Turbulent Open Channel Flow Research Articles

Grain-size distribution in suspension through open channel turbulent flow using space-fractional ADE

The main aim of the present study is to develop a mathematical formulation that can describe the grain-size distribution (GSD) of non-uniform sediments in suspension over erodible sediment beds in a wide open channel under non-equilibrium conditions. The two important characteristics of sediment particles, such as non-local mixing and the hiding-hindering effect during settling, has been considered in the current study. The traditional advection–diffusion equation (ADE) is taken in the modified form as fractional ADE which is capable of capturing non-local movement of particles unlike the traditional diffusion theory where particles jump within a restricted distance along the vertical direction over a small time interval. The equation is further modified for any kth class of non-uniform sediment and the effect of non-local movement is included in the expression of depth averaged sediment diffusivity also. The settling velocity of a particle is taken in a form that contains the effect of hiding and hindering due to the presence of non-uniform particles in the flow. The space-fractional derivative is taken in the Caputo sense where the order α of the fractional derivative varies from 1<α≤2. The non-local effect is considered in the bottom and top boundary conditions also and the governing equation with boundary and initial condition have been solved by Chebyshev collocation method along with Euler’s backward method. The temporal variation of concentration profiles for different size particles is studied by varying α and it is observed that the magnitude of concentration decreases for each size as α increases. Non-local effect on bottom concentration for different size particle is also studied and it is seen that overshooting of bottom concentration gradually decreases as α increases for a particular size. Sensitivity analysis of α on GSD at different heights also has been done. The model has been validated for GSD under equilibrium conditions with available experimental data and it is found that the model aligns well when the non-local mixing effect is taken into account. At the end, an error analysis has been conducted to confirm the accuracy of the presented model.

Influence of particle density on turbulence characteristics over a rough surface

The objective of the study is to use a 3D Acoustic Doppler Velocimeter (ADV) to gauge the typical flow and turbulence characteristics within a non-uniform open channel. The findings of experimental examinations of the subcritical flow along the channel are presented in this work. The behavior of sand grains in turbulent open channel flow across porous and rough bed surfaces was examined in laboratory research, and the results were obtained. The properties of turbulent flow, i.e., turbulence intensity, turbulent kinetic energy, and Reynolds shear stresses, are determined from ADV data. The continuity equation and the Reynolds equation of open-channel flow have been used to build theoretical formulations for the velocity distribution and Reynolds stress distribution in the vertical direction. Measured profiles of vertical velocity and Reynolds stress are compared to the derived expressions. The impact of the size of particles on the distribution of mean flow characteristics is discussed. This work provides a novel origin for the profile and analyzes the behavior of the vertical velocity distribution in the region where fully formed turbulence is dominating in open channels using the Navier–Stokes equations. In comparison to other sand roughness, Chopan sand bed (with greater density) exhibits the strongest turbulence intensities in both vertical and streamwise direction just next to the bed when away from the channel boundary. In contrast to flow across a rough surface, the variance ranges between 150 and 250% concerning the channel bed’s roughness type, impacting the velocity triple products that signifies transfer of turbulent kinetic energy.

Turbulent stratified open channel flow with solar heating up to Pr=7 using Direct Numerical Simulation

This paper investigates the turbulent structure of stratified open-channel flow subjected to a radiative volumetric heat source modelled by the Beer–Lambert law, for Prandtl numbers (Pr) varying from 0.07 to Pr=7. Direct Numerical Simulation (DNS) was employed to model the open-channel flow. To overcome the increased computational resources required to resolve the thermal fields when Pr>1, a multi-resolution method using quadratic interpolation was employed to resolve the temperature and momentum fields on different spatial and temporal resolutions. This scheme was implemented in an in-house computational fluid dynamics (CFD) code. To further reduce the computation cost, the DNS of Pr=2.2 and 7 fluids were initialised using the outputs of minimal channel simulations. The simulations were conducted for Pr=0.07, 0.22, 0.71, 2.2, and 7 under neutral (λ=0), near-neutral (λ=0.1), and stable (λ=0.5) thermal stratification. The results demonstrate that Pr significantly affects the flow structure and turbulence characteristics of stratified flows, particularly near the free surface. This includes higher velocity, temperature gradient, and buoyancy effects for Pr=7 compared to lower Pr values. For stratified Pr=7 flow, examination of the Reynolds stresses and turbulent heat flux reveals significant damping of turbulence near the surface, with flow displaying near-laminar behaviour.

Numerical investigation of turbulent flow over a randomly packed sediment bed using a variable porosity continuum model

A large eddy simulation (LES) is performed for a turbulent open channel flow over a porous sediment bed at permeability Reynolds number of ReK∼2.56 (Reτ = 270) representative of aquatic systems. A continuum approach based on the upscaled, volume-averaged Navier−Stokes (VaNS) equations is used by defining smoothly varying porosity across the sediment water interface (SWI) and modeling the drag force in the porous bed using a modified Ergun equation with Forchheimer corrections for inertial terms. The results from the continuum approach are compared with a pore-resolved direct numerical simulation (PR-DNS) in which turbulent flow over a randomly packed sediment bed of monodispersed particles is investigated [Karra et al.,J. Fluid Mech. 971, A23 (2023)] A spatially varying porosity profile generated from the pore-resolved DNS is used in the continuum approach. Mean flow, Reynolds stress statistics, and net momentum exchange between the freestream and the porous bed are compared between the two studies, showing reasonably good agreement. Small deviations within the transitional region between the sediment bed and the freestream as compared to the PR-DNS results are attributed to the local protrusions of particles in a randomly packed bed that are absent in the continuum approach but are present in the PR-DNS. A better representation of the effective permeability in the top transition layer that accounts for roughness effect of exposed particles is necessary. The continuum approach significantly reduces the computational cost, thereby making it suitable to study hyporheic exchange of mass and momentum in large scale aquatic domains with combined influence of bedform and bed roughness.

Physics-informed data-driven reconstruction of turbulent wall-bounded flows from planar measurements

Obtaining accurate and dense three-dimensional estimates of turbulent wall-bounded flows is notoriously challenging, and this limitation negatively impacts geophysical and engineering applications, such as weather forecasting, climate predictions, air quality monitoring, and flow control. This study introduces a physics-informed variational autoencoder model that reconstructs realizable three-dimensional turbulent velocity fields from two-dimensional planar measurements thereof. Physics knowledge is introduced as soft and hard constraints in the loss term and network architecture, respectively, to enhance model robustness and leverage inductive biases alongside observational ones. The performance of the proposed framework is examined in a turbulent open-channel flow application at friction Reynolds number Reτ=250. The model excels in precisely reconstructing the dynamic flow patterns at any given time and location, including turbulent coherent structures, while also providing accurate time- and spatially-averaged flow statistics. The model outperforms state-of-the-art classical approaches for flow reconstruction such as the linear stochastic estimation method. Physical constraints provide a modest but discernible improvement in the prediction of small-scale flow structures and maintain better consistency with the fundamental equations governing the system when compared to a purely data-driven approach.

Evaluation of spatial resolution effects in rough wall-bounded turbulence

This study investigates the impact of insufficient spanwise spatial resolution on the measurement accuracy of streamwise velocity fluctuations over rough walls. We use a direct numerical simulation (DNS) database of turbulent open-channel flow over three-dimensional sinusoidal roughness with varied wavelengths and roughness heights. Employing a triple decomposition, we investigate both the attenuation of the turbulent fluctuations (about the local mean), u′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u^\\prime$$\\end{document} and the dispersive stresses (roughness-induced fluctuations of the time-averaged mean about the global mean), U~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ilde{U}}$$\\end{document}. A boxcar filter on DNS data is applied to investigate the effects of spanwise spatial filtering on these quantities. Our analysis reveals the significance of two key length-scale ratios for velocity measurements over rough walls: the wire length relative to the spatially and temporally plane-averaged Kolmogorov scale at the roughness crest (l/⟨η⟩k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\langle \\eta \\rangle _k$$\\end{document}), and the wire length relative to the roughness spanwise wavelength (l/Λy\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\Lambda _y$$\\end{document}). We observe that maintaining l/⟨η⟩k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\langle \\eta \\rangle _k$$\\end{document} constant while increasing l/Λy\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\Lambda _y$$\\end{document} attenuates the variance of U~\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ ilde{U}}$$\\end{document} and u′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u^\\prime$$\\end{document} within the roughness sublayer. When fixing l/Λy\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\Lambda _y$$\\end{document}, an increase in l/⟨η⟩k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$l/\\langle \\eta \\rangle _k$$\\end{document} influences the turbulent fluctuations across all wall-normal locations. These findings highlight the necessity of considering both length scales when evaluating spanwise spatial resolution in turbulence measurements over rough walls.

Mapping Microplastic Movement: A Phase Diagram to Predict Nonbuoyant Microplastic Modes of Transport at the Particle Scale.

Microplastics pose numerous threats to aquatic environments, yet understanding their transport mechanisms remains limited. Drawing from natural sediment research provides valuable insights to address this knowledge gap. One key dimensionless number used to describe sediment transport is the transport stage, referring to the ratio between the flow shear velocity and the particle settling velocity. However, variations in physical properties, such as shape and density, raise concerns about the applicability of existing sediment transport theories to microplastics. To address this challenge, we employed a physical modeling approach, examining 24 different nonbuoyant microplastic particles in a turbulent open channel flow. Utilizing 3D particle tracking, a total of 720 trajectories were recorded and analyzed. Microplastic particles exhibited transport modes akin to natural sediments, including rolling/sliding, saltation, and suspension. The transport stage strongly correlated with these modes, as well as with the mean forward velocity and mean position in the water column. Notably, particle shape emerged as a critical factor influencing transport dynamics. Due to their lower settling velocity, fibers tended to stay closer to the water surface with lower forward velocities compared to spheres. Based on the laboratory results, a new phase diagram for microplastics is introduced analogous to an existing diagram for sediments.

Onset for Active Swimming of Microorganisms to Shape Their Transport in Turbulent Open Channel Flows

AbstractResearch on active particles has primarily focused on transport in relatively weak flows, during which their active swimming plays a significant role. However, in natural or manmade waterways, the ambient flow velocity and water depth can be on the order of approximately 1 m/s and 1 m, respectively, generating turbulent diffusion that may be strong enough to potentially dominate the transport process, so that the active swimming might be negligible. In this paper, we propose a theoretical framework aiming at identifying the threshold at which the effects of active swimming become significant, under conditions of insufficient data for motion statistics of swimmers. While deriving the governing equation, we find that only the vertical component of the mean swimming has the potential to significantly influence the transport process. This manifests as the characteristic of inducing a non‐uniform vertical concentration distribution, in competition with the mechanism of turbulent diffusion, which leads to a uniform distribution. We obtain the analytical solution for the vertical concentration distribution, with the key dimensionless parameter α representing the interplay between the active swimming and turbulent diffusion. The threshold is found to be approximately at the order of magnitude of α ∼ 0.1, below which active swimming is considered negligible. The theoretical predictions are validated by numerical simulations employing Direct Numerical Simulation and particle tracking methods. Applying the theory to two types of microorganisms transported under different flow conditions suggests that there are typical scenarios where the active swimming is negligible, and the swimmers can be treated as passive particles.

Effects of steepness on turbulent heat transfer over sinusoidal rough surfaces

We conducted a direct numerical simulation (DNS) study to investigate the impact of surface undulation steepness on rough wall turbulent heat transfer. The flow geometry was turbulent open-channel flow over three-dimensional sinusoidal rough surfaces. To examine the effects of steepness, we systematically varied the streamwise and spanwise wavelengths of the sinusoidal roughness while keeping the roughness height constant. The friction Reynolds number ranged from 180 to 600, and we considered a passive scalar with the fluid Prandtl number was 0.7, assuming air flow conditions. In the fully rough regime, the velocity roughness function is expressed as a function of the inner-scaled equivalent sand grain roughness ks+ independent of steepness, whereas the steeper surfaces with shorter wavelengths result in larger temperature roughness functions at the same ks+ value. Analysis of the physical mechanisms that increases the roughness function shows that the pressure drag primarily contributes to the increase in the velocity roughness function, while the temperature roughness function is mainly augmented by the roughness-induced wall heat transfer term, correlating with the steepness of the surface undulations. It is also suggested that the effective slope, which quantifies the steepness of rough surfaces, could improve the predictive accuracy of existing correlations for the temperature roughness function.

Direct numerical simulation of open-channel flow over a heterogeneous particle bed at low relative submergence

This study investigates turbulent open-channel flows over beds of irregularly arranged particles, using direct numerical simulations at a friction Reynolds number of Reτ=300. Two distinct cases are examined: a polydisperse bed (P800) composed of multiple layers of randomly distributed spheres of varying sizes, and a monodisperse bed (M1015) formed by a random distribution of uniform sized spheres, with a bottommost single layer of varied-sized particles to introduce realistic randomness. Our investigation unveils a rich network of low- and high-speed streaks within the flow field, exhibiting distinctive behaviors in different bed configurations. The P800 case presents a poorly organized flow pattern induced by the varied particle sizes and arrangements, while the M1015 case shows a more regular flow pattern, marked by larger streaks. We also observe that total wall shear stress is substantially influenced by surface roughness-induced drag, extending beyond the effects documented in existing studies of open-channel flows. The present study reveals intricate secondary flow patterns over irregular particle beds. Large-scale circulations are discerned around particle crests in the P800 case and localized circulations with increased turbulence in the M1015 case. Furthermore, analysis of Reynolds stress tensor components indicates that roughness disrupts coherent turbulent eddies, consequently mitigating peak stress. We quantify correlations between drag force and local fluid velocity fluctuations. Notably, a larger deviation in drag is observed in the P800 case compared to M1015, accentuating the influence of particle size and distribution on fluid–particle interactions.

Settling velocity of microplastics in turbulent open-channel flow

The settling behavior of microplastics (MPs) plays a pivotal role in their transport and fate in aquatic environments, but the dominant mechanisms and physics governing the settling of MPs in rivers remain poorly understood. To gain mechanistic insights into the velocity lag of MPs in an open-channel flume under different turbulent flow conditions, an experimental study was conducted using three types of MPs: polystyrene, cellulose acetate, and acrylic, of sphere-shaped particles with diameters ranging from 1 mm to 5 mm. A particle tracking technique was employed to record and analyze the MPs velocity within turbulent flows. The results showed a variation in the vertical settling velocity of MPs ωMP ranging from −26 % to +16 %, when compared to their counterparts in still water (ωs). A new formula for the drag coefficient (Cd) of MP particles was developed by introducing the suspension number (u∗/ωs). The developed Cd formula was used to calculate the resultant velocity lag VMP, with a mean relative error of 16 % compared with the measured values. Further, the study highlighted that the MPs with large Stokes numbers are mainly driven by their own inertia and turbulence has less influence on their settling behavior. This study is crucial for understanding the settling behavior of MPs in turbulent flows and developing their transport and fate models for MPs in riverine systems.

Fractional entropy-based models for S-type velocity distributions in turbulent open-channel flows and turbulent Couette flows

Fractional entropy-based models for S-type velocity distributions in turbulent open-channel flows and turbulent Couette flows

Turbulent kinetic energy budget of sediment-laden open-channel flows: bedload-induced wall-roughness similarity

New experiments in highly turbulent, steady, subcritical and uniform water open-channel flows have been carried out to measure the mean turbulent kinetic energy (TKE) budget of sediment-laden boundary layer flows with two sizes (dp = 3 mm and 1 mm) of Plexiglas particles $({\rm relative\ density}\ = 1.192)$ . The experiments covered energetic sediment transport conditions (Shields number of $0.35 &lt; \theta &lt; 1.2$ ) ranging from non-capacity to full-capacity flows in bedload-to-suspension-dominated transport modes (suspension number of $0.5 &lt; {w_s}/{u_\ast } &lt; 1.3$ where ${w_s}$ is the settling velocity and $u_*$ is the friction velocity) and for weakly to highly inertial, finite size turbulence-particle conditions (Stokes number of 0.1 &lt; St &lt; 3.5 and dp/η &gt; 10 where $\eta$ is the Kolmogorov length scale). It was shown that the effects of sediments on the TKE budget are very pronounced in all large particle experiments for which a bedload layer of several grain diameter thickness is developed above the channel bed. When compared with the corresponding reference clear-water flows, the TKE shear-production rate for the 3 mm particle flows is strongly reduced in the wall region corresponding to the bedload layer. This turbulence damping is seen to increase with sediment load until full capacity for flows with constant Shields value, as well as with Shields number value. Inside this damped TKE shear-production zone, a distinct peak of maximal turbulence production appears to coincide with the upper edge of the bedload layer delimited by a sharp gradient in mean sediment concentration. This vertically upshifted peak of TKE production is accompanied by an enhanced net downward oriented TKE flux when compared with the reference clear-water flows. The downward diffused TKE is found to act in the bedload layer as a local energy source in reasonable balance with the sediment transport term. The mechanism behind this downward TKE transport was further analysed on the basis of coherent flow structure dynamics controlled by ejection- and sweep-type events. The agreement between the height of downward directed mean TKE flux and the height below which sweep-type events dominate the Reynolds shear-stress contribution over ejections, revealed the leading role played by sweeps in mean TKE transport. This agreement holds for all reference clear-water flows supporting the well-known wall-roughness-induced dominance of the sweep contribution in turbulent, rough clear-water boundary layer flows. Furthermore, for all 3 mm particle flows, the two referred to transition levels were significantly and similarly upshifted to the upper edge of the bedload layer. Only for these sediment-laden flows, the bedload layer thickness is seen to exceed the wall-roughness sublayer of the reference clear-water flows. This supports a strong analogy between wall-roughness effects in clear-water flows and bedload layer effects in sediment-laden flows, on the mean TKE budget induced by a similarly modified coherent flow structure dynamics. The bedload layer-controlled wall roughness is finally confirmed by the good prediction of the wall-roughness parameter ks of the logarithmic velocity distribution. An empirical formulation fitting the presented measurements is presented, valid over the range of Shields number values covered herein.

Roll waves in a predictive model for open-channel flows in the smooth turbulent case

A depth-averaged model for turbulent open-channel flows with breaking roll waves on a sloping smooth bottom is derived under an assumption of independence between the wall turbulence and the roller turbulence. The model includes four variables – the water depth, the average velocity, and two variables called enstrophy, the shear enstrophy and the roller enstrophy – which take into account the deviations of the velocity with respect to its depth-averaged value due to shear effect and roller turbulence, respectively. The four equations of the model are the mass, momentum, energy and shear enstrophy balance equations, with the mathematical structure of the Euler equations of compressible fluids, with an additional transport equation and with source terms. The system is hyperbolic. The roller enstrophy is created by shocks. A non-zero value of the roller enstrophy indicates a breaking wave and a turbulent roller. The model is solved by a fast and well-known numerical scheme, with an explicit finite-volume method in one step. The model is used to simulate periodic and natural roll waves with a good agreement with existing experimental results. There is no parameter to calibrate in the model, which gives it a predictive character.

Direct numerical simulation of momentum and scalar internal boundary layers

Direct numerical simulations (DNS) of turbulent open channel flow are performed to study and compare momentum and scalar internal boundary layers (IBL). An internal boundary layer (IBL) forms when a turbulent boundary layer is subjected to heterogeneous surface conditions. For example, a momentum IBL forms with a change in surface roughness and a scalar IBL forms due to a localised heat flux. Momentum IBLs are simulated using both a streamwise-varying roughness body forcing technique and a streamwise-varying wall shear stress. Passive scalar IBLs are simulated using both streamwise-varying scalar wall values and wall fluxes, for a homogeneous smooth wall. The roughness body forcing model is shown to reproduce the same IBL features as with the explicitly resolved roughness study of Rouhi et al. (2019), but at a reduced cost. Three common IBL detection methods are employed to estimate the power-law exponents in the growth rates of the IBL. The exponents for the momentum IBL cases are typically less than 0.7 for these methods, smaller than for the scalar-analogues of these methods. Furthermore, we analyse the streamwise variation of the root-mean-square wall-normal (vertical) velocity. We find that the ‘diffusion analogy’, or that momentum and scalar IBLs behave similarly, may not be an appropriate assumption, especially for rough-to-smooth transitions for momentum IBLs.

Direct numerical simulation of flow in open rectangular ducts

We study turbulent flow in open channels with a free surface and rectangular cross-section, for various Reynolds numbers and duct aspect ratios. Direct numerical simulations are used to obtain accurate characterization of the secondary motions, which are found to be more intense than in closed ducts, and to scale with the bulk, rather than with the friction velocity. A notable feature of open-duct flows is the presence of a velocity dip, namely the peak velocity is achieved at some depth underneath the free surface. We find that the depth of the velocity peak increases with the Reynolds number, and correspondingly the flow becomes more symmetric with respect to the horizontal midplane. This is also confirmed from the change of the topology of the secondary motions, which exhibit a strong corner circulation at the free-surface/wall corners at low Reynolds number, which, however, weakens at higher $Re$ . The structure of the mean velocity field is such that the log law applies with good approximation in the direction normal to the nearest wall, which allows us to explain why predictive friction formulae based on the hydraulic diameter concept are successful. Additional analysis shows that the secondary motions account for a large fraction of the frictional drag (up to $15$ %).

The role of the in-plane solidity on canopy flows

Turbulent open channel flows developing above submerged canopies made of slender cylinders mounted perpendicular to the channel bed are known to be largely governed by the solidity parameter$\lambda =dh/\Delta S^2$($d$and$h$being the diameter and height of the filament, and$\Delta S$the average spacing between filaments). When the filaments are sufficiently slender, the ratio between the height of the stems and the spacing sets the hydrodynamic regime developing inside and outside the canopy. This ratio also establishes the conditions leading to the transition from a dense to a sparse canopy flow regime (Nepf,Annu. Rev. Fluid Mech., vol. 44, 2012, pp. 123–142). In a previous, companion numerical investigation, Montiet al.(J. Fluid Mech., vol. 891, 2020, A9) used large eddy simulation (LES) to study the influence of the canopy height on the onset of the different regimes without modifying the average spacing$\Delta S$between the stems. In that LES study, we were looking at the complementary situation in which the height of the stems is constant while the filaments’ number density of the canopy is changed. It was found that for low values of$\lambda$(i.e. sparse or moderately dense canopies:$\lambda \lessapprox 0.26$), the flows sharing the value of the solidity obtained by either varying$h$or$\Delta S$are very similar. Differently, for higher values of$\lambda$(i.e. in denser canopies), the effects of$h$and$\Delta S$start to diverge although sharing the same nominal value of$\lambda$. In this paper, we analyse the different physical mechanisms that come into play for dense configurations obtained by varying either$\Delta S$or$h$. In particular, we focus on the most relevant length scales and carry out a detailed analysis of the flows using a triple decomposition approach. We show that the inner region of dense canopy flows, characterised by tall stems, is dominated by wall-normal sweeps delivering high momentum in the wall vicinity. Here, the impenetrability condition of the bed redistributes the available momentum in the wall-parallel directions re-energising an otherwise stagnating flow. Differently, in densely packed canopies, the penetration of the outer jet and the momentum transfer from the external flow are limited by the decreasing value of the wall-parallel permeabilities leading to different behaviours, including a reduction of the total drag offered by the canopy.

Turbulence effect on total mechanical energy budget and energy loss of turbulent flows with different hydraulic regimes in open-channel transitions

ABSTRACT In this study, a modified form of the total mechanical energy budget equation is developed for 3-D turbulent flows with different hydraulic regimes in open-channel transitions, from which the effect of all turbulence parameters can be evaluated by applying some equalizations and RANS numerical simulations. The total energy equation is also used to extract an explicit relationship for energy loss based on turbulence parameters. The findings are presented in the form of the application of the relationship to calculate the energy loss based on simulation results for subcritical turbulent flow and hydraulic jump in open-channel transitions, which leads to identifying the effect of non-homogeneity and anisotropy of turbulence on flow energy balance. The results show that the work done by viscous shear stresses, the viscous diffusion of turbulence, and the turbulent diffusion have little to no effect on the total mechanical energy budget of open-channel turbulent flows; instead, the effect of the variations of turbulent kinetic energy and the work done by turbulence stresses is more significant. The benefit of using the modified energy equation is demonstrated by the potential for evaluating the details that were not previously considered.

A Critical Review of Turbulence Characteristics in Open Channel Flow

Abstract: This study subject encompasses a comprehensive evaluation of the available literature on turbulence in open channel flows. Open channel flows are characterized by intricate fluid dynamics, including the production of turbulent eddies and vortices that can profoundly alter transport processes and mixing of diverse fluids. The paper addresses the numerous forms of turbulence that can occur in open channels, such as coherent structures, secondary currents, and bed-generated turbulence. We investigate the elements that determine the intensity and features of these turbulent flows, including channel geometry, flow velocity, fluid properties, and roughness of the channel substrate. The paper also assesses the current theoretical models used to characterise open channel turbulence and the experimental techniques used to quantify and demonstrate turbulent flows in open channels. By critically scrutinising the strengths and limits of the current literature, this review outlines the essential research gaps that need to be addressed to expand our understanding of turbulent open channel flows. This study contributes to the development of enhanced models and techniques for managing and modulating open channel flows in diverse applications.

Coherent structure modification by a shear acting at the surface of a turbulent open channel

Recent experiments in the river Seine have revealed the presence of persistent large rolls. This finding has motivated the present numerical study of a turbulent open channel flow. Our pseudo-spectral direct numerical simulations are aimed at understanding how the shear at the surface, for instance produced by an external wind, can change vortical structures in the bulk. Simulations are run at a Reynolds number in the range [5times 10^3div 10^4], in line with similar laboratory experiments. We investigate how flow structures located near the bottom wall, near the surface or inside the bulk are modified by a surface shear. Statistical signatures are extracted through Fourier analysis of the simulated fields, and typical wavelengths of vortices or streaks are computed. Moreover, instantaneous fields are used to show the existence of upwelling and downwelling motions. These motions can be hindered by the presence of a large enough surface shear. This condition turns out to be necessary for the existence of streaks at the surface as well. Our investigation clarifies the dynamics of vortices in an open channel flow at moderate Reynolds number, indicating that unsteady vortex structures are indeed present, but the existence of long coherent rolls cannot be accounted for by the sole presence of shear at the surface. Numerical studies with a much longer domain and possibly at higher Reynolds numbers are needed to provide a firm answer to the question.