A Numerical Study for Turbulent Flow and Thermal Influence over Inhomogenous Canopy of Roughness Elements

A large-eddy simulation with transitional structure function(TSF) subgrid model we previously proposed was performed to investigate the turbulent flow with thermal influence over an inhomogeneous canopy, which was represented as alternative large and small roughness elements. The aerodynamic and thermodynamic effects of the presence of a layer of large roughness elements were modelled by adding a drag term to the three-dimensional Navier–Stokes equations and a heat source/sink term to the scalar equation, respectively. The layer of small roughness elements was simply treated using the method as described in paper (Moeng 1984, J. Atmos Sci. 41, 2052–2062) for homogeneous rough surface. The horizontally averaged statistics such as mean vertical profiles of wind velocity, air temperature, et al., are in reasonable agreement with Gao et al.(1989, Boundary layer meteorol. 47, 349–377) field observation (homogeneous canopy). Not surprisingly, the calculated instantaneous velocity and temperature fields show that the roughness elements considerably changed the turbulent structure within the canopy. The adjustment of the mean vertical profiles of velocity and temperature was studied, which was found qualitatively comparable with Belcher et al. (2003, J Fluid Mech. 488, 369–398)’s theoretical results. The urban heat island(UHI) was investigated imposing heat source in the region of large roughness elements. An elevated inversion layer, a phenomenon often observed in the urban area (Sang et al., J Wind Eng. Ind. Aesodyn. 87, 243–258)’s was successfully simulated above the canopy. The cool island(CI) was also investigated imposing heat sink to simply model the evaporation of plant canopy. An inversion layer was found very stable and robust within the canopy.     

Modeling the vegetation-atmosphere carbon dioxide and water vapor interactions along a controlled CO2 gradient

Ecosystem functioning is intimately linked to its physical environment by complex two-way interactions. These two-way interactions arise because vegetation both responds to the external environment and actively regulates its micro-environment. By altering stomatal aperture, and therefore the transpiration rate, plants modify soil moisture and atmospheric humidity and these same physical variables, in return, modify stomatal conductance. Relationships between biotic and abiotic components are particularly strong in closed, managed environments such as greenhouses and growth chambers, which are used extensively to investigate ecosystem responses to climatic drivers. Model-assisted designs that account for the physiological dynamics governing two-way interactions between biotic and abiotic components are absent from many ecological studies. Here, a general model of the vegetation-atmosphere system in closed environments is proposed. The model accounts for the linked carbon-water physiology, the turbulent transport processes, and the energy and radiative transfer within the vegetation. Leaf gas exchange is modeled using a carbon gain optimization approach that is coupled to leaf energy balance. The turbulent transport within the canopy is modeled in two-dimensions using first-order closure principles. The model is applied to the Lysimeter CO₂ Gradient (LYCOG) facility, wherein a continuous gradient of atmospheric CO₂ is maintained on grassland assemblages using an elongated chamber where the micro-climate is regulated by variation in air flow rates. The model is employed to investigate how species composition, climatic conditions, and the imposed air flow rate affect the CO₂ concentration gradient within the LYCOG and the canopy micro-climate. The sensitivity of the model to key physiological and climatic parameters allows it to be used not only to manage current experiments, but also to formulate novel ecological hypotheses (e.g., by modeling climatic regimes not currently employed in LYCOG) and suggest alternative experimental designs and operational strategies for such facilities.     

Interaction between flow, transport and vegetation spatial structure

This paper summarizes recent advances in vegetation hydrodynamics and uses the new concepts to explore not only how vegetation impacts flow and transport, but also how flow feedbacks can influence vegetation spatial structure. Sparse and dense submerged canopies are defined based on the relative contribution of turbulent stress and canopy drag to the momentum balance. In sparse canopies turbulent stress remains elevated within the canopy and suspended sediment concentration is comparable to that in unvegetated regions. In dense canopies turbulent stress is reduced by canopy drag and suspended sediment concentration is also reduced. Further, for dense canopies, the length-scale of turbulence penetration into the canopy, δ _e , is shown to predict both the roughness height and the displacement height of the overflow profile. In a second case study, the relation between flow speed and spatial structure of a seagrass meadow gives insight into the stability of different spatial structures, defined by the area fraction covered by vegetation. In the last case study, a momentum balance suggests that in natural channels the total resistance is set predominantly by the area fraction occupied by vegetation, called the blockage factor, with little direct dependence on the specific canopy morphology.     

Particle laden flows through an inverted chimney with applications to ocean carbon sequestration

Plumes of negatively buoyant hydrate particles, formed by reacting liquid CO₂ with seawater at ocean depths of 1000–1500 m, have been suggested as a way to help sequester CO₂. The vertical flux of CO₂ can be increased by constructing a shroud around the hydrate particle source to shelter the plume from effects of ambient stratification and current. The shroud also serves as an inverted chimney, inducing a down draft that will transport the dissolving particles to a depth of lower ambient disturbance. Laboratory PIV measurements are compared to an analysis of an idealized shroud that is long, frictionless and driven by a single phase source of buoyancy distributed uniformly over the shroud base. Results indicate that induced draft, and hence dilution of dissolved CO₂, increases with plume buoyancy, and shroud length and diameter, but efficiency decreases with increasing ratio of particle slip velocity divided by the characteristic induced draft velocity. While larger particles show reduced plume-like behavior and hence are less efficient in inducing draft, they still generated about half of the theoretically predicted flow.     

PIXGRO: A model for simulating the ecosystem CO2 exchange and growth of spring barley

A model, PIXGRO, developed by coupling a canopy flux sub-model (PROXEL_NEE; PROcess-based piXEL Net Ecosystem CO₂ Exchange) to a vegetation structure submodel (CGRO), for simulating both net ecosystem CO₂ exchange (NEE) and growth of spring barley is described. PIXGRO is an extension of the stand-level CO₂ and H₂O-flux model PROXEL_NEE, that simulates the NEE on a process basis, but goes further to include the dry matter production, partitioning, and crop development for spring barley. Dry matter partitioned to the leaf was converted to leaf area index (LAI) using relationships for the specific leaf area (SLA). The canopy flux component, PROXEL_NEE was calibrated using information from the literature on C3 plants and was tested using CO₂ flux data from an eddy-covariance (EC) method in Finland with long-term observations. The growth component (CGRO) was calibrated using data from the literature on spring barley as well as data from the Finland site. It was then validated against field data from two sites in Germany and partly via the use of MODIS remotely sensed LAI from the Finland site.Both the diurnal and the seasonal patterns of gross CO₂ uptake were very well simulated (R² = 0.92). A slight seasonal bias may be attributed to leaf ageing. Crop growth was also well simulated; simulated dry matter agreed with field observed data from Germany (R² = 0.90). For LAI, the agreement between the simulated and observed was good (R² = 0.80), giving an indication that functions describing the conversion of fixed CO₂ to dry matter and the subsequent partitioning leaf dry matter and LAI simulation were robust and provided reliable estimates.The MODIS LAI at a resolution of 1000 m agreed poorly (R² = 0.45) with the PIXGRO simulated LAI and the observed LAI at the Finland site in 2001. We attributed this to the coarse resolution of the image and/or the small size of the barley field (about 17 ha or 0.25 km²) at the Finland site. By deriving a regression relation between the observed LAI and NDVI from a higher resolution MODIS (500 m resolution), the MODIS-recalculated LAI agreed better with the PIXGRO-simulated LAI (R² = 0.86).PIXGRO provides a prototype model bridging the disciplines of plant physiology, crop modeling and remote sensing, for use in a spatial context in evaluating carbon balances and plant growth at stand level, landscape, regional, and with some care, continental scales. Since almost 50% of the European land surface is covered by crops, such a model is needed for the dynamic estimation of LAI and NEE of croplands.     

CO2 fluxes near a forest edge: a numerical study

In contrast with recent advances on the dynamics of the flow at a forest edge, few studies have considered its role on scalar transport and, in particular, on CO2 transfer. The present study addresses the influence of the abrupt roughness change on forest atmosphere CO2 exchange and contrasts the concentration and flux fields against those of a uniform forested surface. We use an atmospheric boundary layer two-equation closure model that accounts for the flow dynamics and vertical divergence of CO2 sources/sinks within a plant canopy. This paper characterizes the spatial variation of CO2 fluxes as a function of both sources/sinks distribution and the vertical structure of the canopy. Results suggest that the ground source plays a major role in the formation of wave-like vertical CO2 flux behavior downwind of a forest edge, despite the fact that the contribution of foliage sources/sinks changes monotonously. Such a variation is caused by scalar advection in the trunk space and reveals itself as a decrease or increase in vertical fluxes over the forest relative to carbon dioxide exchange of the underlying forest. The effect was more pronounced in model forests where the leaf area is concentrated in the upper part of the canopy. These results can be useful both for interpretation of existing measurements of net ecosystem exchange of CO2 (NEE) from flux towers in limited fetch conditions and in planning future CO2 transport experiments.     

Large eddy simulation of flow and scalar transport in a vegetated channel

Predicting flow and mass transport in vegetated regions has a broad range of applications in ecology and engineering practice. This paper presents large eddy simulation (LES) of turbulent flow and scalar transport within a fully developed open-channel with submerged vegetation. To properly represent the scalar transport, an additional diffusivity was introduced within the canopy to account for the contribution of stem wakes, which were not resolved by the LES, to turbulent diffusion. The LES produced good agreement with the velocity and concentration fields measured in a flume experiment. The simulation revealed a secondary flow distributed symmetrically about the channel centerline, which differed significantly from the circulation in a bare channel. The secondary circulation accelerated the vertical spread of the plume both within and above the canopy layer. Quadrant analysis was used to identify the form and shape of canopy-scale turbulent structures within and above the vegetation canopy. Within the canopy, sweep events contributed more to momentum transfer than ejection events, whereas the opposite occurred above the canopy. The coherent structures were similar to those observed in terrestrial canopies, but smaller in scale due to the constraint of the water surface.     

Instantaneous transport of a passive scalar in a turbulent separated flow

The results of large-eddy simulations of flow and transient solute transport over a backward facing step and through a 180° bend are presented. The simulations are validated successfully in terms of hydrodynamics and tracer transport with experimental velocity data and measured residence time distribution curves confirming the accuracy of the method. The hydrodynamics are characterised by flow separation and subsequent recirculation in vertical and horizontal directions and the solute dispersion process is a direct response to the significant unsteadiness and turbulence in the flow. The turbulence in the system is analysed and quantified in terms of power density spectra and covariance of velocity fluctuations. The injection of an instantaneous passive tracer and its dispersion through the system is simulated. Large-eddy simulations enable the resolution of the instantaneous flow field and it is demonstrated that the instabilities of intermittent large-scale structures play a distinguished role in the solute transport. The advection and diffusion of the scalar is governed by the severe unsteadiness of the flow and this is visualised and quantified. The analysis of the scalar mass transport budget quantifies the mechanisms controlling the turbulent mixing and reveals that the mass flux is dominated by advection.     

Evaluation of numerical simulations of CO2 transport in a city block with field measurements

Studying urban air-transport phenomena is highly complex, because of the heterogenous flow patterns that can arise. The main reason for these is the variable topology of urban areas, however, there is a large number of influencing variables such as meteorological conditions (e.g., wind situation, temperature) and anthropogenic factors such as traffic emissions. During a one-year CO₂ measurement campaign in the city of Basel, Switzerland, steep CO₂ gradients were measured around a large building. The concentration differences showed a strong dependency on the local flow regimes. Analysis of the field data alone did not provide a complete explanation for the mechanisms underlying the observed phenomena. The key numerical parameters were defined and the influence of turbulent kinetic energy dependency on the time interval for the Reynolds decomposition was studied. A Reynolds-Average Navier-Stokes Computational Fluid Dynamics (CFD) approach was applied in the study area and the CO₂ concentrations were simulated for six significant meteorological situations and compared to the measured data. Two flow regimes dependent on the wind situation, which either enhanced or suppressed the concentration of CO₂ in the street canyon, were identified. The enhancement of CO₂ in the street canyon led to a large difference in CO₂ concentration between the backyard- and street-sides of a building forming the one wall of the canyon. The specific characteristics of the flow patterns led to the identification of the processes determining the observed differences in CO₂ concentrations. The combined analysis of measurement and modeling showed the importance of reliable field measurements and CFD simulations with a high spatial resolution to assess transport mechanisms in urban areas.     

The three-dimensionality of obstructed shear flows

Obstructed shear flows (i.e. those over permeable media) are common in the environment. An archetypal example, flow over a submerged vegetation canopy, is investigated here. Like any flow through complex geometry, canopy flows are characterised by strong spatial gradients. The focus of this experimental study is the three-dimensionality of aquatic canopy flow, in particular that of the coherent interfacial vortices that govern mixing into and out of the canopy. It is shown here that the vortices have a finite lateral scale that is comparable to their vertical scale; both are of the order of the drag length scale of the canopy, (C _D a)⁻¹, where a is the frontal area density and C _D is a bulk drag coefficient. The finite lateral extent of the vortices generates strong lateral hydrodynamic gradients, both instantaneously and in the long-term. The instantaneous gradients, which can contribute greatly to the dispersion of dissolved and particulate species, are far more pronounced. Finally, the potential for canopies to generate differential roughness secondary circulation is examined. In the consideration of vertical scalar transport, this circulation can be of the same order as turbulent diffusion.     

A σ-coordinate transport model coupled with rotational boussinesq-type equations

This paper describes a σ-coordinate scalar transport model coupled with a Boussinesq-type hydrodynamic model. The Boussinesq model has the ability to calculate both three-dimensional velocity distributions and the water surface motion. To capture ‘dispersion’ processes in open channel flow, horizontal vorticity effects induced by a bottom shear stress are included in the Boussinesq model. Thus, a reasonable representation of vertical flow structure can be captured in shallow and wavy flow fields. To solve the coupled Boussinesq and scalar transport system, a finite-volume method, based on a Godunov-type scheme with the HLL Riemann solver, is employed. Basic advection and advection–diffusion numerical tests in a non-rectangular domain were carried out and the computed results show good agreement with analytic solutions. With quantitative comparisons of dispersion experiments in an open channel, it is verified that the proposed coupled model is appropriate for both near and far field scalar transport predictions. From numerical simulations in the surf zone, physically reasonable results showing expected vertical variation are obtained.     

Does the canopy mixing layer model apply to highly flexible aquatic vegetation? Insights from numerical modelling

Vegetation is a characteristic feature of shallow aquatic flows such as rivers, lakes and coastal waters. Flow through and above aquatic vegetation canopies is commonly described using a canopy mixing layer analogy which provides a canonical framework for assessing key hydraulic characteristics such as velocity profiles, large-scale coherent turbulent structures and mixing and transport processes for solutes and sediments. This theory is well developed for the case of semi-rigid terrestrial vegetation and has more recently been applied to the case of aquatic vegetation. However, aquatic vegetation often displays key differences in morphology and biomechanics to terrestrial vegetation due to the different environment it inhabits. Here we investigate the effect of plant morphology and biomechanical properties on flow–vegetation interactions through the application of a coupled LES-biomechanical model. We present results from two simulations of aquatic vegetated flows: one assuming a semi-rigid canopy and the other a highly flexible canopy and provide a comparison of the associated flow regimes. Our results show that while both cases display canopy mixing layers, there are also clear differences in the shear layer characteristics and turbulent processes between the two, suggesting that the semi-rigid approximation may not provide a complete representation of flow–vegetation interactions.     

The Structure of the Shear Layer in Flows over Rigid and Flexible Canopies

Flume experiments were conducted with rigid and flexible model vegetation to study the structure of coherent vortices (a manifestation of the Kelvin–Helmholtz instability) and vertical transport in shallow vegetated shear flows. The vortex street in a vegetated shear layer creates a pronounced oscillation in the velocity profile, with the velocity near the top of a model canopy varying by a factor of three during vortex passage. In turn, this velocity oscillation drives the coherent waving of flexible canopies. Relative to flows over rigid vegetation, the oscillation in canopy geometry has the effect of decreasing the amount of turbulent vertical momentum transport in the shear layer. Using a waving plant to determine phase in the vortex cycle, each vortex is shown to consist of a strong sweep at its front (during which the canopy is most deflected), followed by a weak ejection at its rear (when the canopy height is at a maximum). Whereas in unobstructed mixing layers the vortices span the entire layer, they encompass only 70% of the flexibly obstructed shear layer studied here.     

Experimental Study of the Criteria of Flow Laminarization in Two-Dimensional Dense Gas Plumes

Laminarization of flow in a two-dimensional dense gas plume was experimentally investigated in this study. The plume was created by releasing CO₂ through a ground-level line source into a simulated turbulent boundary layer over an aerodynamically rough surface in a meteorological wind tunnel. The bulk Richardson number (Ri_*), based on negative plume buoyancy, plume thickness, and friction velocity, was varied over a wide range so that the effects of stable stratification on plume laminarization could be observed. A variety of ambient wind speeds as well as three different sizes of roughness arrays were used so that possible effects of roughness Reynolds number (Re_*) on plume laminarization could also be identified. Both flow visualization methods and quantitative measurements of velocity and intermittency of turbulence were used to provide quantitative assessments of plume laminarization.Flow visualization provided an overall picture of how the plume was affected by the negative buoyancy. With increasing Ri_*, both the plume depth and the vertical mixing were significantly suppressed, while upstream propagation of the plume from the source was enhanced. The most important feature of the flow revealed by visualization was the laminarization of flow in the lower part of the plume, which appeared to be closely related to both Ri_* and Re_*.Measurements within the simulated dense gas plumes revealed the influence of the stable stratification on mean velocity and turbulence intensity profiles. Both the mean velocity and turbulence intensity were significantly reduced near the surface; and these reductions systematically depended on Ri_*. The roughness Reynolds number also had considerable influence on the mean flow and turbulence structure of the dense gas plumes.An intermittency analysis technique was developed and applied to the digitized instantaneous velocity signals. It not only confirmed the general flow picture within the dense plume indicated by the flow visualization, but also clearly demonstrated the changes of flow regime with variations in Ri_* and Re_*. Most importantly, based on this intermittency analysis, simple criteria for characterizing different flow regimes are formulated; these may be useful in predicting when plume laminarization might occur.     

Turbulent velocity profile in fully-developed open channel flows

The determination of velocity profile in turbulent narrow open channels is a difficult task due to the significant effects of the anisotropic turbulence that involve the Prandtl’s second type of secondary flow occurring in the cross section. With these currents the maximum velocity appears below the free surface that is called dip phenomenon. The well-known logarithmic law describes the velocity distribution in the inner region of the turbulent boundary layer but it is not adapted to define the velocity profile in the outer region of narrow channels. This paper relies on an analysis of the Navier–Stokes equations and yields a new formulation of the vertical velocity profile in the center region of steady, fully developed turbulent flows in open channels. This formulation is able to predict time averaged primary velocity in the outer region of the turbulent boundary layer for both narrow and wide open channels. The proposed law is based on the knowledge of the aspect ratio and involves a parameter C_Ar depending on the position of the maximum velocity (ξ_dip). ξ_dip may be derived, either from measurements or from an empirical equation given in this paper. A wide range of longitudinal velocity profile data for narrow open channels has been used for validating the model. The agreement between the measured and the computed velocities is rather good, despite the simplification used.     

Multiple sources of predictive uncertainty in modeled estimates of net ecosystem CO2 exchange

Net ecosystem CO₂ exchange (NEE) is typically measured directly by eddy covariance towers or is estimated by ecosystem process models, yet comparisons between the data obtained by these two methods can show poor correspondence. There are three potential explanations for this discrepancy. First, estimates of NEE as measured by the eddy-covariance technique are laden with uncertainty and can potentially provide a poor baseline for models to be tested against. Second, there could be fundamental problems in model structure that prevent an accurate simulation of NEE. Third, ecosystem process models are dependent on ecophysiological parameter sets derived from field measurements in which a single parameter for a given species can vary considerably. The latter problem suggests that with such broad variation among multiple inputs, any ecosystem modeling scheme must account for the possibility that many combinations of apparently feasible parameter values might not allow the model to emulate the observed NEE dynamics of a terrestrial ecosystem, as well as the possibility that there may be many parameter sets within a particular model structure that can successfully reproduce the observed data. We examined the extent to which these three issues influence estimates of NEE in a widely used ecosystem process model, Biome-BGC, by adapting the generalized likelihood uncertainty estimation (GLUE) methodology. This procedure involved 400,000 model runs, each with randomly generated parameter values from a uniform distribution based on published parameter ranges, resulting in estimates of NEE that were compared to daily NEE data from young and mature Ponderosa pine stands at Metolius, Oregon. Of the 400,000 simulations run with different parameter sets for each age class (800,000 total), over 99% of the simulations underestimated the magnitude of net ecosystem CO₂ exchange, with only 4.07% and 0.045% of all simulations providing satisfactory simulations of the field data for the young and mature stands, even when uncertainties in eddy-covariance measurements are accounted for. Results indicate fundamental shortcomings in the ability of this model to produce realistic carbon flux data over the course of forest development, and we suspect that much of the mismatch derives from an inability to realistically model ecosystem respiration. However, difficulties in estimating historic climate data are also a cause for model-data mismatch, particularly in a highly ecotonal region such as central Oregon. This latter difficulty may be less prevalent in other ecosystems, but it nonetheless highlights a challenge in trying to develop a dynamic representation of the terrestrial biosphere.     

Stability and Mixing of a Vertical Axisymmetric Buoyant Jet in Shallow Water

The stability, mixing and effect of downstream control on axisymmetric turbulent buoyant jets discharging vertically into shallow stagnant water is studied using 3D Reynolds-averaged Navier–Stokes equations (RANS) combined with a buoyancy-extended k –ε model. The steady axisymmetric turbulent flow, temperature (or tracer concentration) and turbulence fields are computed using the finite volume method on a high resolution grid. The numerical predictions demonstrate two generic flow patterns for different turbulent heated jet discharges and environmental parameters (i) a stable buoyant discharge with the mixed fluid leaving the vertical jet region in a surface warm water layer; and (ii) an unstable buoyant discharge with flow recirculation and re-entrainment of heated water. A stratified counterflow region always appears in the far-field for both stable and unstable buoyant discharges. Provided that the domain radius L exceeds about 6H, the near field interaction and hence discharge stability is governed chiefly by the jet momentum length scale to depth ratio l_M/H, regardless of downstream control. The near field jet stability criterion is determined to be l_M/H = 3.5. A radial internal hydraulic jump always exists beyond the surface impingement region, with a 3- to 6-fold increase in dilution across the jump compared with vertical buoyant jet mixing. The predicted stability category, velocity and temperature/concentration fields are well-supported by experiments of all previous investigators.     

Turbulence and aeration in hydraulic jumps: free-surface fluctuation and integral turbulent scale measurements

In an open channel, a change from a supercritical to subcritical flow is a strong dissipative process called a hydraulic jump. Herein some new measurements of free-surface fluctuations of the impingement perimeter and integral turbulent time and length scales in the roller are presented with a focus on turbulence in hydraulic jumps with a marked roller. The observations highlighted the fluctuating nature of the impingement perimeter in terms of both longitudinal and transverse locations. The results showed further the close link between the production and detachment of large eddies in jump shear layer, and the longitudinal fluctuations of the jump toe. They highlighted the importance of the impingement perimeter as the origin of the developing shear layer and a source of vorticity. The air–water flow measurements emphasised the intense flow aeration. The turbulent velocity distributions presented a shape similar to a wall jet solution with a marked shear layer downstream of the impingement point. The integral turbulent length scale distributions exhibited a monotonic increase with increasing vertical elevation within 0.2 < L_z/d₁ < 0.8 in the shear layer, where L_z is the integral turbulent length scale and d₁ the inflow depth, while the integral turbulent time scales were about two orders of magnitude smaller than the period of impingement position longitudinal oscillations.     

Assessment of canopy stomatal conductance models using flux measurements

Stomatal conductance (g) is a key parameter in controlling energy and water exchanges between canopy and the atmosphere. Stomatal conductance models proposed by Ball, Woodrow and Berry (BWB) and Leuning have been increasingly used in land surface schemes. In a recent study, a new diagnostic index was developed by Wang et al. to examine the response of g to humidity and new models were proposed to resolve problems identified in the BWB and Leuning models. This approach is theoretically sound, but relies on canopy latent heat and CO₂ fluxes and environmental variables at the leaf surface which are not available at most eddy correlation (EC) observation sites. In this study, we tested the diagnostic index by empirically correcting EC measurements to canopy-level fluxes and by replacing leaf surface variables by their corresponding ambient air variables, and re-examined the stomatal conductance models of BWB, Leuning, and Wang et al. We found that the impact of the above modifications on the evaluation of g–humidity relationships is very small. This study provides a practical approach to investigate the stomatal response to humidity using routine EC measurements.