Dominant features in three-dimensional turbulence structure: comparison of non-uniform accelerating and decelerating flows

The results are presented from an experimental study to investigate three-dimensional turbulence structure profiles, including turbulence intensity and Reynolds stress, of different non-uniform open channel flows over smooth bed in subcritical flow regime. In the analysis, the uniform flow profiles have been used to compare with those of the non-uniform flows to investigate their time-averaged spatial flow turbulence structure characteristics. The measured non-uniform velocity profiles are used to verify the von Karman constant κ and to estimate sets of log-law integration constant B_r and wake parameter П, where their findings are also compared with values from previous studies. From κ, B_r and П findings, it has been found that the log-wake law can sufficiently represent the non-uniform flow in its non-modified form, and all κ, B_r and П follow universal rules for different bed roughness conditions. The non-uniform flow experiments also show that both the turbulence intensity and Reynolds stress are governed well by exponential pressure gradient parameter β equations. Their exponential constants are described by quadratic functions in the investigated β range. Through this experimental study, it has been observed that the decelerating flow shows higher empirical constants, in both the turbulence intensity and Reynolds stress compared to the accelerating flow. The decelerating flow also has stronger dominance to determine the flow non-uniformity, because it presents higher Reynolds stress profile than uniform flow, whereas the accelerating flow does not.     

Hydrodynamics and contaminant transport on a degraded bed at a 90-degree channel confluence

Channel confluences at which two channels merge have an important effect on momentum exchange and contaminant diffusion in both natural rivers and artificial canals. In this study, a three-dimensional numerical model, which is based on the Reynolds Averaged Navier–Stokes equations and Reynolds Stress Turbulence model, is applied to simulate and compare flow patterns and contaminant transport processes for different bed morphologies. The results clearly show that the distribution of contaminant concentrations is mainly controlled by the shear layer and two counter-rotating helical cells, which in turn are affected by the discharge ratio and the bed morphology. As the discharge ratio increases, the shear flow moves to the outer bank and the counter-clockwise tributary helical cell caused by flow deflection is enlarged, leading the mixing happens near the outer bank and the mixing layer distorted. The bed morphology can induce shrinkage of the separation zone and increase of the clockwise main channel helical cell, which is initiated by the interaction between the tributary helical cell and the main channel flow and strengthened by the deep scour hole. The bed morphology can also affect the distortion direction of the mixing layer. Both a large discharge ratio and the bed morphology could lead to an increase in mixing intensity.     

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.     

Three-dimensional analysis of coherent turbulent flow structure around a single circular bridge pier

The coherent turbulent flow around a single circular bridge pier and its effects on the bed scouring pattern is investigated in this study. The coherent turbulent flow and associated shear stresses play a major role in sediment entrainment from the bed particularly around a bridge pier where complex vortex structures exist. The conventional two-dimensional quadrant analysis of the bursting process is unable to define sediment entrainment, particularly where fully three-dimensional flow structures exist. In this paper, three-dimensional octant analysis was used to improve understanding of the role of bursting events in the process of particle entrainment. In this study, the three-dimensional velocity of flow was measured at 102 points near the bed of an open channel using an Acoustic Doppler Velocity meter (Micro-ADV). The pattern of bed scouring was measured during the experiment. The velocity data were analysed using the Markov process to investigate the sequential occurrence of bursting events and to determine the transition probability of the bursting events. The results showed that external sweep and internal ejection events were an effective mechanism for sediment entrainment around a single circular bridge pier. The results are useful in understanding scour patterns around bridge piers.     

Advent of sheet flow in suction affected alluvial channels

The presence of suction (flow of water from channel to ground water) affects the channel hydrodynamics and increases the bed shear stress. At high bed shear stress in alluvial channels made of the non-cohesive material, sediment transport occurs as sheet flow layer of high sediment concentration. The sediment transport in the form of sheet flow has been observed in the present study when suction was applied to the non-transporting channels designed on incipient motion condition. The erosion of the channel banks contributed to the sheet flow because of the increased channel bed shear stress. An empirical relation for the thickness of sheet flow layer has been developed which includes suction as independent parameter along with others.     

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.     

Variations of bed elevations due to turbulence around submerged cylinder in sand beds

This paper presents the spatio-temporal variations in bed elevations and the near-bed turbulence statistics over the deformed bed generated around the submerged cylindrical piers embedded vertically on loose sediment bed at a constant flow discharge. Experiments were carried out in a laboratory flume for three blockage ratios in the range of 0.04–0.06 using three different sizes of submerged cylinders individually placed vertically at the centerline of the flume. Clear-water experimental conditions were maintained over the smooth sediment bed surface with a constant flow discharge (\(Q = 0.015\,{\rm m}^3/{\rm sec}\)), thereby giving three different cylinder Reynolds numbers \(Re_{D_c} = \frac{U_mD_c}{\nu }\) (=10200, 12750, 15300) away from the cylinder locations, where \(U_m\) is the maximum mean velocity, \(D_c\) is the cylinder diameter and \(\nu\) is the kinematic viscosity of fluid. Instantaneous sand bed elevations around the cylinders were recorded using a SeaTek 5MHz ultrasonic ranging system of net 24 transducers to estimate bed form migration, and the near-bed velocity data at transducer locations over the stable deformed bed around the pier-like structures were collected using down-looking three-dimensional (3D) Micro-acoustic Doppler velocimeter to estimate the bottom Reynolds shear stresses and the contributions of bursting events to the dominant shear stress component. The flow perturbation generated due to relatively lower flow blockage ratio favored to achieve the stable bed condition more rapidly than the others, and larger upstream scour-depth and deformed areas were noticed for greater flow blockage ratio due to larger cylinder diameter. For larger blockage ratio in the upstream of scour-hole near the bed, occurrences of probabilities of both boundary-ward interactions (Q1 and Q3) were the dominant; whereas in the downstream of the scoured region, occurrences of probabilities of second and third quadrant events (Q2 and Q4) were dominant. On the other hand, for the lower blockage ratio, quadrant (Q2) was dominant over Q4 in the downstream of scour-hole, and in the upstream of scour-hole, quadrant Q4 was the dominant.     

Coupling between free-surface fluctuations,velocity fluctuations and turbulent Reynolds stresses during the upstream propagation of positive surges,bores and compression waves

In open channel, canals and rivers, a rapid increase in flow depth will induce a positive surge, also called bore or compression wave. The positive surge is a translating hydraulic jump. Herein new experiments were conducted in a large-size rectangular channel to characterise the unsteady turbulent properties, including the coupling between free-surface and velocity fluctuations. Experiments were repeated 25 times and the data analyses yielded the instantaneous median and instantaneous fluctuations of free-surface elevation, velocities and turbulent Reynolds stresses. The passage of the surge front was associated with large free-surface fluctuations, comparable to those observed in stationary hydraulic jumps, coupled with large instantaneous velocity fluctuations. The bore propagation was associated with large turbulent Reynolds stresses and instantaneous shear stress fluctuations, during the passage of the surge. A broad range of shear stress levels was observed underneath the bore front, with the probability density of the tangential stresses distributed normally and the normal stresses distributed in a skewed single-mode fashion. Maxima in normal and tangential stresses were observed shortly after the passage of a breaking bore roller toe. The maximum Reynolds stresses occurred after the occurrence of the maximum free-surface fluctuations, and this time lag implied some interaction between the free-surface fluctuations and shear stress fluctuations beneath the surge front, and possibly some causal effect.     

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.     

Turbulent burst-sweep events around fully submerged vertical square cylinder over plane bed

Environmental Fluid Mechanics - The subtle variations of the turbulent shear stress affect the entrainment of bed sediments into the flow as well as sediment transport around submerged...     

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.     

Surface signatures of submerged heated jet

The flow induced at the surface of a water body by a submerged heated horizontal turbulent jet was investigated experimentally with the aim of developing parameterizations for surface mean temperature/velocity fields. The jet nozzle diameter was fixed, the depth of the jet beneath the free surface was varied, and two jet Reynolds numbers (5020, 11300) were considered. The surface temperature was measured using a highly sensitive infrared camera, and the near-surface horizontal velocity field was measured using particle image velocimetry. The experimental results were explained using a model based on similarity solutions with variable turbulent viscosity. While classical Schlichting’s solution with constant turbulent viscosity predicts complete similarity for transverse velocity/temperature distributions only in a plane that coincides with the flow axis, the present solution predicts similarity in an arbitrary plane parallel to the flow axis, which was confirmed using data collected at the surface. Comparisons of present data with available previous results also showed general agreement.     

Flow regimes in gaps within stands of flexible vegetation: laboratory flume simulations

Analyses of results from laboratory flume experiments are presented in which flow within gaps in canopies of flexible, submerged aquatic vegetation simulations is investigated. The aims of the work are (a) to identify the different flow regimes that may be found within such gaps, using Morris’ classical definitions of skimming flow, wake interference flow and isolated roughness flow as a template, (b) to determine the parameter space in which those flow regimes are most consistently delineated, and (c) to provide quantitative measurements of the loci of each flow regime within that parameter space for these experiments. The sedimentary and biological implications of each flow regime are also discussed. The results show that five flow regimes may be identified, expanding on Morris’ original set of three. The five are: (i) skimming flow; (ii) recirculation flow; (iii) boundary layer recovery; (iv) canopy through-flow; and (v) isolated roughness flow, the last being assumed to occur in some cases though it is not directly observed in these experiments. A Reynolds number based on the canopy overflow speed and the gap depth, and the gap aspect ratio are found to be the key parameters that determine these flow regimes, though a Froude number is found to be important for determining bed shear stress, and the length of leaves overhanging the gap from the upstream canopy is found to be important in determining the location of flow recirculation cells within the gap.     

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.     

Enhancing transverse mixing in streams with submerged vanes

In order to maintain the water quality of moving streams, it is essential to know the process of pollutant mixing. The transverse mixing is very important which is needed to be modeled to understand mixing phenomenon. It was observed that transverse mixing is a strong function of secondary currents, thus, submerged vanes, which are aerofoil skewed at angle of 10°–40° with respect to flow, generate transverse circulations that can be utilized to induce secondary currents in the flow to enhance transverse mixing. Present study is an attempt to utilize submerged vanes as an instrument to enhance the transverse mixing by incorporating various vane configurations. In order to study the effect of vane generated circulations on transverse mixing, experimentations were conducted on three vane sizes and for various row arrangements of vanes attached to bed. An attempt is made to investigate the effect of submerged vane size and rows on transverse velocity, concentration profile and transverse mixing coefficient. It was observed by measurement of concentration profile that transverse mixing was more enhanced for submerged vanes of higher height. It was also observed that as the number of rows is proportional to the transverse mixing. By measuring the transverse velocity profile, it was observed that more and more fluid was advected in transverse direction for higher rows of vanes. By utilizing the observed transverse mixing coefficients, number of vane rows and relative height of vane, a predictor was derived to predict transverse mixing coefficient in the presence of submerged vane rows. It was observed that the derived predictor shows a fair amount of agreement in the result predicted.     

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.     

Visualization of the internal flow properties and the material exchange interface in an entraining viscous Newtonian gravity current

In order to simulate a simple entraining geophysical flow, a viscous Newtonian gravity current is released from a reservoir by a dam-break and flows along a rigid horizontal bed until it meets a layer of entrainable material of finite depth, identical to the current. The goal is to examine the entrainment mechanisms by observing the interaction between the incoming flow and the loose bed. The sole parameter varied is the initial volume of the gravity current, thus altering its height and velocity. The gravity current plunges or spills into the entrainable bed and the velocity of the flow front becomes linear with time. The bed material is directly affected: motion is generated in the fluid far downstream of, and in that lying beneath the encroaching front. Shear bands are identified, separating horizontal flow downstream from flow with a strong vertical component close to the step. Downstream of the step the flow is horizontal and stratified, with no slip on the bottom boundary and very low shear near the surface. Between these two regions may lie transitional zones with linear velocity profiles, separated by horizontal bands of high shear; the number of transitional zones in the cross-section varies with the initial volume of the dam-break.     

Fourier analysis of the roll-up and merging of coherent structures in shallow mixing layers

The current study investigates the role of nonlinearity in the development of two-dimensional coherent structures (2DCS) in shallow mixing layers. A nonlinear numerical model based on the depth-averaged shallow water equations is used to investigate temporal shallow mixing layers, where the mapping from temporal to spatial results is made using the velocity at the center of the mixing layer. The flow is periodic in the stream-wise direction and the transmissive boundary conditions are used in the cross-stream boundaries to prevent reflections. The numerical results are examined with the aid of Fourier decomposition. Results show that the previous success in applying local linear theory to shallow mixing layers does not imply that the flow is truly linear. Linear stability theory is confirmed to be only valid within a short distance from the inflow boundary. Downstream of this linear region, nonlinearity becomes important for the roll-up and merging of 2DCS. While the energy required for the merging of 2DCS is still largely provided by the velocity shear, the merging mechanism is one where nonlinear mode interaction changes the velocity field of the subharmonic mode and the gradient of the along-stream velocity profile which, in turn, changes the magnitude of the energy production of the subharmonic mode by the velocity shear implicitly. The nonlinear mode interaction is associated with energy up-scaling and is consistent with the inverse energy cascade which is expected to occur in shallow shear flows. Current results also show that such implicit nonlinear interaction is sensitive to the phase angle difference between the most unstable mode and its subharmonic. The bed friction effect on the 2DCS is relatively small initially and grows in tandem with the size of the 2DCS. The bed friction also causes a decrease in the velocity gradient as the flow develops downstream. The transition from unstable to stable flow occurs when the bed friction balances the energy production. Beyond this point, the bed friction is more dominant and the 2DCS are progressively damped and eventually get annihilated. The energy production by the velocity shear plays an important role from the upstream end all the way to the point of transition to stable flow. The fact that linear stability theory is valid only for a short distance from the inflow boundary suggests that some elements of nonlinearity is incorporated in the mean velocity profile in experiments by the averaging process. The implicit nature of nonlinear interaction in shallow mixing layers and the sensitivity of the nonlinear interaction to phase angle difference between the most unstable mode and its subharmonic allows local linear theory to be successful in reproducing features of the instability such as the dominant mode of the 2DCS and its amplitude.