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.     

Experimental investigation of bubbly flow and turbulence in hydraulic jumps

Many environmental problems are linked to multiphase flows encompassing ecological issues, chemical processes and mixing or diffusion, with applications in different engineering fields. The transition from a supercritical flow to a subcritical motion constitutes a hydraulic jump. This flow regime is characterised by strong interactions between turbulence, free surface and air–water mixing. Although a hydraulic jump contributes to some dissipation of the flow kinetic energy, it is also associated with increases of turbulent shear stresses and the development of turbulent eddies with implications in terms of scour, erosion and sediment transport. Despite a number of experimental, theoretical and numerical studies, there is a lack of knowledge concerning the physical mechanisms involved in the diffusion and air–water mixing processes within hydraulic jumps, as well as on the interaction between the free-surface and turbulence. New experimental investigations were undertaken in hydraulic jumps with Froude numbers up to Fr = 8.3. Two-phase flow measurements were performed with phase-detection conductivity probes. Basic results related to the distributions of void fraction, bubble frequency and mean bubble chord length are presented. New developments are discussed for the interfacial bubble velocities and their fluctuations, characterizing the turbulence level and integral time scales of turbulence representing a “lifetime” of the longitudinal bubbly flow structures. The analyses show good agreement with previous studies in terms of the vertical profiles of void fraction, bubble frequency and mean bubble chord length. The dimensionless distributions of interfacial velocities compared favourably with wall-jet equations. Measurements showed high turbulence levels. Turbulence time scales were found to be dependent on the distance downstream of the toe as well as on the distance to the bottom showing the importance of the lower (channel bed) and upper (free surface) boundary conditions on the turbulence structure.     

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.     

Energy dissipation, flow resistance and gas-liquid interfacial area in skimming flows on moderate-slope stepped spillways

With the re-evaluation and revision of a number of design floods, several embankment overtopping protection systems have been developed and a common technique is the construction of a stepped spillway on the downstream slope. For such moderate slope stepped channels, detailed air–water flow measurements were performed in a large facility with a focus on the rate of energy dissipation, flow resistance, air–water interfacial areas and re-aeration rates. Past and present experimental results showed a significant aeration of the flow. The median dimensionless residual head was about 3 × d_c for the 21.8° sloping chute and smaller than that for flatter slopes (θ = 3.4° and 15.9°). The flow resistance results yielded an equivalent Darcy friction factor of about 0.25 implying a larger flow resistance for the 21.8° slope angle than for smaller slope angles. The re-aeration rate was deduced from the integration of the mass transfer equation using measured air–water interfacial areas and air–water flow velocities. The results suggested an increasing re-aeration rate with increasing rate of energy dissipation. The stepped invert contributed to intense turbulence production, free-surface aeration and large interfacial areas. The experimental data showed however some distinctive seesaw pattern in the longitudinal distribution of air–water flow properties with a wave length of about two step cavities. While these may be caused by the interactions between successive adjacent step cavities and their interference with the free-surface, the existence of such “instabilities” implies that the traditional concept of normal flow might not exist in skimming flows above moderate-slope stepped spillways.     

A numerical (LES) investigation of a shallow-water, mid-latitude, tidally-driven boundary layer

We investigate turbulent mixing in a tidally driven, mid-latitude, shallow-water basin. The study is carried out numerically at a laboratory-scale, using large-eddy simulation. We compared the results of the simulation with those of a correspondent purely oscillatory flow (Stokes boundary layer). The effect of rotation on the flow dynamics is twofold. First, rotation gives rise to a mean spanwise flow that concurs to redistribute the turbulent energy among the Reynolds stresses, in particular between the horizontal directions, thus increasing the mixing across the water column and thickening the layer where developed turbulence is observable. Second, the presence of the horizontal component of the background vorticity (latitude effect) breaks the symmetry between the two semi-cycles of the oscillation, since turbulence results suppressed/enhanced during the first/second semi-cycle. These two effects significantly modify the turbulent characteristics with respect to the purely oscillating flow, although the mechanisms that generates turbulence present similar features. The qualitative agreement between our results and some measurements carried out in two sites with characteristics similar to the case analyzed suggests that the outcomes here provided may be of general use for the analysis of mid-latitude, neutrally stratified, shallow-water basins mainly driven by semi-diurnal tidal currents.     

Two-phase flow insights into open-channel flows with suspended particles of different densities

The effect of particle density on the turbulent open-channel flow carrying dilute particle suspensions is investigated using two specific gravities and three concentrations of solid particles. The particles, identical in size and similar in shape, were natural sand and a neutrally buoyant plastic. The particles were fully suspended, and formed no particle streaks on the channel’s bed. Accordingly, the changes in the flow are attributed to the interactions between suspended particles and flow turbulence structures. Measurements were obtained by means of image velocimetry enabling simultaneous, but distinct, measurement of liquid and particle velocities. The experimental results show that, irrespective of particle specific gravity, particle suspension influences bulk velocity of flow and the Kármán coefficient, while friction velocity essentially remains constant. The results also show that particles in suspension modify local water turbulence over the flow depth, but in ways not accurately predicted using the customary parameters for characterizing turbulence modification.     

Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped spillways

We present and discuss the results of a comprehensive study addressing the non-aerated region of the skimming flow in steep stepped spillways. Although flows in stepped spillways are usually characterized by high air concentrations concomitant with high rates of energy dissipation, the non-aerated region becomes important in small dams and/or spillways with high specific discharges. A relatively large physical model of such spillway was used to acquire data on flow velocities and water levels and, then, well-resolved numerical simulations were performed with a commercial code to reproduce those experimental conditions. The numerical runs benefited from the ability of using multi-block grids in a Cartesian coordinate system, from capturing the free surface with the TruVOF method embedded in the code, and from the use of two turbulence models: the k-e{k{-}\varepsilon} and the RNGk-e{k{-}\varepsilon} models. Numerical results are in good agreement with the experimental data corresponding to three volumetric flow rates in terms of the time-averaged velocities measured at diverse steps in the spillway, and they are in very satisfactory agreement for water levels along the spillway. In addition, the numerical results provide information on the turbulence statistics of the flow. This work also discusses important aspects of the flow, such as the values of the exponents of the power-law velocity profiles, and the characteristics of the development of the boundary layer in the spillway.     

Flow structure and turbulence characteristics downstream of a spanwise suspended linear array

Laboratory experiments are conducted to quantify the mean flow structure and turbulence properties downstream of a spanwise suspended linear array in a uniform ambient water flow using Particle Tracking Velocimetry. Eighteen experimental scenarios, with four depth ratios (array depth to water column depth) of 0.35, 0.52, 0.78, and 0.95 and bulk Reynolds number (length scale is the array depth) from 11,600 to 68,170, are investigated. Three sub-layers form downstream of the array: (1) an internal wake zone, where the time-averaged velocity decreases with increasing distance downstream, (2) a shear layer which increases in vertical extent with increasing distance downstream of the array, and the rate of the increase is independent of the bulk Reynolds number or the depth ratio, and (3) an external wake layer with enhanced velocity under the array. The location of the shear layer is dependent on the depth ratio. The spatially averaged and normalized TKE of the wake has a short production region, followed by a decay region which is comparable to grid turbulence decay and is dependent on the depth ratio. The results suggest that the shear layer increases the transfer of horizontal momentum into the internal wake zone from the fluid outside of the array and that the turbulence in the internal wake zone can be modeled similarly to that of grid turbulence.     

Analytical model for vertical velocity profiles in flows with submerged shrub-like vegetation

An analytical solution for the vertical profiles of the horizontal velocity of channel flow with submerged shrub-like vegetation is investigated in this paper. At first, a shape function is proposed to fit the diameter change of different types of shrub-like vegetation. Using the momentum theorem and the mixing-length turbulence model, an analytical solution for the vertical profile of the horizontal velocity within the vegetation is obtained. The velocity distribution of the whole column is determined in tandem with the logarithmic velocity profile above the vegetation. The solution is compared with experimental data in excellent agreement. The results show that the flow above the vegetation has a logarithmic velocity profile while the flow within the vegetation is impacted greatly by the shape and density of vegetation. The flows within shrub-like vegetations are non-uniform and vary inversely with the shrub diameter.     

Turbulent flow characteristics and drag over 2-D forward-facing dune shaped structures with two different stoss-side slopes

The present paper explores the characteristics of turbulent flow and drag over two artificial 2-D forward-facing waveform structures with two different stoss side slopes of $50^{\circ }$ and $90^{\circ },$ respectively. Both structures possessed a common slanted lee side slope of $6^{\circ }.$ Flume experiments were conducted at the Fluvial Mechanics Laboratory of Indian Statistical Institute, Kolkata. The velocity data were analyzed to identify the spatial changes in turbulent flow addressing the flow separation region with recirculating eddy, the Reynolds stresses, the turbulent events associated with burst-sweep cycles and the drag over two upstream-facing bedforms for Reynolds number $Re_h=1.44\times 10^5.$ The divergence at the stoss side slope between the two structures revealed significant changes in the mean flow and turbulence. Comparison showed that during the flood-tide condition there was no flow separation region on the gentle lee side of the structure with smaller slope at the stoss side, while for the other structure with vertical stoss side slope a thick flow separation region with recirculating eddy was observed at the gentle lee side just downstream of the crest. The recirculating eddy induced on the lee-side had a strong influence on the resistance that the structure exerts to the flow due to loss of energy through turbulence. In contrast, a great amount of reduction in drag was observed in the case of smaller stoss side sloped structure as there was no flow separation. The quadrant analysis was also used to highlight the turbulent event evolution along the bed form structures under flood-tide conditions.     

Advection and resulting CO2 exchange uncertainty in a tall forest in central Germany

Potential losses by advection were estimated at Hainich Forest, Thuringia, Germany, where the tower is located at a gentle slope. Three approaches were used: (1) comparing nighttime eddy covariance fluxes to an independent value of total ecosystem respiration by bottom-up modeling of the underlying processes, (2) direct measurements of a horizontal CO2 gradient and horizontal wind speed at 2 m height in order to calculate horizontal advection, and (3) direct measurements of a vertical CO2 gradient and a three-dimensional wind profile in order to calculate vertical advection. In the first approach, nighttime eddy covariance measurements were compared to independent values of total ecosystem respiration by means of bottom-up modeling of the underlying biological processes. Turbulent fluxes and storage term were normalized to the fluxes calculated by the bottom-up model. Below a u(*) threshold of 0.6 m/s the normalized turbulent fluxes decreased with decreasing u(*), but the flux to the storage increased only up to values less than 20% of the modeled flux at low turbulence. Horizontal advection was measured by a horizontal CO2 gradient over a distance of 130 m combined with horizontal wind speed measurements. Horizontal advection occurred at most of the evenings independently of friction velocity above the canopy. Nevertheless, horizontal advection was higher when u(*) was low. The peaks of horizontal advection correlated with changes in temperature. A full mass balance including turbulent fluxes, storage, and horizontal and vertical advection resulted in an increase of spikes and scatter but seemed to generally improve the results from the flux measurements. The comparison of flux data with independent bottom-up modeling results as well as the direct measurements resulted in strong indications that katabatic flows along the hill slope during evening and night reduces the measured apparent ecosystem respiration rate. In addition, anabatic flows may occur during the morning. We conclude that direct measurements of horizontal and vertical advection are highly necessary at sites located even on gentle hill slopes.     

A model of vertical distribution of suspended matter in an open channel flow

A quasi-stationary model of vertical distribution of concentration of suspended particular matter in the bottom layer of 1D open channel with a sloped bottom and varying free surface slope is discussed. The model proceeds from the balance between the turbulent diffusion and settling with the buoyancy flux effects on the medium turbulence neglected. The model outcome is formulated in the form of an analytic formula for the vertical distribution of concentration. It is shown that the derived formula embraces two basic types of vertical distribution of concentration, one with a monotonic decrease of concentration gradient and the other with a gradient maximum (lutocline) located at some distance from the bottom. The first distribution type realizes for a relatively large settling velocity or low intensity of turbulence and the second type for a small settling velocity or high intensity of turbulence. The skill of the model to mimic realistic situations is demonstrated on data measured in the Jiaojiang Estuary (China).     

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.     

Instantaneous transport of a passive scalar in a turbulent separated flow

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

Turbulence Perturbations in the Neutrally Stratified Surface Layer due to the Interaction of a Katabatic Flow with a Steep Ridge

Turbulence measurements were performed in Antarctica, on the Nansen Ice Sheet, dominated by westerly katabatic winds. The measurements were taken at two sites aligned with the katabatic wind fall-line. The measuring stations were located in the middle of a wide, flat iced area at a distance of 14 km from the base of a sloping surface and at the top of a steep ridge (Inexpressible Island). The aim was to investigate the perturbation of turbulence close to the ground generated by the interaction of the flow with the ridge. We present an analysis comparing the data measured at the upstream unperturbed station with those at the top of the obstacle. Moments and spectra of velocity components have been calculated for almost steady periods. The topography and roughness change produce a combined effect on the flow acceleration (of the opposite sign) and on the turbulent stresses (of the same sign). Spectra of velocity components measured at the top of the ridge and scaled by unperturbed quantities evidence an increment of energy in the high frequency subrange with respect to the up-stream flow. Moreover, the horizontal velocity components display a shift in turbulence maximum towards higher frequencies. The vertical velocity spectrum exhibits an energy increment at low frequencies with respect to the upstream spectrum.     

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.     

Verification of a 3D CFD model for vertical slot fish-passes

In the present work, we verified a 3D computational fluid dynamics model for vertical slot fish-passes (VSFs) that employs the renormalization-group k-epsilon turbulence model (RNG KE) and the volume of fluid (VOF) method. We compared model calculations with experiments in two pool designs T1 and T2 of an experimental VSF and with 2D calculations using the shallow water equations (SWE) and the standard k-epsilon (2D SKE) model. Calculations of the 3D model showed (1) good agreement with experiments and 2D calculations in predicting mean flow velocities, (2) better performance in the determination of the water surface in the VSF, which is attributed to the accurate VOF method, (3) superior prediction of turbulence characteristics than the 2D model, which is due to the 3D RNG KE model that overcomes the problem of turbulence overestimation of the 2D SKE model, and to the fact that the 3D model takes into account the 3D features of the flow in the fish pass. Moreover, the present 3D calculations showed that the common assumptions in VSFs that (1) the flow is 2D, and (2) the simulation of 4 pools of a VSF is sufficient to obtain satisfactory results, are not always valid. Flow can be considered as 2D only in pool design T2 and for certain geometries and flow characteristics in pool design T1; while, eventually, all the pools of a fish pass need to be modeled to ensure accurate results. Finally, the present work illustrates the need to perform fish experiments simultaneously with flow experiments.     

Large-scale turbulent structure of uniform shallow free-surface flows

The hydrodynamics of super- and sub-critical shallow uniform free-surface flows are assessed using laboratory experiments aimed at identifying and quantifying flow structure at scales larger than the flow depth. In particular, we provide information on probability distributions of horizontal velocity components, their correlation functions, velocity spectra, and structure functions for the near-water-surface flow region. The data suggest that for the high Froude number flows the structure of the near-surface layer resembles that of two-dimensional turbulence with an inverse energy cascade. In contrast, although large-scale velocity fluctuations were also present in low Froude number flow its behaviour was different, with a direct energy cascade. Based on our results and some published data we suggest a physical explanation for the observed behaviours. The experiments support Jirka’s [Jirka GH (2001) J Hydraul Res 39(6):567–573] hypothesis that secondary instabilities of the base flow may generate large-scale two-dimensional eddies, even in the absence of transverse gradients in the time-averaged flow properties.     

Measurements and modeling of open-channel flows with finite semi-rigid vegetation patches

The hydrodynamics of flows through a finite length semi-rigid vegetation patch (VP) were investigated experimentally and numerically. Detailed measurements have been carried out to determine the spatial variation of velocity and turbulence profiles within the VP. The measurement results show that an intrusion region exists in which the peak Reynolds stress remains near the bed. The velocity profile is invariant within the downstream part of the VP while the Reynolds stress profile requires a longer distance to attain the spatially invariant state. Higher vegetation density leads to a shorter adjustment length of the transition region, and a higher turbulence level within the VP. The vegetation density used in the present study permits the passing through of water and causes the peak Reynolds stress and turbulence kinetic energy each the maximum at the downstream end of the patch. A 3D Reynolds-averaged Navier–Stokes model incorporating the Spalart–Allmaras turbulence closure was employed subsequently to replicate the flow development within the VP. The model reproduced transitional flow characteristics well and the results are in good agreement with the experimental data. Additional numerical experiments show that the adjustment length can be scaled by the water depth, mean velocity and maximum shear stress. Empirical equations of the adjustment lengths for mean velocity and Reynolds stress were derived with coefficients quantified from the numerical simulation results.