Maximum Reynolds Stress Research Articles

Numerical simulation of landscape ecological river flow structure based on vegetation patch distribution and fragmentation.

The self-organizing biological characteristics of vegetation and human activities lead to the disruption of the continuous spatial attributes of natural watersheds, which are significant factors affecting river wetland ecosystems. To clarify the landscape ecological flow characteristics of vegetation patch distribution and fragmentation, this study used the three-dimensional Reynolds stress turbulence model in ANSYS Fluent software. The model considered three vegetation patch coverages under two different submersion states and four fragmentation types of vegetation patches under the same coverage conditions within specific vegetation areas. The flow characteristics of longitudinally discontinuous rigid vegetation patches, occupying half of the width of the river channel, were numerically simulated. The model's applicability was verified by indoor open-channel flume experiments. The results indicated that: (1) The streamwise velocity in vegetated areas is significantly lower than in non-vegetated areas, and the difference in flow capacity between vegetated and non-vegetated areas increases with patch coverage and fragmentation degree. (2) In the non-submerged state, the maximum Reynolds stress in the vegetated area is located at the bottom of the vegetation and is negatively correlated with patch coverage but positively correlated with fragmentation degree. In the submerged state, the maximum Reynolds stress is located near the top of the canopy and is positively correlated with both patch coverage and fragmentation degree. (3) The longitudinal turbulent kinetic energy in the vegetated area is significantly higher than in the non-vegetated area. In the non-submerged state, the turbulent kinetic energy in the vegetated area is negatively correlated with patch coverage but positively correlated with fragmentation degree. In the submerged state, the turbulent kinetic energy of the longitudinal distribution in the free layer of the vegetated area is positively correlated with patch coverage, negatively correlated with fragmentation degree, and is only reflected in the upstream vegetation area.

Influence of aortic valve tilt angle on flow patterns in the ascending aorta

Transcatheter aortic valve implantation (TAVI) has become the alternative procedure to high-risk patients who are diagnosed with aortic valve stenosis. Differently from the traditional open-chest surgical procedure, a small variation on the prosthetic aortic valve deployment angle is expected with the TAVI procedure. The hemodynamic patterns of the blood flow in the ascending aorta are related to the development of many cardiovascular diseases. There are, however, few data available in the literature correlating the aortic valve tilt angle to hemodynamic effects. In this work, a 3D printed aorta model made of a transparent silicon resin was produced, based on the anatomy of a specific patient submitted to a TAVI procedure. The stereoscopic Particle Image Velocimetry technique was employed to measure three-component velocity fields at closely spaced cross-sectional planes, along the ascending aorta. The measurements were performed for a constant flow rate corresponding to the peak of the systolic phase of the cardiac cycle. Averaged velocity fields and turbulent quantities were determined for both, the base case, with no valve tilt, and for cases with an inclination of 4° and 8°, oriented at the four anatomical directions of the human body reference system, namely anterior, posterior, right and left. The results revealed the dominant flow patterns in the ascending aorta formed by a jet-like inlet flow impinging on the curved aorta right wall, inducing a significant eccentricity on the axial velocity profile. Regions of reverse flow were identified and linked to the abrupt area change associated with the typical reduced inlet diameter of TAVI implants. The impinging flow and wall curvature effects established circulation patterns defining a helical flow structure. The influence of the inlet flow orientation on the flow turbulent characteristics was assessed by the spatial evolution of the turbulent kinetic energy (TKE), Reynolds and viscous stresses. The maximum values of TKE were found around the inlet jet boundaries and concentrated in the neighborhood of the right aorta wall where the eccentric axial flow prevailed. Spatial distributions of the maximum Reynolds stresses were similar to the TKE distributions and presented maximum stresses typically one order of magnitude higher than the maximum average viscous shear stresses. Maximum average viscous stress distributions were revealed at the jet-like flow boundaries and in the vicinity of the right wall, displaying moderate stress levels that, according to the literature, can be sufficient to produce cell damage and platelet activation. The complex nature of the flow field was revealed by streamlines obtained from the measured flow fields, allowing the identification of the influence of the inlet flow orientation and tilt angle on the position of the stagnation point on the aorta right wall, as well as the angle of incidence of the jet-like flow on the wall. A simple model based on momentum balance was used to estimate the pressure increment on the wall due to flow impingement. The model captured the influence of the inlet flow orientation, indicating that pressure increases of the order of 40% in relation to the base case condition were obtained for the 8°, left inlet flow orientation.

Effects of coral colony morphology on turbulent flow dynamics.

Local flow dynamics play a central role in physiological processes like respiration and nutrient uptake in coral reefs. Despite the importance of corals as hosts to a quarter of all marine life, and the pervasive threats facing corals, characterizing the hydrodynamics between the branches of scleractinian corals has remained a significant challenge. Here, we investigate the effects of colony branch density and surface structure on the local flow field using three-dimensional immersed boundary, large-eddy simulations for four different colony geometries under unidirectional oncoming flow conditions. The first two colonies were from the Pocillopora genus, one with a densely branched geometry, and one with a comparatively loosely branched geometry. The second pair of geometries were derived from a scan of a single Montipora capitata colony, one with the roughness elements called verrucae covering the surface intact, and one with the verrucae removed. For the Pocillopora corals, we found that the mean velocity profiles changed substantially in the center of the dense colony, becoming significantly reduced at middle heights where flow penetration was poor, while the mean velocity profiles in the loosely branched colony remained similar in character from the front to the back of the colony. For the Montipora corals, somewhat counterintuitively, the colony without verrucae produced almost double the maximum Reynolds stress magnitude above the colony compared to the colony without verrucae. This implies that the smooth colony will have enhanced mass transport and higher bed shear stress and friction velocity values relative to the colony with verrucae.

The effect of turbulence on transitional flow in the FDA's benchmark nozzle model using large-eddy simulation.

The Food and Drug Administration's (FDA) benchmark nozzle model has been studied extensively both experimentally and computationally. Although considerable efforts have been made on validations of a variety of numerical models against available experimental data, the transitional flow cases are still not fully resolved, especially with regards to detailed comparison of predicted turbulence quantities with experimental measurements. This study aims to fill this gap by conducting large-eddy simulations (LES) of flow through the FDA's benchmark model, at a transitional Reynolds number of 2000. Numerical results are compared to previous interlaboratory experimental results, with an emphasis on turbulence characteristics. Our results show that the LES methodology can accurately capture laminar quantities throughout the model. In the pre-jet breakdown region, predicted turbulence quantities are generally larger than high resolution experimental data acquired with laser Doppler velocimetry. In the jet breakdown regions, where maximum Reynolds stresses occur, Reynolds shear stresses show excellent agreement. Differences of up to 4% and 20% are observed near the jet core in the axial and radial normal Reynolds stresses, respectively. Comparisons between viscous and Reynolds shear stresses show that peak viscous shear stresses occur in the nozzle throat reaching a value of 18 Pa in the boundary layer, whilst peak Reynolds shear stresses occur in the jet breakdown region reaching a maximum value of 87 Pa. Our results highlight the importance in considering both laminar and turbulent contributions towards shear stresses and that neglecting the turbulence effect can significantly underestimate the total shear force exerted on the fluid.

Experimental investigation on local shear stress and turbulence intensities over a rough non-uniform bed with and without sediment using 2D particle image velocimetry

The current work focuses on locally resolving velocities, turbulence, and shear stresses over a rough bed with locally non-uniform character. A nonporous subsurface layer and fixed interfacial sublayer of gravel and sand were water-worked to a nature-like bed form and additionally sealed in a hydraulic flume. Two-dimensional Particle Image Velocimetry (2D-PIV) was applied in the vertical plane of the experimental flume axis. Runs with clear water and weak sediment transport were done under slightly supercritical flow to ensure sediment transport conditions without formation of considerable sediment deposits or dunes. The study design included analyzing the double-averaged flow parameters of the entire measurement domain and investigating the flow development at 14 consecutive vertical subsections. Local geometrical variabilities as well the presence of sediment were mainly reflected in the vertical velocity component. Whereas the vertical velocity decreased over the entire depth in presence of sediment transport, the streamwise velocity profile was reduced only within the interfacial sublayer. In the region with decelerating flow conditions, however, the streamwise velocity profile systematically increased along the entire depth extent. The increase in the main velocity (reduction of flow resistance) correlated with a decrease of the turbulent shear and main normal stresses. Therefore, effects of rough bed smoothening and drag force reduction were experimentally documented within the interfacial sublayer due to mobile sediment. Moreover, the current study leads to the conclusion that in non-uniform flows the maximum Reynolds stress values are a better predictor for the bed shear stress than the linearly extrapolated Reynolds stress profile. This is an important finding because, in natural flows, uniform conditions are rare.

PIV measurement of turbulent flow downstream of mixing vane spacer grid in 5×5 rod bundle

Axial and cross flow downstream a split-type mixing vane spacer grid in a 5×5 rod bundle are measured with particle image velocimetry (PIV) at sub-channel Reynolds number (Resc) of 6600, 13,200, 26,400 and 39,600. The cross flow in the sixteen inner sub-channels are obtained at five elevations, i.e. 3Dh, 5Dh, 10Dh, 15Dh and 20Dh downstream of the spacer grid. The axial flow measurement is conducted in a plane parallel to the bundle axis. The satisfactory convergence of turbulent statistics is achieved with the sampling number of 2000. The maximum standard uncertainty of statistical quantities normalized by the bulk velocity for all the test conditions is less than 0.6%. The flow characteristics and structures were determined by the mixing vanes located on the upper edge of support grids in rod bundle, and the flow downstream the spacer grid can be divided into the advection zone, the reorganization zone and the dumping zone. And the maximum lateral velocity decreases from 44% of the bulk velocity (Wb) at 3Dh to 16%Wb at 20Dh. The mixing vanes generate drastic turbulence flow downstream the spacer grid, and the lateral root mean square (RMS) fluctuating velocity decays in exponential way. The maximum lateral RMS fluctuating velocity decays rapidly from 20%Wb at 3Dh to 9%Wb at 20Dh. The maximum lateral Reynolds stress decreases from 0.6%Wb2 at 3Dh to 0.3%Wb2 at 20Dh. The normalized mean velocity and turbulent statistics show similarity for the Reynolds above 13,200, while the low Reynolds number effect at Re = 6600 is observed for the axial mean velocity and axial RMS fluctuating velocity.

Experimental Study of Overland Flow through Rigid Emergent Vegetation with Different Densities and Location Arrangements

The effect of vegetation density on overland flow dynamics has been extensively studied, yet fewer investigations have focused on vegetation arrangements with different densities and position features. Flume experiments were conducted to investigate the hydrodynamics of flow through rigid emergent vegetation arranged in combinations with three densities (Dense, Middle, and Sparse) and three positions (summit, backslope, and footslope). This study focused on how spatial variations regulated hydrodynamic parameters from two dimensions: direction along the slope and water depth. The total hydrodynamic parameters of bare slopes were significantly different from those of vegetated slopes. The relationship between Re and f illustrated that Re was not a unique predictor of hydraulic roughness on vegetated slopes. In the slope direction, all hydrodynamic parameters on vegetated slopes exhibited fluctuating downward/upward trends due to the clocking effect before the vegetated area and the rapid conveyance effect in the vegetated area, whereas constant values were observed on bare slopes. The performance of hydrodynamics parameters suggested that the dense rearward arrangement (SMD) was the optimal vegetation pattern to regulate flow conditions. Specifically, the vertical profiles of the velocity and turbulence features of the SMD arrangement at different sections demonstrated the significant role of vegetation density in identifying the velocity layers along the water depth. The maximum velocity and Reynolds Stress Number (RSN) indicated the position where local scour was most likely to occur, which would improve our basic understanding of the mechanisms underlying hydraulic and soil erosion processes.

Flow characteristics in a partly vegetated channel with emergent vegetation and seepage

The flow characteristic in a partly vegetated channel with emergent condition is studied by covering a finite length of the channel with natural Oryza sativa (rice) stems with downward seepage. Spatial study of velocity profiles shows that vegetation reduces the flow velocity lengthways of vegetation zone even with the presence of downward seepage. Reynolds stress increases at the downstream end of the interface section because of higher velocity fluctuations between vegetated and un-vegetated zone. The increase in Reynolds stress at the downstream of interface section is attributed to higher lateral flow and momentum exchange in this transition zone between vegetated and un-vegetated area. For the vegetated section, vegetation serves as a barrier for the vegetated section in reducing the maximum Reynolds stress in the range of 17–20% along the flow direction. It is also observed that downward seepage increases the Reynolds stress as well as turbulence intensities. Integral scales increase with increase in percentage of downward seepage resulting in higher Reynolds stresses with downward seepage. Presented work will help in analyzing the changes in flow field with partially emergent vegetation in alluvial channel subjected to downward seepage. The overall results of this study may enhance the comprehensive understanding of the vegetation effects on flow characteristics in partly emerged vegetated channel and may also provide some guidance for the practice of river ecological restoration on river bed or banks.

MODEL VERSUS NATURE: HYDRODYNAMICS IN MANGROVE PNEUMATOPHORES

Water flows through submerged and emergent vegetation control the transport and deposition of sediment in coastal wetlands. Many past studies into the hydrodynamics of vegetation fields have used idealized vegetation mimics, mostly rigid dowels of uniform height. In this study, a canopy of real mangrove pneumatophores was reconstructed in a flume to quantify flow and turbulence within and above this canopy. At a constant flow forcing, an increase in pneumatophore density, from 71 m-2 to 268 m-2, was found to cause a reduction of the within-canopy flow velocities, whereas the over-canopy flows increased. Within-canopy velocities reduced to 46% and 27% of the free-stream velocities for the lowest and highest pneumatophore densities, respectively, resulting in stronger vertical shear and hence greater turbulence production around the top of the denser pneumatophore canopies. The maximum Reynolds stress was observed at 1.5 times the average pneumatophore height, in contrast to uniform-height canopies, in which the maximum occurs at approximately the height of the vegetation. The ratios of the within-canopy velocity to the free-stream velocity for the pneumatophores were found to be similar to previous observations with uniform-height vegetation mimics for the same vegetation densities. However, maxima of the scaled friction velocity were two times smaller over the real pneumatophore canopies than for idealized dowel canopies, due to the reduced velocity gradients over the variable-height pneumatophores compared to uniform-height dowels. These findings imply that results from previous studies with idealized and uniform vegetation mimics may have limited application when considering sediment transport and deposition in real vegetation, as the observed turbulence characteristics in non-uniform canopies deviate significantly from those in dowel canopies.

Turbulent boundary layer response to large-scale wavy topographies

Flat-plate turbulent boundary layer adjustment to large-scale 2D and 3D wavy topographies was experimentally studied using high-resolution particle image velocimetry in a refractive-index-matching flume. The flow was characterized at a Reynolds number Re = 4×104, based on the channel half height and incoming free-stream velocity. Two ratios of amplitude (a) to incoming boundary layer thickness (δ0) were considered for each topography (a∕δ0 = 0.12 and 0.81). The 2D topography is described by a sinusoidal wave in the streamwise direction with an amplitude to wavelength ratio a∕λx = 0.05, while the 3D topography is defined with an additional wave superimposed in the spanwise direction. The results show that the spanwise variability of the topography leads to a much milder response in both a∕δ0 ratios. The regions of strong acceleration and deceleration over the crests and troughs of the topography are reduced over the 3D topography due to the alternate flow path around the 3D elements. Furthermore, the boundary layer thickness and integral parameters experienced milder variations over the 3D topography for both a∕δ0. The Reynolds shear stress shows distinctive evolution with downstream distance. In the 3D case, maximum Reynolds stress similar to those in the developed region is achieved within the first three wavelengths past the topographic change indicating that the dynamics of the downstream evolution is dominated by vertical diffusion and redistribution. This is in contrast with the 2D case with a∕δ0 = 0.12 where the Reynolds stress did not achieve the levels observed in the developed region.

Transition to turbulent heat transfer in heated vertical channel - Scaling analysis

A thermally driven flow in a vertical channel with heated walls is studied through a scaling analysis and results are compared with the experimental data reported in [1]. As the geometry is symmetrical with respect to the vertical axis, the half-channel is considered. The domain is split into seven zones in which the flow behaviour results from a balance between several phenomena. This zonal analysis exhibits the main phenomena that drive the flow in each zone. The study leads to an expression of the wall temperature profile below and above the transition. An expression is given for the driving pressure that is found to increase along the channel. The increase rate is much more important above the transition due to the fluid heating in the center of the channel. Finally, The maximum Reynolds stress is expressed in terms of the mean velocity values and is found to fit well with the experimental data.

Turbulence Characteristics of Vegetated Channel With Downward Seepage

Experimental studies were carried out for investigating changes in flow characteristics with the presence of flexible vegetation in a channel. The study focuses on the effect of introducing downward seepage on velocity profiles, Reynolds shear stress (RSS), and different turbulent length scales in a vegetative channel. The presence of vegetation provides drag and reduces the flow velocity. The turbulence generation mainly comes from the oscillations occurring near the top of the vegetation as is evident from the achievement of maximum Reynolds stress near the top of the vegetation. Application of downward seepage results in a higher velocity zone in the lower vegetation zone and a higher Reynolds stress. Quadrant analysis shows that sweep and ejection contribute most to Reynolds stress. The dominance of sweep event over ejection event is more with the application of downward seepage which means more bed transport. Different turbulent length and time scales increase with increase in downward seepage percentage due to reduction in energy dissipation. The increase in the length scale and time scale with downward seepage infers that higher level of turbulence prevail near the bed with an increased eddy size resulting in higher Reynolds stresses with downward seepage. The universal probability distribution functions (PDFs) of velocity fluctuations, RSS, and conditional RSS of vegetative channel follow Gram Charlier (GC) series based on exponential distribution except that a slight departure of inward and outward interactions of conditional RSS is observed which may be due to weaker events.

Channel Hydrodynamics of Submerged, Flexible Vegetation with Seepage

AbstractThe presence of aquatic vegetation changes the flow characteristics in a channel. The impact of the presence of submerged, flexible vegetation in a channel with an additional parameter such as downward seepage is analyzed in the present work. Two patterns, staggered and uniform, and two different vegetation spacing, 15 and 10 cm center–center, were adopted. Experiments were conducted for the case of no seepage, 10% seepage, and 15% seepage. Velocity profiles show the presence of an inflection point near the top of the vegetation where maximum Reynolds stress is achieved. The velocity profiles measured in the unobstructed region of uniform pattern are higher compared to the velocity measured in line with the vegetation stems. Downward seepage increases the velocity, Reynolds stress, and turbulent intensities in the average range of 10–15% as compared to the no-seepage case. Higher-order turbulent statistics such as moment analysis, quadrant analysis, and turbulent kinetic budget are derived through...

Hydrodynamics of discontinuous rigid submerged vegetation patches in open-channel flow

We investigate the effects of discontinuous rigid submerged vegetation patches on flow turbulence. Two laboratory flume experiments are performed to validate the large eddy simulation (LES) model. The obtained LES data are in good agreement with the experimental data. They are also highly accurate in capturing the secondary peaks of the mean velocity near the channel bed. The coherent vortices, which are generated by the shear between the slower canopy flow and the faster overlying flow, are associated with the velocity inflection and maximum Reynolds stress around the interface. The mean velocity in the gap regions is evidently slower than that in the canopy regions. A high canopy density and Reynolds number are more conducive for the fully developed flow state of discontinuous vegetation patches. The velocity distinctly increases within the first two patches with a high canopy density. The velocity profile in the large gaps is more stable than that in the small gaps below the vegetation height, whereas the effect of patch distribution is not evident in the overlying flow layer. A spectral analysis shows that two vortex scales, namely, stem-scale and shear-scale vortices, influence the turbulence of flow through discontinuous vegetation patches. The power spectral densities are consistent with Kolmogorov theory for a −5/3 slope when the dominant eddy frequency exceeds 0.04 Hz.

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.

Turbulent flow statistics of vegetative channel with seepage

The present study is carried out for studying the impact of submerged, flexible vegetation in a channel where downward seepage occurs. Laboratory experiments on artificial vegetation of two different heights, 8cm and 6cm, were conducted for no-seepage, 10% seepage and 15% seepage cases. Vegetation height is an important parameter in influencing the flow characteristics in a vegetated channel, where velocity is reduced near the top of the vegetation. Results show that velocity measured at upstream vegetation section is always higher than the downstream section even with the application of downward seepage. The maximum value of Reynolds stress occurs near the top of the vegetation. When the flow enters the vegetation section, the local effect of the presence of vegetation on sediment transport is more at the upstream vegetation section and then decreases which is shown by higher Reynolds stress at the upstream as compared to downstream vegetation section highlighting the importance of vegetation in providing as an erosion control. The maximum Reynolds stress at no seepage is increased by a percentage of 17% for 10% seepage and average of 30.5% for 15% seepage. The turbulence intensities at no seepage are increased by an average value of 15% for 10% seepage and 25% for 15% seepage. The reduction of Reynolds stress and turbulent intensities along the longitudinal direction implies the importance of using vegetation as a river restoration measure providing considerable stability to channels. Third order moments highlight that downward seepage increases the streamwise flux and decreases the upward flux.

Flow and turbulence in vegetation in a channel

The distribution of aquatic vegetation within conveyance channels plays a key role in the determination of their hydraulic characteristics, especially where the vegetation is patchy, as is commonly found in nature. This paper reports the results of a laboratory flume study on flow and turbulence conditions caused by patches of the emergent rush Lepironia articulata. Acoustic Doppler velocimeter measurements were taken within and downstream of single- and multiple-patch configurations of this plant, and the effects of varying incident flow rate (0·16–0·32 m/s) and stem-scale porosity (12–4% solid volume fraction) were investigated. The results showed that flow encountering a single patch formed a turbulent wake downstream of the vegetation. Within this wake, the Reynolds stress increased downstream initially, and then decayed. When a second patch was positioned within the region of maximum Reynolds stress, the Reynolds stress decreased by between 25 and 50%. The amount of this reduction was dependent on the porosity of the vegetation and the flow rate, and was greater at lower flow rates and porosities. These changes in turbulent flow fields around patches of emergent vegetation are likely to be important in determining sediment budgets in their vicinity.

Negative surges and unsteady turbulent mixing induced by rapid gate opening in a channel

A negative surge is an unsteady open channel flow characterised by a drop in water surface elevation. In this study, a negative surge generated by the rapid gate opening was investigated experimentally with three types of bed roughness. Both instantaneous free-surface and velocity measurements were performed and the results were ensemble-averaged. The experimental data showed a rapid flow acceleration beneath the negative surge, and large and rapid fluctuations in all instantaneous velocity components were observed during the passage of the negative surge leading edge. The Reynolds stress data showed large ensemble-average and fluctuation levels, significantly larger than in the initially steady flow, occurring slightly after the passage of the surge leading edge. The time difference between the maximum Reynolds stress and surge leading edge was observed to increase with increasing distance from the gate, and it was comparable to the time delay for the occurrence of maximum free-surface fluctuations. The findings suggested that the unsteady flow properties were little affected by the bed roughness, despite the broad range of equivalent sand roughness heights tested herein.

Mixing layer in open-channel junction flows

When two open-channel flows merge in a three-branch subcritical junction, a mixing layer appears at the interface between the two inflows. If the width of the downstream channel is equal to the width of each inlet channel, this mixing layer is accelerated and is curved due to the junction geometry. The present work is dedicated to simplified geometries, considering a flat bed and a \(90^{\circ }\) angle where two configurations with different momentum ratios are tested. Due to the complex flow pattern in the junction, the so-called Serret–Frenet frame-axis based on the local direction of the velocity must be employed to characterize the flow pattern and the mixing layer as Cartesian and cylindrical frame-axes are not adapted. The analysis reveals that the centerline of the mixing layer, defined as the location of maximum Reynolds stress and velocity gradient, fairly fits the streamline separating at the upstream corner, even though a slight shift of the mixing layer towards the center of curvature is observed. The shape of the mixing layer appears to be strongly affected by the streamwise acceleration and the complex lateral confinement due to the side walls and the corners of the junction, leading to a streamwise increase of the mean velocity along the centerline and a decrease of the velocity difference. This results in a specific streamwise evolution of the mixing layer width, which reaches a plateau in the downstream region of the junction. Finally, the evaluation of the terms in the Reynolds-Averaged-Navier–Stokes equations reveals that the streamwise and normal acceleration and the pressure gradient remain dominant, which is typical of accelerated and rotational flows.

LABORATORY MEASUREMENTS OF A STEADY BREAKER USING PIV AND BIV

Image-based particle image velocimetry (PIV) and bubble image velocimetry (BIV) techniques were employed to measure the flow field in both the non-aerated and aerated regions in a steady hydraulic jump. The jump has a Froude number of 4.62 with a large amount of air entrainment. The mean velocities and turbulence properties were obtained by ensemble averaging the repeated measurements. The spatial variations of mean velocity profiles, turbulent intensity, and Reynolds stress were discussed in details. The results show that the ratio between the maximum bubble velocity and the maximum water velocity is almost constant with a value about 0.6. The turbulence intensity of bubbles is very high in the aerated region and reaches about 0.4, while the turbulence velocity of water below the roller is significantly lower. The Reynolds stress is mostly negative and increases as elevation increases. The maximum Reynolds stress occurs at the free surface.