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.     

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.     

Turbulence characteristics within sparse and dense canopies

Boundary layer interactions with canopies control various environmental processes. In the case of dense and homogeneous canopies, the so-called mixing layer analogy is most generally used. When the canopy becomes sparser, a transition occurs between the mixing layer and the boundary layer perturbed by interactions between element wakes. This transition has still to be fully understood and characterized. The experimental work presented here deals with the effect of the canopy density on the flow turbulence and involves an artificial canopy placed in a fully developed turbulent boundary layer. One and two-component velocity measurements are performed, both within and above the canopy. The influence of the spacing between canopy elements is studied. Longitudinal velocity statistical moments and Reynolds stresses are calculated and compared to literature data. For spacings greater than the canopy height, evidences of this transition are found in the evolution of the skewness factor, shear length scale and mixing length.     

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.     

Simulation of exchange flow between open water and floating vegetation using a modified RNG <Emphasis Type="Italic">k</Emphasis>-<Emphasis Type="Italic">ε</Emphasis> turbulence model

The paper focuses on the numerical simulation of the exchange flow between open water and floating vegetation, which plays an important role in maintaining the ecological balance by transporting nutrient matter. The simulation was conducted using a new solver developed upon OpenFOAM. A modified RNG k-ε turbulence model, which is expected to model both the high- and low-Reynolds number flows correctly, was used to determine the eddy viscosity. Several particular terms were added into the momentum equations and turbulence model equations to model the effects of vegetation and buoyancy. Among these terms, the term for the effect of vegetation in the ε-equation was re-modelled. The model was validated by properly predicting the profiles of mean velocity and turbulent kinetic energy for flows through suspended canopies. The density flow between open and vegetated water was simulated with the same conditions as those of the experiment conducted by Zhang and Nepf. The predicted results agreed well with the experimental data and provided more detailed information of such exchange flow. The convection between the root layer and the layer beneath the roots, which was not observed in the experiment, was observed in the numerical simulation.     

Effects of seagrasses and algae of the Caulerpa family on hydrodynamics and particle-trapping rates

The widespread decline of seagrass beds within the Mediterranean often results in the replacement of seagrasses by opportunistic green algae of the Caulerpa family. Because Caulerpa beds have a different height, stiffness and density compared to seagrasses, these changes in habitat type modify the interaction of the seafloor with hydrodynamics, influencing key processes such as sediment resuspension and particle trapping. Here, we compare the effects on hydrodynamics and particle trapping of Caulerpa taxifolia, C. racemosa, and C. prolifera with the Mediterranean seagrasses Cymodocea nodosa and Posidonia oceanica. All macrophyte canopies reduced near-bed volumetric flow rates compared to bare sediment, vertical profiles of turbulent kinetic energy revealed peak values around the top of the canopies, and maximum values of Reynolds stress increased by a factor of between 1.4 (C. nodosa) and 324.1 (P. oceanica) when vegetation was present. All canopies enhanced particle retention rates compared to bare sediment. The experimental C. prolifera canopy was the most effective at particle retention (m² habitat); however, C. racemosa had the largest particle retention capacity per structure surface area. Hence, in terms of enhancing particle trapping and reducing hydrodynamic forces at the sediment surface, Caulerpa beds provided a similar or enhanced function compared to P.oceanica and C. nodosa. However, strong seasonality in the leaf area index of C. racemosa and C. taxifolia within the Mediterranean, combined with a weak rhizome structure, suggests that sediments maybe unprotected during winter storms, when most erosion occurs. Hence, replacement of seagrass beds with Caulerpa is likely to have a major influence on annual sediment dynamics at ecosystem scales.     

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.     

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.     

Hierarchical modeling of the dilute transport of suspended sediment in open channels

We propose, discuss and validate a theoretical and numerical framework for sediment-laden, open-channel flows which is based on the two-fluid-model (TFM) equations of motion. The framework models involve mass and momentum equations for both phases (sediment and water) including the interactive forces of drag, lift, virtual mass and turbulent dispersion. The developed framework is composed by the complete two-fluid model (CTFM), a partial two-fluid model (PTFM), and a standard sediment-transport model (SSTM). Within the umbrella of the Reynolds-Averaged Navier-Stokes (RANS) equations, we apply K–ε type closures (standard and extended) to account for the turbulence in the carrier phase (water). We present the results of numerical computations undertaken by integrating the differential equations over control volumes. We address several issues of the theoretical models, especially those related to coupling between the two phases, interaction forces, turbulence closure and turbulent diffusivities. We compare simulation results with various recent experimental datasets for mean flow variables of the carrier as well as, for the first time, mean flow of the disperse phase and turbulence statistics. We show that most models analyzed in this paper predict the velocity of the carrier phase and that of the disperse phase within 10% of error. We also show that the PTFM provides better predictions of the distribution of sediment in the wall-normal direction as opposed to the standard Rousean profile, and that the CTFM is by no means superior to the PTFM for dilute mixtures. We additionally report and discuss the values of the Schmidt number found to improve the agreement between predictions of the distribution of suspended sediment and the experimental data.     

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.     

Canopy-wake dynamics and wind sheltering effects on Earth surface fluxes

The atmospheric boundary layer adjustment at the abrupt transition from a canopy (forest) to a flat surface (land or water) is investigated in a wind tunnel experiment. Detailed measurements examining the effect of canopy turbulence on flow separation, reduced surface shear stress and wake recovery are compared to data for the classical case of a solid backward-facing step. Results provide new insights into the interpretation for flux estimation by eddy-covariance and flux gradient methods and for the assessment of surface boundary conditions in turbulence models of the atmospheric boundary layer in complex landscapes and over water bodies affected by canopy wakes. The wind tunnel results indicate that the wake of a forest canopy strongly affects surface momentum flux within a distance of 35–100 times the step or canopy height, and mean turbulence quantities require distances of at least 100 times the canopy height to adjust to the new surface. The near-surface mixing length in the wake exhibits characteristic length scales of canopy flows at the canopy edge, of the flow separation in the near wake and adjusts to surface layer scaling in the far wake. Components of the momentum budget are examined individually to determine the impact of the canopy wake. The results demonstrate why a constant flux layer does not form until far downwind in the wake. An empirical model for surface shear stress distribution from a forest canopy to a clearing or lake is proposed.     

Turbulence suppression by suspended sediment within a geophysical flow

Experiments are performed in a mixing box to evaluate the effect of suspended sediment on turbulence generated by an oscillating grid. Quartz-density sand of varying sizes and concentrations is used, and particle image velocimetry is employed to quantify only the fluid phase. Results show that (1) while a relatively large secondary flow field is present in the box, turbulence is a maximum near the grid and it decreases systematically toward the water surface; (2) relatively high concentrations of fine sediment can markedly alter this secondary flow field and significantly decrease both the time-mean and turbulent kinetic energy within the flow, yet these same sediment concentrations have little effect on the integral time and length scales derived for each velocity component; and (3) the overall turbulence suppression observed can be related to the transfer of energy from the fluid to the sediment and the maintenance of a suspended sediment load rather than commonly employed turbulence modulation criteria. These experimental data demonstrate unequivocally that the presence of a suspended sediment load can significantly reduce overall turbulent kinetic energy, and these results should be applicable to a range of sediment-laden geophysical flows.     

Numerical study of wave–current–vegetation interaction in coastal waters

Research on interactions among wave, current, and vegetation has received increasing attention. An explicit depth-averaged hydrodynamic model coupled with a wave spectral model (CMS-wave) was proposed in this study in order to simulate the wave and wave-induced current in coastal waters. The hydrodynamic model was based on the finite volume method while the intercell flux was computed by employing the Harten–Lax–van Leer approximate Riemann solver to investigate the dry-to-wet interface, and the drag force of vegetation was modeled as the sink terms in the momentum equations. The CMS-wave model was used to investigate the non-breaking and the breaking random waves propagation in vegetation fields. Afterwards, an empirical wave energy dissipation term with plant effect was derived to represent the resistance induced by aquatic vegetation in the wave-action balance equation. The established model was calibrated and validated with both the experimental and field data. The results showed that the wave height decreased significantly along the wave propagation direction in the presence of vegetations. The sensitivity analysis for the plant density, the wave height, and the water depth were performed by comparing the numerical results for the wave height attenuation. In addition, wave and wave-induced current through a finite patch of vegetation in the surf zone were investigated as well. The strong radiation stress gradient could be produced due to the variation of the energy dissipation by vegetation effect in the nearshore zone, which impacted the direction and amplitude of the longshore current. The calculated results showed that the coupling model had good performance in predicting wave propagation and the current over vegetated water regions.     

Flows through forest canopies in complex terrain

Recent progress on boundary layer flow within and above tall forest canopies in complex terrain is reviewed from the perspective of developing methods to interpret carbon dioxide fluxes from tower measurements in real terrain. Two examples of complex terrain are considered in detail: a forest edge, which exemplifies nonuniform forests, and hilly terrain, which can lead to drainage currents at night. Dynamical arguments show that, when boundary layer winds approach a forest edge, the mean wind adjusts on a length scale of approximately 3L(c), where L(c) is the canopy drag length scale, which depends inversely on the leaf area density of the forest. Over a further distance that also scales on L(c), turbulence in the flow adjusts, and the mixing and transport in the canopy approaches the homogeneous limit. Even low hills change the neutral flow within and above the forest canopy substantially. When the canopy is tall, pressure gradients drive flow up both the upwind and downwind slopes of the hill, leading to an ejection of air out of the top of the canopy just downwind of the crest. This flow at the crest can then advect scalar out of the top of the forest, leading to large variations in the flux of scalar across the hill. At night, when the air near the ground cools and becomes stably stratified, turbulence within the canopy can collapse, even when the flow above the canopy remains turbulent. This leads to a decoupling of the air motions within the canopy from those above. The air above the canopy can then continue to pass up and over the hill, as it does in the neutral case, but at the same time, air within the canopy drains down the hill slopes as drainage currents. These analyses will help us understand when flux towers are reliably measuring the net ecosystem exchange and suggest ways of correcting the flux tower data in more complex situations.     

The effects of intensive aquaculture on nutrient residence time and transport in a coastal embayment

Aquaculture in many countries around the world has become the biggest source of seafood for human consumption. While it alleviates the pressure on wild capture fisheries, the long-term impacts of large-scale, intensive aquaculture on natural coastal systems need to be better understood. In particular, aquaculture may alter habitat and exceed the carrying capacity of coastal marine ecosystems. In this paper, we develop a high-resolution numerical model for Sanggou Bay, one of the largest kelp and shellfish aquaculture sites in Northern China, to investigate the effects of aquaculture on nutrient transport and residence time in the bay. Drag from aquaculture is parameterized for surface infrastructure, kelp canopies, and bivalve cages. A model for dissolved inorganic nitrogen (DIN) includes transport, vertical turbulent mixing, sediment and bivalve sources, and a sink due to kelp uptake. Test cases show that, due to drag from the dense aquaculture and thus a reduction of horizontal transport, kelp production is limited because DIN from the Yellow Sea is consumed before reaching the interior of the kelp farms. Aquaculture drag also causes an increase in the nutrient residence time from an average of 5 to 10 days in the middle of Sanggou Bay, and from 25 to 40 days in the shallow inner bay. Low exchange rates and a lack of DIN uptake by kelp make these regions more susceptible to phytoplankton blooms due to high nutrient retention. The risk is further increased when DIN concentrations rise due to river inflows.     

Spatial evolution of coherent motions in finite-length vegetation patch flow

A number of experimental studies on submerged canopy flows have focused on fully-developed flow and turbulent characteristics. In many natural rivers, however, aquatic vegetation occurs in patches of finite length. In such vegetated flows, the shear layer is not formed at the upstream edge of the vegetation patch and coherent motions develop downstream. Therefore, more work is neededz to reveal the development process for large-scale coherent structures within vegetation patches. For this work, we considered the effect of a limited length vegetation patch. Turbulence measurements were intensively conducted in open-channel flows with submerged vegetation using Particle Image Velocimetry (PIV). To examine the transition from boundary-layer flow upstream of the vegetation patch to a mixing-layer-type flow within the patch, velocity profiles were measured at 33 positions in a longitudinal direction. A phenomenological model for the development process in the vegetation flow was developed. The model decomposed the entire flow region into four zones. The four zones are the following: (i) the smooth bed zone, (ii) the diverging flow zone, (iii) the developing zone and (iv) the fully-developed zone. The PIV data also confirmed the efficiency of the mixing-layer analogy and provided insight into the spatial evolution of coherent motions.     

Integral Model for Turbulent Buoyant Jets in Unbounded Stratified Flows. Part I: Single Round Jet

The mechanics of buoyant jet flows issuing with a general three-dimensional geometry into an unbounded ambient environment with uniform density or stable density stratification and under stagnant or steady sheared current conditions is investigated. An integral model is formulated for the conservation of mass, momentum, buoyancy and scalar quantities in the turbulent jet flow. The model employs an entrainment closure approach that distinguishes between the separate contributions of transverse shear (leading to jet, plume, or wake internal flow dynamics) and of azimuthal shear mechanisms (leading to advected momentum puff or thermal flow dynamics), respectively. Furthermore, it contains a quadratic law turbulent drag force mechanism as suggested by a number of recent detailed experimental investigations on the dynamics of transverse jets into crossflow. The model is validated in several stages: First, comparison with basic experimental data for the five asymptotic, self-similar stages of buoyant jet flows, i.e., the pure jet, the pure plume, the pure wake, the advected line puff, and the advected line thermal, support the choice and magnitude of the turbulent closure coefficients contained in the entrainment formulation. Second, comparison with many types of non-equilibrium flows support the proposed transition function within the entrainment relationship, and also the role of the drag force in the jet deflection dynamics. Third, a number of spatial limits of applicability have been proposed beyond which the integral model necessarily becomes invalid due to its parabolic formulation. These conditions, often related to the breakdown of the boundary layer nature of the flow, describe features such as terminal layer formation in stratification, upstream penetration in jets opposing a current, or transition to passive diffusion in a turbulent ambient shear flow. Based on all these comparisons, that include parameters such as trajectories, centerline velocities, concentrations and dilutions, the model appears to provide an accurate and reliable representation of buoyant jet physics under highly general flow conditions.     

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.     

Feedbacks between bivalve density, flow, and suspended sediment concentration on patch stable states

We explore the role of biophysical feedbacks occurring at the patch scale (spatial scale of tens of meters) that influence bivalve physiological condition and affect patch stability by developing a numerical model for the pinnid bivalve, Atrina zelandica, in cohesive sediments. Simulated feedbacks involve bivalve density, flow conditions (assumed to be primarily influenced by local water depth and peak current speed), suspended sediment concentration (evaluated through a balance between background concentration, deposition, and erosion), and changes in the physiology of Atrina derived from empirical study. The model demonstrates that high bivalve density can lead to skimming flow and to a concomitant decrease in resuspension that will affect suspended sediment concentration over the patch directly feeding back on bivalve physiology. Consequently, for a given flow and background suspended sediment load, the stability of a patch directly depends on the size and density of bivalves in the patch. Although under a range of conditions patch stability is ensured independently of bivalve density, simulations clearly indicate that sudden changes in bivalve density or suspended sediment concentration can substantially affect patch structure and lead to different stable states. The model highlights the role of interactions between organisms, flow, and broader scale environmental conditions in providing a mechanistic explanation for the patchy occurrence of benthic suspension feeders.     

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.