A new view of dispersion in well-mixed estuaries

A two-dimensional simulation of Delaware estuary hydrodynamics has been constructed. This simulation has been achieved through a rational estimate of the character of natural turbulence. Non-homogeneous velocities, on the cross-section, are employed in two-dimensional, laterally homogeneous species mass balances. In turn, concentration profiles are interpreted in the form of classical, one-dimensional dispersion coefficients. Variation of dispersion as a function of both freshwater inflow and longitudinal distance was generated. Variation of dispersion in time within a tidal cycle was found to be insignificant while no significant variation from one tidal cycle to the next has been detected.The modeling process involves the solution of tractable equations by implicit numerical methods and is capable of being excited by a wide range of input conditions.A study of the sensitivity of dispersion due to vertical mass diffusion revealed that longitudinal mixing characteristics are inversely proportional to vertical eddy diffusivity and analysis of the numerical results showed the dispersion coefficient is essentially insensitive to variation of longitudinal mass diffusivity. This leads to the conclusion that turbulent diffusivity of mass in the longitudinal direction may be taken as constant for most purposes in the study of a two-dimensional species mass balance model.A field program was carried out near the Delaware Memorial Bridge to collect velocity profiles. Substantial portions of the scheme have been verified (i.e. one- and two-dimensional tidal dynamic models) through the use of these data.     

Prediction of longitudinal dispersion coefficients in natural rivers using artificial neural network

An artificial neural network (ANN) model is developed for predicting the longitudinal dispersion coefficient in natural rivers. The model uses few rivers’ hydraulic and geometric characteristics, that are readily available, as the model input, and the target output is the longitudinal dispersion coefficient (K). For performance evaluation of the model, using published field data, predictions by the developed ANN model are compared with those of other reported important models. Based on various performance indices, it is concluded that the new model predicts the longitudinal dispersion coefficient more accurately. Sensitive analysis performed on input parameters indicates stream width, flow depth, stream sinuosity, flow velocity, and shear velocity to be the most influencing parameters for accurate prediction of the longitudinal dispersion coefficient.     

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.     

Characteristics of flow structure of free-surface flow in a partly obstructed open channel with vegetation patch

Free-surface flows over patchy vegetation are common in aquatic environments. In this study, the hydrodynamics of free-surface flow in a rectangular channel with a bed of rigid vegetation-like cylinders occupying half of the channel bed was investigated and interpreted by means of laboratory experiments and numerical simulations. The channel configurations have low width-to-depth aspect ratio (1.235 and 2.153). Experimental results show that the adjustment length for the flow to be fully developed through the vegetation patch in the present study is shorter than observed for large-aspect-ratio channels in other studies. Outside the lateral edge of the vegetation patch, negative velocity gradient (\(\partial \overline{u}/\partial z < 0\)) and a local velocity maximum are observed in the vertical profile of the longitudinal velocity in the near-bed region, corresponding to the negative Reynolds stress (\(- \overline{{u^{\prime}w^{\prime}}} < 0\)) at the same location. Assuming coherent vortices to be the dominant factor influencing the mean flow field, an improved Spalart–Allmaras turbulence model is developed. The model improvement is based on an enhanced turbulence length scale accounting for coherent vortices due to the effect of the porous vegetation canopy and channel bed. This particular flow characteristic is more profound in the case of high vegetation density due to the stronger momentum exchange of horizontal coherent vortices. Numerical simulations confirmed the local maximum velocity and negative gradient in the velocity profile due to the presence of vegetation and bed friction. This in turn supports the physical interpretation of the flow processes in the partly obstructed channel with vegetation patch. In addition, the vertical profile of the longitudinal velocity can also be explained by the vertical behavior of the horizontal coherent vortices based on a theoretical argument.     

Analytical solution of two-dimensional advection–dispersion equation with spatio-temporal coefficients for point sources in an infinite medium using Green’s function method

In the present study analytical solutions of a two-dimensional advection–dispersion equation (ADE) with spatially and temporally dependent longitudinal and lateral components of the dispersion coefficient and velocity are obtained using Green’s Function Method (GFM). These solutions describe solute transport in infinite horizontal groundwater flow, assimilating the spatio-temporal dependence of transport properties, dependence of dispersion coefficient on velocity, and the particulate heterogeneity of the aquifer. The solution is obtained in the general form of temporal dependence and the source term, from which solutions for instantaneous and continuous point sources are derived. The spatial dependence of groundwater velocity is considered non-homogeneous linear, whereas the dispersion coefficient is considered proportional to the square of spatial dependence of velocity. An asymptotically increasing temporal function is considered to illustrate the proposed solutions. The solutions are validated with the existing solutions derived from the proposed solutions in three special cases. The effect of spatially/temporally dependent heterogeneity on the solute transport is also demonstrated. To use the GFM, the ADE with spatio-temporally dependent coefficients is reduced to a dispersion equation with constant coefficients in terms of new position variables introduced through properly developed coordinate transformation equations. Also, a new time variable is introduced through a known transformation.     

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.     

Tree species control rates of free-living nitrogen fixation in a tropical rain forest

Tropical rain forests represent some of the most diverse ecosystems on earth, yet mechanistic links between tree species identity and ecosystem function in these forests remains poorly understood. Here, using free-living nitrogen (N) fixation as a model, we explore the idea that interspecies variation in canopy nutrient concentrations may drive significant local-scale variation in biogeochemical processes. Biological N fixation is the largest "natural" source of newly available N to terrestrial ecosystems, and estimates suggest the highest such inputs occur in tropical ecosystems. While patterns of and controls over N fixation in these systems remain poorly known, the data we do have suggest that chemical differences among tree species canopies could affect free-living N fixation rates. In a diverse lowland rain forest in Costa Rica, we established a series of vertical, canopy-to-soil profiles for six common canopy tree species, and we measured free-living N fixation rates and multiple aspects of chemistry of live canopy leaves, senesced canopy leaves, bulk leaf litter, and soil for eight individuals of each tree species. Free-living N fixation rates varied significantly among tree species for all four components, and independent of species identity, rates of N fixation ranged by orders of magnitude along the vertical profile. Our data suggest that variations in phosphorus (P) concentration drove a significant fraction of the observed species-specific variation in free-living N fixation rates within each layer of the vertical profile. Furthermore, our data suggest significant links between canopy and forest floor nutrient concentrations; canopy P was correlated with bulk leaf litter P below individual tree crowns. Thus, canopy chemistry may affect a suite of ecosystem processes not only within the canopy itself, but at and beneath the forest floor as well.     

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.     

Vertical oil dispersion profile under non-breaking regular waves

An experimental program was conducted to investigate vertical oil dispersion of surface oil spills under non-breaking regular waves. The variation in oil concentration caused by oil dispersion in a water column was studied to determine the vertical oil dispersion profile. The experiments were performed using different waves characteristics for different volumes of oil spill to evaluate the variation in oil concentration at three depths at two sampling stations. The correlations between oil concentration and the main parameters of wave characteristics, oil spill volume, sampling depth, and distance of sampling stations to spill location were assessed. The results revealed that the trend of variation in oil concentration versus wave steepness is linear. The results obtained from experimental measurements indicated that the oil concentrations at mid-depth were 44–77 % and the concentrations near the flume bed were 12–33 % of the concentration near the water surface.     

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.     

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.     

Large-eddy simulation of low-level jet-like flow in a canopy

The computational method of Large-Eddy Simulations has been used to study the weak, neutrally stable drainage flow within tree canopies. The computational results show that a secondary velocity maximum that resembles a jet is formed within the canopy under the nocturnal flow conditions. This jet-like flow is important in the analysis and measurements of the net ecosystem-atmosphere exchange (NEE) for carbon dioxide (CO₂). A uniformly distributed, plane source was placed within the canopy in order to simulate the nocturnal production of CO₂. The NEE is calculated as the sum of the integration of the rate of change of the concentration of CO₂ over the computational domain, the vertical turbulent flux measured directly by eddy-covariance (EC) method, and the advection terms, which are not taken into account in the EC method. Numerical results of the velocity and concentration fields, within and above the canopy, are presented and their impact on the CO₂ transport is investigated in detail. The computational results show that 15–20% of NEE is drained out by the advection process under the canopy. The results also show that the turbulent fluctuations in the lateral direction are also significant and may result in 2–5% CO₂ transport.     

Compound channel flow with a longitudinal transition in hydraulic roughness over the floodplains

Flows in a compound open-channel (two-stage geometry with a main channel and adjacent floodplains) with a longitudinal transition in roughness over the floodplains are experimentally investigated in an 18 m long and 3 m wide flume. Transitions from submerged dense vegetation (meadow) to emergent rigid vegetation (wood) and vice versa are modelled using plastic grass and vertical wooden cylinders. For a given roughness transition, the upstream discharge distribution between main channel and floodplain (called subsections) is also varied, keeping the total flow rate constant. The flows with a roughness transition are compared to flows with a uniformly distributed roughness over the whole length of the flume. Besides the influence of the downstream boundary condition, the longitudinal profiles of water depth are controlled by the upstream discharge distribution. The latter also strongly influences the magnitude of the lateral net mass exchanges between subsections, especially upstream from the roughness transition. Irrespective of flow conditions, the inflection point in the mean velocity profile across the mixing layer is always observed at the interface between subsections. The longitudinal velocity at the main channel/floodplain interface, denoted \(U_{int}\), appeared to be a key parameter for characterising the flows. First, the mean velocity profiles across the mixing layer, normalised using \(U_{int}\), are superimposed irrespective of downstream position, flow depth, floodplain roughness type and lateral mass transfers. However, the profiles of turbulence quantities do not coincide, indicating that the flows are not fully self-similar and that the eddy viscosity assumption is not valid in this case. Second, the depth-averaged turbulent intensities and Reynolds stresses, when scaled by the depth-averaged velocity \(U_{d,int}\) exhibit two plateau values, each related to a roughness type, meadow or wood. Lastly, the same results hold when scaling by \(U_{d,int}\) the depth-averaged lateral flux of momentum due to secondary currents. Turbulence production and magnitude of secondary currents are increased by the presence of emergent rigid elements over the floodplains. The autocorrelation functions show that the length of the coherent structures scales with the mixing layer width for all flow cases. It is suggested that coherent structures tend to a state where the magnitude of velocity fluctuations (of both horizontal vortices and secondary currents) and the spatial extension of the structures are in equilibrium.     

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 turbulence near a tall forest edge: the backward-facing step flow analogy revisited

Flow disturbances near tall forest edges are receiving significant attention in diverse disciplines including ecology, forest management, meteorology, and fluid mechanics. Current theories suggest that near a forest edge, when the flow originates from a forest into a large clearing, the flow retains its forest canopy turbulence structure at the exit point. Here, we propose that this framework is not sufficiently general for dense forested edges and suggest that the flow shares several attributes with backward-facing step (BFS) flow. Similar analogies, such as rotor-like circulations, have been proposed by a number of investigators, though the consequences of such circulations on the primary terms in the mean momentum balance at the forest clearing edge have rarely been studied in the field. Using an array of three triaxial sonic anemometers positioned to measure horizontal and vertical gradients of the velocity statistics near a forest edge, we show that the flow structure is more consistent with an intermittent recirculation pattern, rather than a continuous rotor, whose genesis resembles the BFS flow. We also show that the lateral velocity variance, v'2, is the moment that adjusts most slowly with downwind distance as the flow exits from the forest into the clearing. Surprisingly, the longitudinal and vertical velocity variances (u'2 and w'2) at the forest edge were comparable in magnitude to their respective values at the center of a large grass-covered forest clearing, suggesting rapid adjustment at the edge. Discussions on how the forest edge modifies the spectra and co-spectra of momentum fluxes, effective mixing length, and static pressure are also presented.     

Model of turbulence penetration into a suspension layer on a sediment bed and effect on vertical solute transfer

The vertical diffusional mass (solute) transfer through a suspended sediment layer, e.g. at the bottom of a lake, reservoir or estuary, by the propagation of velocity fluctuations from above was investigated. The attenuation of the velocity fluctuations in the suspension layer and the associated effect on solute transfer through the suspension layer was simulated. To represent large eddies traveling downstream in water over a high-concentration suspended sediment layer, a streamwise velocity fluctuation moving in downstream direction was imposed along the upper boundary of the suspension layer. Velocity fluctuations and downstream velocity were normalized by the shearvelocity (U_*) at the top of the suspension layer. Streamwise and vertical velocity components inside the suspension layer, were obtained from the 2-D continuity and the Navier–Stokes equations. The persistence of turbulence with depth—as it penetrates from the overlying water into the suspension layer—was found to depend on its amplitude, its period, and on the apparent viscosity of the suspension. The turbulence was found to propagate efficiently into the suspension layer when its frequency is low, and the apparent viscosity of the suspension is high. Effects on vertical mass transfer were parameterized by penetration depth and effective diffusion coefficient, and related to apparent viscosity of the suspension, Schmidt number and shear velocity on top of the suspension layer. The enhancement of turbulence penetration by viscosity is similar to the flow near an oscillating flat plate (Stokes’ second problem), but is opposite to turbulence penetration into a stationary porous and permeable sediment bed. The information is applicable to water quality modeling mear the sediment/water interface of lakes, river impoundments and estuaries.     

Photosynthetic characteristics of giant kelp (Macrocystis pyrifera) determined in situ

Rates of net photosynthesis and nocturnal respiration by individual blades of the giant kelp Macrocystis pyrifera (L.) C. Agardh in southern California, were determined in situ by measuring oxygen production in polyethylene bags during spring/summer of 1983. Mature blades from different depths in the water column exhibited different photosynthetic characteristics. Blades from the surface canopy (0 to 1 m depth) exhibited higher photosynthetic capacity under saturating irradiance and higher photosynthetic efficiency at low irradiances than blades from 3 to 5 or 7 to 9 m depths. Saturating irradiance was lower for canopy blades than for deeper blades. Canopy blades showed no short-term photoinhibition, but photosynthetic rates of deeper blades were significantly reduced during 1 to 2 h incubations at high irradiances. Results of 1 to 2 wk acclimation experiments indicated that differences between photosynthetic characteristics of blades from different depths were primarily attributable to acclimation light conditions. Vertical displacement of blades within the kelp canopy occurred on a time-scale of 1 min to 1 h. Blades continually moved between the unshaded surface layer and deeper, shaded layers. Vertical movement did not maximize photosynthesis by individual blades; only a small proportion of blades making up a dense surface canopy maintained light-saturated photosynthetic rates during midday incubations. The relatively high photosynthetic rates exhibited by canopy blades over the entire range of light conditions probably resulted from acclimation to intermittent high and low irradiances, a consequence of vertical displacement. Vertical displacement also reduced the afternoon depression in photosynthesis of individual canopy blades. The overall effect of vertical displacement was optimization of total net photosynthesis by the kelp canopy and, therefore, optimization of whole-plant production.     

Linking fruit traits to variation in predispersal vertebrate seed predation, insect seed predation, and pathogen attack

The importance of vertebrates, invertebrates, and pathogens for plant communities has long been recognized, but their absolute and relative importance in early recruitment of multiple coexisting tropical plant species has not been quantified. Further, little is known about the relationship of fruit traits to seed mortality due to natural enemies in tropical plants. To investigate the influences of vertebrates, invertebrates, and pathogens on reproduction of seven canopy plant species varying in fruit traits, we quantified reductions in fruit development and seed germination due to vertebrates, invertebrates, and fungal pathogens through experimental removal of these enemies using canopy exclosures, insecticide, and fungicide, respectively. We also measured morphological fruit traits hypothesized to mediate interactions of plants with natural enemies of seeds. Vertebrates, invertebrates, and fungi differentially affected predispersal seed mortality depending on the plant species. Fruit morphology explained some variation among species; species with larger fruit and less physical protection surrounding seeds exhibited greater negative effects of fungi on fruit development and germination and experienced reduced seed survival integrated over fruit development and germination in response to vertebrates. Within species, variation in seed size also contributed to variation in natural enemy effects on seed viability. Further, seedling growth was higher for seeds that developed in vertebrate exclosures for Anacardium excelsum and under the fungicide treatment for Castilla elastica, suggesting that predispersal effects of natural enemies may carry through to the seedling stage. This is the first experimental test of the relative effects of vertebrates, invertebrates, and pathogens on seed survival in the canopy. This study motivates further investigation to determine the generality of our results for plant communities. If there is strong variation in natural enemy attack among species related to differences in fruit morphology, then quantification of fruit traits will aid in predicting the outcomes of interactions between plants and their natural enemies. This is particularly important in tropical forests, where high species diversity makes it logistically impossible to study every plant life history stage of every species.     

重气连续泄漏扩散的盐水模拟实验

根据相似理论,分析了用盐水模拟方法研究意外泄漏的重气在大气中扩散过程的可行性,通过假设重气为不可压缩气体以及在均匀温度场中扩散等条件,推导出模拟实验的准则数.采用缩比模型的盐水模拟实验,对重气在大气中的扩散速度及浓度变化进行了分析,证实了重气扩散过程中的重力沉降、密度分层以及近源区分叉等现象.实验表明,在满足主导准则数相等的条件下,盐水在清水中的扩散可以较好地再现重气在大气中的扩散特征.     

Stratified flow interactions with a suspended canopy

Field observations of the interactions between a stratified flow and a canopy suspended from the free surface above a solid boundary are described and analysed. Data were recorded in and around the canopy formed by a large long-line mussel farm. The canopy causes a partial blockage of the water flow, reducing velocities in the upper water column. Deceleration of the approaching flow results in a deepening of isopycnals upstream of the canopy. Energy considerations show that the potential for an approaching stratified flow to be diverted beneath a porous canopy is indicated by a densimetric Froude number. Strong stratification or low-velocities inhibit vertical diversion beneath the canopy, instead favouring a horizontal diversion around the sides. The effect on vertical mixing is also considered with a shear layer generated beneath the canopy and turbulence generated from drag within the canopy. In the observations, stratification is shown to be of sufficient strength to limit the effectiveness of the first mixing process, while the turbulence within the canopy is likely to enhance vertical exchange. Velocity and temperature microstructure measurements are used to investigate the effect of the canopy on turbulent dissipation and show that dissipation is enhanced within the canopy.