicitly includes both spatial and temporal correlation functions. In order to investigate the effect of the turbulent geometrical structure on a scalar concentration profile, we performed numerical simulations with two different covariance parameterizations, the first one isotropic and the second anisotropic. We show that the accumulation of scalars near the ground is due to the anisotropic geometrical properties of the turbulent boundary layer.

Publisher's Note: Mean scalar concentration profile in a sheared and thermally stratified atmospheric surface layer [Phys. Rev. E87, 023004 (2013)

Publisher's Note: Mean scalar concentration profile in a sheared and thermally stratified atmospheric surface layer [Phys. Rev. E<b>87</b>, 023004 (2013)

Mean scalar concentration profile in a sheared and thermally stratified atmospheric surface layer

Using only dimensional considerations, Monin and Obukhov proposed a "universal" stability correction function φ(c)(ζ) that accounts for distortions caused by thermal stratification to the mean scalar concentration profile in the atmospheric surface layer when the flow is stationary, planar homogeneous, fully turbulent, and lacking any subsidence. For nearly 6 decades, their analysis provided the basic framework for almost all operational models and data interpretation in the lower atmosphere. However, the canonical shape of φ(c)(ζ) and the departure from the Reynold's analogy continue to defy theoretical explanation. Here, the basic processes governing the scalar-velocity cospectrum, including buoyancy and the scaling laws describing the velocity and temperature spectra, are considered via a simplified cospectral budget. The solution to this cospectral budget is then used to derive φ(c)(ζ), thereby establishing a link between the energetics of turbulent velocity and scalar concentration fluctuations and the bulk flow describing the mean scalar concentration profile. The resulting theory explains all the canonical features of φ(c)(ζ), including the onset of power laws for various stability regimes and their concomitant exponents, as well as the causes of departure from Reynold's analogy.

The Effect of the Vertical Source Distribution on Scalar Statistics within and above a Forest Canopy

Little is known about in-canopy processes that may alter forest–atmosphere exchanges of trace gases and aerosols. To improve our understanding of in-canopy mixing, we use large-eddy simulation to study the effect of scalar source/sink distributions on scalar concentration moments, fluxes, and correlation coefficients within and above an ideal forest canopy. Scalars are emitted from: (1) the ground, (2) the canopy, and (3) both the ground and the canopy; a scalar is also deposited onto the canopy. All scalar concentration moments, fluxes, and correlation coefficients are affected by the source location/distribution, as is the scalar segregation intensity. We conclude that vertical source/sink distribution has a profound impact on scalar concentration profiles, fluxes, correlation coefficient, and scalar segregation.

Scalar Transport over Forested Hills

Numerical simulations of scalar transport in neutral flow over forested ridges are performed using both a 1.5-order mixing-length closure scheme and a large-eddy simulation. Such scalar transport (particularly of CO2) has been a significant motivation for dynamical studies of forest canopy–atmosphere interactions. Results from the 1.5-order mixing-length simulations show that hills for which there is significant mean flow into and out of the canopy are more efficient at transporting scalars from the canopy to the boundary layer above. For the case with a source in the canopy this leads to lower mean concentrations of tracer within the canopy, although they can be very large horizontal variations over the hill. These variations are closed linked to flow separation and recirculation in the canopy and can lead to maximum concentrations near the separation point that exceed those over flat ground. Simple scaling arguments building on the analytical model of Finnigan and Belcher (Q J Roy Meteorol Soc 130:1–29, 2004) successfully predict the variations in scalar concentration near the canopy top over a range of hills. Interestingly this analysis suggests that variations in the components of the turbulent transport term, rather than advection, give rise to the leading order variations in scalar concentration. The scaling arguments provide a quantitative measure of the role of advection, and suggest that for smaller/steeper hills and deeper/sparser canopies advection will be more important. This agrees well with results from the numerical simulations. A large-eddy simulation is used to support the results from the mixing-length closure model and to allow more detailed investigation of the turbulent transport of scalars within and above the canopy. Scalar concentration profiles are very similar in both models, despite the fact that there are significant differences in the turbulent transport, highlighted by the strong variations in the turbulent Schmidt number both in the vertical and across the hill in the large-eddy simulation that are not represented in the mixing-length model.

Scalar Concentration Profiles in the Canopy and Roughness Sublayer

The mean flow and scalar concentration profiles within and above a tall canopy are well known to violate the standard boundary-layer flux-gradient relationships. We present a theory for the scalar concentration profile that is comprised of a canopy exchange model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing-layer analogy for the flow at canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the profiles depend and a set of criteria that allows a reduction in the empiricism associated with earlier forms in the literature. Predictions of the mean scalar concentration profiles are shown to match observations over a wide range of diabatic stabilities for both potential temperature and water vapour.

Mixing analysis of a swirling recirculating flow using DNS and experimental data

Fluid flow and mixing of a recirculating, swirling flow at moderate Reynolds number was investigated by direct numerical simulation (DNS) as well as experimentally using laser Doppler velocimetry (LDV) and spontaneous Raman scattering. Using these techniques together allows for a cross validation of the data. Furthermore, each technique can compensate for the restrictions of the other making the full data set more complete. Detailed one and two point statistics for velocity and scalar concentration are presented and discussed. The high swirl momentum leads to a fluid mechanical instability, a so-called precessing vortex core (PVC), which will be characterized especially with respect to its interaction with the scalar field. The results show that due to the reverse flow zone the PVC strongly modifies the mixing process leading to a precessing scalar concentration field. However, the level of the mean square deviation for the scalar field is considerably smaller than the corresponding value for the velocity field due to the different nature of the radial mean velocity and scalar concentration profiles in the near nozzle region.

Estimating Co2 Source/Sink Distributions Within A Rice Canopy Using Higher-Order Closure Model

Source/sink strengths and vertical flux distributions of carbon dioxide within and above a rice canopy were modelled using measured mean concentration profiles collected during an interna- tional rice experiment in Okayama, Japan (IREX96). The model utilizes an Eulerian higher-order closure approach that permits coupling of scalar and momentum transport within vegetation to infer sources and sinks from mean scalar concentration profiles; the so-called 'inverse problem'. To compute the required velocity statistics, a Eulerian second-order closure model was considered. The model well reproduced measured first and second moment velocity statistics inside the canopy. Using these modelled velocity statistics, scalar fluxes within and above the canopy were computed and compared with CO2 eddy-correlation measurements above the canopy. Good agreement was obtained between model calculations of fluxes at the top of the canopy and measurements. Close to the ground, the model predicted higher respiratory fluxes when the paddy was drained compared to when it was flooded. This is consistent with the floodwater providing a barrier to diffusion of CO2 from the soil to the atmosphere. The Eulerian sources and flux calculations were also compared to source and flux distributions estimated independently using a Lagrangian Localized Near Field theory, the first study to make such a comparison. Some differences in source distributions were predicted by these analyses. Despite this, the calculated fluxes by the two approaches compared well provided a closure constant, accounting for the influence of 'near-field' sources in the Eulerian flux transport term, was given a value of 1.5 instead of the value of 8 found in laboratory studies.

Scaling Isoprene Fluxes from Leaves to Canopies: Test Cases over a Boreal Aspen and a Mixed Species Temperate Forest

The rate at which isoprene is emitted by a forest depends on an array of environmental variables, the forest’s biomass, and its species composition. At present it is unclear whether errors in canopy-scale and process-level isoprene emission models are due to inadequacies in leaf-to-canopy integration theory or the imperfect assessment of the isoprene-emitting biomass in the flux footprint. To address this issue, an isoprene emission model (CANVEG) was tested over a uniform aspen stand and a mixed-species, broad-leaved forest. The isoprene emission model consists of coupled micrometeorological and physiological modules. The micrometeorological module computes leaf and soil energy exchange, turbulent diffusion, scalar concentration profiles, and radiative transfer through the canopy. Environmental variables that are computed by the micrometeorological module, in turn, drive physiological modules that calculate leaf photosynthesis, stomatal conductance, transpiration and leaf, bole and soil/root respiration, and rates of isoprene emission. The isoprene emission model accurately predicted the diurnal variation of isoprene emission rates over the boreal aspen stand, as compared with micrometeorological flux measurements. The model’s ability to simulate isoprene emission rates over the mixed temperate forest, on the other hand, depended strongly upon the amount of isoprene-emitting biomass, which, in a mixed-species forest, is a function of the wind direction and the horizontal dimensions of the flux footprint. When information on the spatial distribution of biomass and the flux footprint probability distribution function were included, the CANVEG model produced values of isoprene emission that compared well with micrometeorological measurements. The authors conclude that a mass and energy exchange model, which couples flows of carbon, water, and nutrients, can be a reliable tool for integrating leaf-scale, isoprene emission algorithms to the canopy dimension over dissimilar vegetation types as long as the vegetation is characterized appropriately.

A ‘Lagrangian’ revision of the resistors in the two-layer model for calculating the energy budget of a plant canopy

This paper completes the construction of a two-layer model for the energy balance of sparse canopies begun by Van den Hurk and McNaughton (1994). The model is based on the Lagrangian theory of Raupach (1989). In the earlier work, we showed that the average effect of the near-field component of the scalar concentration profile can be represented by a ‘near-field’ resistor. Here we calculate values for the upper and lower ‘far-field’ resistors using Raupach's expression for the far-field diffusivity and his empirical descriptions of the profiles of vertical velocity variance and Lagrangian integral time scale (Raupach, 1988). The boundary-layer resistance for the foliage of the overstorey canopy is also reassessed. Calculations are carried out for a range of possible canopies. Representative values are chosen for use where a detailed description of the vegetation is unavailable. The resistors of the new model are compared with those of earlier two-layer models. The new ‘far-field’ resistors are smaller than the corresponding ‘aerodynamic’ resistors of the earlier models of Shuttleworth and Wallace (1985) and Choudhury and Monteith (1988) while the new boundary-layer resistor can be somewhat larger, depending on the choices made in the calculation. We could not find experimental data on canopy energy balances suitable for deciding which model is best. Instead, we have attempted to verify the model using measurements of surface temperature and calculated values of the ‘excess’ resistance, but the results are not definitive. A major conclusion is that turbulent transport near the ground beneath an overstorey canopy is poorly known and therefore is poorly represented in all models. Another conclusion is that current models for the excess resistance are inadequate.

A lagrangian random-walk model for simulating water vapor, CO2 and sensible heat flux densities and scalar profiles over and within a soybean canopy

An integrated canopy micrometeorological model is described for calculating CO2, water vapor and sensible heat exchange rates and scalar concentration profiles over and within a crop canopy. The integrated model employs a Lagrangian random walk algorithm to calculate turbulent diffusion. The integrated model extends previous Lagrangian modelling efforts by employing biochemical, physiological and micrometeorological principles to evaluate vegetative sources and sinks. Model simulations of water vapor, CO2 and sensible heat flux densities are tested against measurements made over a soybean canopy, while calculations of scalar profiles are tested against measurements made above and within the canopy. The model simulates energy and mass fluxes and scalar profiles above the canopy successfully. On the other hand, model calculations of scalar profiles inside the canopy do not match measurements.

Mixing at large Schmidt number in the self-similar far field of turbulent jets

We present results from an experimental investigation of turbulent transport and molecular mixing of a Sc [Gt ] 1 conserved scalar in the fully developed self-similar far field of a steady, axisymmetric, momentum-driven, free turbulent jet issuing into a quiescent medium. Our experiments cover the axial range from the jet exit to 350 diameters downstream, and span the range of Reynolds numbers from 1500 to 20000. Flow visualizations of the scalar concentration field directly verify the presence of an underlying characteristic large-scale organization in the jet far field essentially consistent with a simplified conceptual picture proposed in an earlier study (Dahm &amp; Dimotakis 1987). High-resolution imaging measurements of successive instantaneous scalar concentration profiles in the jet support the presence of such a large-scale organization and provide details of its implications for mixing. These results also establish the proper similarity scaling for the mean concentration in the jet far field and give the scaling constant on the jet centreline as 5.4. We also present conserved scalar concentration p.d.f.s throughout the jet far field, and introduce a chemical reaction method for measuring the p.d.f.s with potentially molecular resolution. The amount of unmixed ambient fluid that reaches the jet centreline is found to decrease with increasing Reynolds number over the range investigated. The distribution of mixed fluid compositions in the concentration p.d.f. also appears to change over this range of Reynolds numbers, indicating that some aspects of large Schmidt number mixing in the jet far field have not yet become Reynolds number independent.

Applying Lagrangian fluid mechanics to infer scalar source distributions from concentration profiles in plant canopies

It is well known that gradient-diffusion theory does not describe the transfer of scalar entities (such as heat, water vapour, CO 2 and pollutant gases) through the air in and just above plant canopies. An effective replacement is offered by an analytic Lagrangian method for calculating the concentration field of a scalar emanating from a steady spatially extensive source in an inhomogeneous flow. The method can be labelled “localized near-field” or LNF theory. This paper first summarizes the assumptions and results of the LNF theory, leading to a simple solution for the “forward problem” of predicting the mean scalar concentration profile C( z) maintained by a given source density profile S( z). It is then shown how the theory can be applied to solve the “inverse problem” of inferring S( z) from measurements of C( z).

Stand overstorey processes

Typical turbulent eddies in a plant canopy are coherent over much of the canopy depth, making gradient-diffusion theory inappropriate for describing the vertical transfer of scalars and momentum. A better description of scalar transfer is obtained by regarding the canopy as an assembly of source elements (individual leaves), each releasing a plume of scalar material into the turbulent flow. The contrasting behaviours of the plume from each leaf in the near and far fields (or small and large travel times, in comparison with the turbulence time scale) account naturally for observed phenomena such as counter-gradient fluxes within the canopy. With two hypotheses, this paradigm yields a simple, analytic expression for the scalar concentration profile corresponding to a given source density in the canopy, effectively replacing gradient-diffusion theory.