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.     

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.     

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.     

Estimation of far-field horizontal and vertical turbulent diffusion coefficients from the concentration field of a wastewater plume near the Akashi Strait

We carried out a field study of the plume discharged by a near-shore wastewater outfall near the Akashi Strait, Japan. Using an Acoustic Doppler Current Profiler and a tow-body CTD, we measured the near-surface salinity and temperature fields in the region throughout an M₂ tidal cycle. We filtered the data in T–S space to remove water masses other than the wastewater, and then used the adiabatic mixing assumption to calculate the concentration of wastewater in the far field of this plume. Averaging the T–S fields of repeated surveys over a time period during which the tidal regime did not change substantially, allowed comparison of the time-averaged plume with the analytical solution for a plume diffusing in both the horizontal and vertical dimensions. The resulting vertical turbulent diffusion coefficients agreed well with those resulting from Thorpe scales determined via a vertically-profiling CTD, as well as with the canonical value for open channel flow of D _z = 0.067hu _*. The corresponding horizontal turbulent diffusion coefficients, however, were two orders of magnitude larger than those typically observed in straight channels, and an order of magnitude larger than those observed in meandering rivers. This is likely a result of enhanced horizontal mixing due to barotropic eddies generated by the interaction of strong tidal flow with headlands and levees, as well as due to the time-varying nature of tidal flow, and baroclinic spreading of the buoyant wastewater plume.     

Turbulence structure and coherent vortices in open-channel flows with wind-induced water waves

When wind-induced water waves appear over the free-surface flows such as natural rivers and artificial channels, large amounts of oxygen gas and heat are transported toward the river bed through the interface between water and wind layers. In contrast, a bed region is a kind of turbulent boundary layer, in which turbulence generation and its transport is promoted by the production of bed shear stress. In particular, coherent hairpin vortices, together with strong ejection events toward the outer part of the layer, promote mass and momentum exchanges between the inner and outer layers. It is inferred that such a near-bed turbulence may be influenced significantly by these air–water interfacial fluctuations accompanied with free-surface velocity shear and wind-induced water waves. However, these wind effects on the wall-turbulence structure are less understood. To address these exciting and challenging topics, we conducted particle imagery velocimetry (PIV) measurements in open-channel flows combined with air flows, and furthermore the present measured data allows us to investigate the effects of air–water interactions on turbulence structure through the whole depth region.     

Diapycnal Mixing in the Thermocline of Lakes: Estimations by Different Methods

In order to evaluate the performance of different methods for estimation of the vertical eddy diffusivity in thermally stratified lakes, two field studies were conducted in Lake Biwa, Japan and Lake Kinneret, Israel. Lake Biwa experienced three typhoons during the campaign while Lake Kinneret experienced high winds in the afternoons. Microstructure profiles were collected by a portable flux profiler (PFP) during calm and disturbed periods. Then, the vertical eddy diffusivity was estimated by three indirect methods. The estimated vertical eddy diffusivities varied more than one order of magnitude, from 4.7× 10⁻⁷ to 7.7× 10⁻⁶ m² s⁻¹. The comparison of results with previous buoyancy flux measurements and scaling arguments showed that the Dillon–Park’s method is not appropriate and Osborn–Cox method performs better than Osborn method in the studied case. Furthermore, the low value of vertical eddy diffusivity within the thermocline suggests that within the thermocline of these lakes, diffusive vertical transport can be neglected.     

Hydrodynamics and turbulence in emergent and sparsely vegetated open channel flow

This present study reports the results of an experimental study characterizing thorough variation of turbulent hydrodynamics and flow distribution in emergent and sparsely vegetated open channel flow. An emergent and rigid sparse vegetation patch with regular spacing between stems along the flow and transverse directions was fixed in the central region of the cross-section of open channel. Experiments were conducted in subcritical flow conditions and velocity measurements were obtained with an acoustic Doppler Velocimetry system. Large variations of the turbulence intensities, Reynolds shear stress, turbulent kinetic energy and vortical motions are found in and around the vegetation patch. At any cross-section through the interior of the vegetation patch, streamwise velocity decreases with increase in streamwise length and the velocity profiles converge from the log-law to a linear profile with increasing slope. Time-averaged lateral and vertical velocities inside the vegetation patch increase with increasing streamwise distance and converge from negative values to positive values. Turbulence intensities interior of the sparse vegetation patch are more than those of without the vegetation patch. Similar to the trend of streamwise velocity profiles inside the vegetation, turbulence intensities and longitudinal-normal Reynolds shear stress profile decreases with streamwise direction. In the interior of the vegetation patch and downstream of the trailing edge, turbulent kinetic energy profiles are exhibiting irregular fluctuations and the maximum values are occurring in the outer layer. Analysis of flow distribution confirms sparse vegetation patch is inducing a serpentine flow pattern in its vicinity. At the leading edge, flow is rushing towards the right hand sidewall, and at the trailing edge, flow is turning to the left hand sidewall. In between the leading and trailing edges, the streamlines are following a zig-zag fashion at varied degree along the streamwise and lateral directions. Immediate upstream of the leading edge and in the interior of the vegetation patch, vortex motion is clearly visible and the vortices are stretched along the width of the channel with streamwise direction.     

Structure of turbulent plumes from a momentumless source in a smooth bed

The spatial development of a passive scalar plume is studied within the inhomogeneous turbulence of a boundary layer flow in a recirculating laboratory flume with a smooth bed. The source of the scalar is located flush with the bed, and the low-momentum source design is intended to simulate a diffusive-type scalar release. A weakly diffusive fluorescent dye is used as the scalar. Planar laser-induced fluorescence (PLIF) techniques were used to record the structure of the plume at a spatial resolution of 150 μm. The measured structure of the mean concentration field is compared to an analytical solution for shear-free, homogeneous turbulence. The laboratory plume exhibits spatial development in the mean concentration field that deviates from the self-similar behavior predicted by the analytical solution; this deviation is due to the mean shear and inhomogeneity of the turbulence. In particular, the influence of the viscous sublayer on the plume development is seen to be significant. Nonetheless, the analytical solution replicates some of the features seen in the laboratory plume, and the solution suggests methods of reducing the laboratory data even for cases where the results deviate from the analysis. We also examine the spatial development of the root-mean-square (rms) fluctuating concentration field, and use scalar probability density functions to examine the relationship between the mean and fluctuating concentrations.     

Prediction of mass and momentum transport in turbulent plane wall jets over smooth and transitionally rough surfaces

This paper is concerned with the prediction of mass and momentum transport in turbulent wall jets developing over smooth and transitionally rough plane walls. The ability to accurately predict the resulting wall shear stresses and vertical profiles of the Reynolds stresses in these flows is prerequisite to the accurate prediction of bed scour, sediment re-suspension and transport by turbulent diffusion. The computations were performed by solving the Reynolds-averaged forms of the equations describing conservation of mass, momentum and concentration. The unknown correlations that arise from the averaging process (the Reynolds stresses in the case of the momentum equation, and the turbulent mass fluxes in the case of concentration) were obtained from the solution of modeled differential equations that describe their conservation. Since these models are somewhat more complex than those typically used in practice, their benefits are demonstrated by comparisons with results obtained from simpler, eddy-viscosity based closures. Comparisons with experimental data show that results of acceptable accuracy can be obtained only by using the appropriate combination of models for the turbulent fluxes of mass and momentum that properly account for the reduction of the Reynolds stresses due to wall damping effects, and for the modification of the mass transfer rates due to interactions with the mean rates of strain.     

Mixing at a sediment concentration interface in turbulent open channel flow

In this work we address the role of turbulence on mixing of clear layer of fluid with sediment-laden layer of fluid at a sediment concentration interface. This process can be conceived as the entrainment of sediment-free fluid into the sediment-laden layer, or alternatively, as the transport of sediment into the top sediment-free flow. This process is governed by four parameters—Reynolds number of the flow \(Re_\tau\), non-dimensional settling velocity of the sediment (proxy for sediment size) \(\tilde{V}\), Richardson number \(Ri_\tau\) and Schmidt number Sc. For this work we have performed direct numerical simulations for fixed Reynolds and Schmidt numbers while varying the values of Richardson number and particle settling velocity. In the simple model considered here, the flow’s momentum and turbulence pre-exists over the entire layer of fluid, while the sediment is initially confined to a layer close to the bed. Mixing of sediment-free fluid with the sediment-laden layer is associated primarily with upward transport of sediment and buoyancy. There is no simultaneous upward transport of fluid momentum and turbulence into the sediment-free fluid layer, which is already in motion and turbulent. The analysis performed shows that the ability of the flow to transport a given sediment size decreases with the distance from the bottom, and thus only fine enough sediment particles are transported across the sediment concentration interface. For these cases, the concentration profiles evolve to a final steady state in good agreement with the well-known Rouse profile. The approach towards the Rouse profile happens through a transient self-similar state. This behavior of the flow is not seen for larger particles. Detailed analysis of the three dimensional structure of the sediment concentration interface shows the mechanisms by which sediment particles are lifted up by tongues of sediment-laden fluid with positive correlation between vertical velocity and sediment concentration. Finally, the mixing ability of the flow is addressed by monitoring the time evolution of the center of mass of the sediment-laden layer and the vertical location of the sediment-free/sediment-laden interface.     

Secondary flow within a river bed and contaminant transport

We have developed a numerical method to simulate the transport of non-sorbing contaminants within the sediment layer of a stream and the leaching of these contaminants in the steam. Typical stream bottom surfaces are uneven with triangularly shaped undulation forms. The flow of the water above such triangular surfaces causes external pressure changes that result in a “pumping effect” and a secondary flow within the sediment. The latter causes a significant contaminant advection within the sediment layer. The flow field in the porous sediment layer is obtained by solving numerically Darcy’s equations. The unsteady mass transfer equation is solved by using a finite-difference method with an up-wind scheme. The effects of parameters, such as channel slope, hydraulic head and dispersion, are studied by quantitatively comparing the numerical results of the total mass flow rate from the contaminant source, the concentration front propagation, and the contaminant mass flow rate into the water column. The “pumping effect,” increases the flow in the vertical direction and, thus, enhances the vertical advective mass transport of the contaminant. This bedform-shape induced flow is largely responsible for the mass transfer of contaminants into the water column. The numerical results also show that the mechanical dispersion inside the sediment bed will significantly increase the contaminant mass flow rate from the source.     

Markovian–Octant analysis based stable turbulent shear stresses in near-bed bursting phenomena of vortex settling chamber

The coherent structure in near-bed turbulent boundary layer of vortex chamber, particularly the bursting events and their associated shear stresses play the main role in sediment flushing process and consequently the trap efficiency of the vortex settling chamber. Hence, three-dimensional velocity measurements were made at 48 points near the bed of physical model of vortex chamber by using Micro-ADV. The pattern of sediment deposition at the bed of vortex settling chamber reveals three separate regions formed by three predominant currents of inlet flow, flushing flow and outlet over flow. Additionally, due to the instability and three-dimensional nature of the bursting events near the bed of chamber, the new method of Markovian–Octant analysis was applied to study the different classes of near-bed stable shear stresses of vortex chamber in three dimensions. Moreover, the role of each class of stable shear stresses on Sediment transport mechanism at the bed of vortex chamber is investigated.     

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.     

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.     

Sensitivity of air quality model prediction to parameterization of vertical eddy diffusivity

This paper investigates the effects of vertical eddy diffusivities derived from the 3 different planetary boundary layer (PBL) schemes on predictions of chemical components in the troposphere of East Asia. Three PBL schemes were incorporated into a regional air quality model (RAQM) to represent vertical mixing process and sensitivity simulations were conducted with the three schemes while other options are identical. At altitudes <2km, all schemes exhibit similar skill for predicting SO₂ and O₃, but more difference in the predicted NO_x concentration. The Gayno–Seaman scheme produces the smallest vertical eddy diffusivity (Kz) among all schemes, leading to higher SO₂ and NO_x concentrations near the surface than that from the other 2 schemes. However, the effect of vertical mixing on O₃ concentration is complex and varies spatially due to chemistry. The Gayno–Seaman scheme predicts lower O₃ concentrations than the other two schemes in the parts of northern China (generally VOC-limited) and higher ones in most parts of southern China (NO_x-limited). The Byun and Dennis scheme produces the largest mixing depth in the daytime, which bring more NO_x into upper levels, and the mixing depth predicted by the Gayno–Seaman scheme is the smallest, leading to higher NO_x and lower O₃ concentrations near the surface over intensive emission regions.     

On the behaviour of the residence time at the bottom of the mixed layer

To understand why the findings of Deleersnijder et al. [(2006), Environ Fluid Mech 6: 25–42]—the residence time in the mixed layer in not necessarily zero at the pycnocline—are consistent with those of Delhez and Deleersnijder [(2006), Ocean Dyn 56:139–150]—the residence time in a control domain vanishes at the open boundaries of this control domain—, it is necessary to consider a control domain that includes part of the pycnocline, in which the eddy diffusivity is assumed to be zero. Then, depending on the behaviour of the eddy diffusivity near the bottom of the mixed layer, the residence time may be seen to exhibit a discontinuity at the interface between the mixed layer and the pycnocline. If such a discontinuity exists, the residence time is non-zero in the former and zero in the latter. This is illustrated by analytical solutions obtained under the assumption that the eddy diffusivity is constant in the mixed layer.     

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.     

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.     

A closure approach with multi-scale mixing length,and its application to wind and shear stress profiles within the atmospheric boundary layer

A method to determine flow specific first-order closure for the turbulent flux of momentum in the atmospheric boundary layer (ABL) is presented. This is based on the premise that eddy viscosity is a flow rather than a fluid property, and the physically more realistic assumption that the transfer of momentum and other scalar quantities in a turbulent flow takes place by a large, but finite number of length scales, than the often used single length scale, the ‘mixing length’. The resulting eddy viscosity is flow specific and when applied to the study of the ABL, yields the vertical profiles of shear stress and mean wind velocity in good agreement with observations. The method may be extended to other types of turbulent flows, however it should be recognized that each type of flow may yield a different eddy viscosity profile. Using the derived eddy viscosity the paper presents simple analytical solutions of the ABL equations to determine observationally consistent wind speed and shear stress profiles in the ABL for a variety of practical applications including air pollution modelling.     

Numerical Simulation of Interaction of the Heavy Gas Cloud with the Atmospheric Surface Layer

The numerical time-dependent three-dimensional model [Kovalets, I.V. and Maderich, V.S.: 2001, Int. J. Fluid Mech. Res. 30, 410–429] of the heavy gas dispersion in the atmospheric boundary layer has been improved by parameterizing momentum and heat fluxes on the surface of Earth using Monin–Obukhov similarity theory. Three parameterizations of heat exchange with the surface of Earth were considered: (A) formula of Yaglom A.M. and Kader B.A. [1974, J. Fluid Mech. 62, 601–623] for forced convection, (B) interpolation formula for mixed convection and (C) similarity relationship for mixed convection [Kader, B.A. and Yaglom, A.M.: 1990, J. Fluid Mech. 212, 637–662]. Two case studies were considered. In the first study based on experiment of Zhu et al., J. Hazard Mater 62, 161–186], the interaction of an isothermal heavy gas plume with an atmospheric surface layer was simulated. It was found that stable stratification in the cloud essentially suppresses the turbulence in the plume, reducing the turbulent momentum flux by a factor of down to 1/5 in comparison with the undisturbed value. This reduction essentially influences velocities in the atmospheric boundary layer above the cloud, increasing the mean velocity by a factor of up to 1.3 in comparison with the undisturbed value. A simulation of cold heavy gas dispersion was carried out in the second case based on field experiment BURRO 8. It was shown that both forced and free convections under moderate wind speeds significantly influence the plume. The relative rms and bias errors of prediction the plume’s height were σ_H ≈ 30% and ɛ_H = − 10%, respectively, for parameterization B, while for A and C the errors were σ_H ≈ 80% and ɛ_H ≈ − 65%. It is therefore advised to use the simple parameterization B in dense gas dispersion models.