Rigid Bed Research Articles

A meshless model for three-dimensional direct numerical simulation of local scour around cylinder bridge foundation

A meshless local scour model for cylinder bridge foundation based on the smoothed particle hydrodynamics (SPH) method is proposed in this paper. Differing from the traditional Eulerian mesh model used for monopile local scour, it overcomes the high requirements of mesh quality and density for capturing large deformations at the fluid interface. Unlike the transient sediment erosion SPH model used for dam-break, sediment flushing, and water jet, the meshless approach is innovatively applied to the continuous simulation of bridge local scour under steady flow conditions. The present SPH model is established based on the SPH multi-phase fluid model, integrating a classical fluid model combined with numerical stabilization algorithms to govern water particle motion and a sediment model from Zhang et al. (2024) to govern sediment evolution, and tests a new scheme for boundary treatment in the model based on DualSPHysics. Furthermore, a novel scour visualization method that aims at extracting both visible and actual bed surfaces from discrete particles is proposed. The model is validated through comparison with rigid bed and live bed experiments, demonstrating favorable agreement in terms of flow and scour simulation. Importantly, the model results reveal a discrepancy between the elevation of the post-scour visible bed surface derived from the conventional Eulerian mesh model and experimental data, compared to the actual bed surface unaffected by water flow erosion. This indicates the necessity for incorporating a safety margin in foundation design when utilizing experimental results to determine the maximum scour depth.

Experimental investigation of flow and sediment transport on an equilibrium beach formed by surging breaker

Flow patterns and sediment transport induced by breaking waves on a beach profile have been studied in a laboratory wave flume. Two parallel experiments were conducted on the same profiled rigid bed and sediment (mobile) bed, each subjected to identical wave forcing. The rigid bed experiments include measurements of bed shear stress and water-surface elevation, while the sediment bed experiments involve the measurement of pore-water pressures. The beach profile features a beach step leading to the generation of a hydraulic jump at the end of the rundown phase and accordingly forms a backwash vortex. The bed shear stress measurements revealed that the maximum onshore directed mean bed shear stress occurs after the wave breaking whereas the offshore directed one occurs during rundown at the same section. The increase of the bed shear stress with respect to that in the approaching wave boundary layer during the wave breaking and hydraulic jump processes can be by as much as a factor of 13 and 4, respectively. The effect of the wave breaking on turbulence is also more pronounced by a factor of 2.2 than the hydraulic jump in terms of r.m.s values of the fluctuating component of the bed shear stress. The pore pressure measurements showed that the vortex generated during the wave breaking creates an impulsive, upward-directed pressure gradient force that can be up to 1.2 times the submerged weight of the sediment. The sediment transport occurs in the sheet flow regime in a large part of the beach profile. The turbulence generated by the backwash vortex and the hydraulic jump at the beach step directly impacts the local sediment suspension which serves as the source for the advected sediment in the swash zone. The results are compared with a previous study that used the same methodology but involved plunging waves and the initial bed profile.

Fluid-evolving landform interaction by a surface-tracking method

This paper introduces a continuous finite element model to simulate fluid flow-bedform interaction problems. The approach utilizes a non-oscillatory finite element algorithm to compute the fluid dynamics by solving the complete Navier–Stokes equations. Additionally, it addresses the evolution of the fluid–bedform interface as a consequence of spatially non-balanced sediment fluxes through the solution of a conservation equation for the erodible layer thickness. A sign preservation algorithm is particularly relevant for landform tracking because a positive definite thickness of the erodible sediment layer is essential to model the interaction between evolving cohesionless sediment layers and rigid beds. The fluid/terrain interface is explicitly captured through a surface tracking methodology. First, new nodes fitting the interface are incorporated into the finite element mesh; then, elements beneath this interface are deactivated, while intersected elements are restructured to get a mesh composed exclusively of tetrahedral elements. Numerical experiments demonstrate capabilities of the method by exploring relevant problems related with civil engineering, such as the evolution of trenches and the scour of a submerged pile.

Corrigendum: AQUA - Water Infrastructure, Ecosystems and Society 1 September 2023; 72 (9): 1748–1769. Turbulence modelling for depth-averaged velocity and boundary shear stress of a dense rigid grass bed open channel, Sarjati Sahoo, Jnana Ranjan Khuntia, Kamalini Devi, B. Sree Sai Prasad, Kishanjit Kumar Khatua, https://dx.doi.org/10.2166/aqua.2023.093

Corrigendum: <i>AQUA - Water Infrastructure, Ecosystems and Society</i> 1 September 2023; 72 (9): 1748–1769. Turbulence modelling for depth-averaged velocity and boundary shear stress of a dense rigid grass bed open channel, Sarjati Sahoo, Jnana Ranjan Khuntia, Kamalini Devi, B. Sree Sai Prasad, Kishanjit Kumar Khatua, https://dx.doi.org/10.2166/aqua.2023.093

Reynolds stress anisotropy with higher-order turbulence in flow through rigid emergent vegetation: An experimental study

The flow turbulence and Reynolds stress anisotropy in flow over the smooth rigid bed with the emergent rigid vegetation in a straight channel have been experimentally investigated. Higher-order turbulence such as turbulent diffusivity, third-order moments of velocity fluctuation, quadrant analysis and flux of turbulence kinetic energy have been analysed. Reynolds stress anisotropy has been investigated by Anisotropic invariant maps (AIMs) with the use of eigenvalues for both vegetation and non-vegetation condition. In the vegetation zone, more diffusivity occurs and an apparent decrease in velocity causes larger eddies in the outer layer; whereas in the non-vegetation zone, larger eddies formation at near-bed has been found. Quadrant analysis has been done based on relative signs of velocity fluctuation which signifies that Reynolds shear stress is transported from the bed surface to the free surface when flow enters in the vegetation zone from the non-disturbed region. The longitudinal distribution of the anisotropy tensor near the bed surface for the vegetation zone provides the higher anisotropic flow than those of non-vegetation zone. Although, transverse and vertical distributions of the anisotropy tensor in the vicinity of the bed surface for the non-vegetation zone provide a lower anisotropic stream. Flow anisotropy can be understood by AIMs indicating axis-symmetric expansion in a non-vegetation zone whereas axis-symmetric contraction is in the vegetation zone. The outcomes of this study deliver a significant and detailed view of turbulent flow structures in vegetation and non-vegetation zone in an open channel flow.

An SPH study on viscoplastic surges overriding mobile beds: The many regimes of entrainment

Flow-type landslides entrain mobile bed material, but the processes involved are diverse and require systematic study. We perform direct numerical simulations using the open-source SPH package DualSPHysics with a regularized Herschel–Bulkley rheology. We then compare model output with physical test data, and hence investigate the effects of varying the bed yield stress τy,b and bed depth hb, interpreting the results using a newly-identified set of dimensionless numbers. Results reveal diverse interaction regimes between surges and mobile beds, including “rigid bed”, “lubrication”, “shallow ploughing”, “surfing”, “plunging”, and “deep ploughing”. Shallow, borderline-stable beds “lubricate” the surge: once destabilized, these beds cause strong acceleration of the combined flow front. Deeper borderline-stable beds allow the surge material to “plunge” downward, massively displacing bed material upward and downstream. For stabler beds, “ploughing” and “surfing” are associated with intermediate and high values of τy,b, respectively. In both cases, beds retard the surge, with mobile dams forming for “ploughing” regimes. Across all regimes identified, the influence of τy,b is non-monotonic, with intermediate values decelerating the combined flow fronts the most. Furthermore, the different interaction regimes exhibit unique velocity profiles. We develop phase diagrams based on three dimensionless numbers, demarcating these regimes.

Deposit-scale controls of hypozonal gold mineralization in amphibolite facies metaturbidites: 3D modelling of the Twin Hills deposit, Damara Belt, Namibia

The recently discovered Twin Hills deposit is a new resource in the Pan-African Damara Belt of central Namibia, described by a finely dispersed, low-grade and high tonnage disseminated and vein-style gold mineralization. The underlying assumption of the 3D implicit modelling followed in this study is that the integration of gold grades and ore shells with structural and lithological data from oriented core logging reflects the underlying controls of hydrothermal fluid flow and mineralization at Twin Hills. The deposit comprises distinct clusters of economic-grade gold mineralization, measuring several hundred meters along strike, separated by several kilometer-long intervals of only sporadic and sub-economic gold grades. Mineralization is developed on the subvertical southern limb of a regional-scale syncline hosted in highly-strained compositionally heterogeneous, amphibolite facies metaturbidites. Additionally, the stretch of the main mineralization in the central parts of the ∼12 km long east-northeast-trending mineralized Twin Hills corridor coincides with the change of the fold vergence direction. We suggest that the steep orientation of the wall-rock strata generated high-permeability fluid conduits for focusing regional fluid flow during flexural-slip folding and associated local dextral strike-slip component of D2/3 deformation. Disseminated sulfide mineralization is mostly developed in pelitic units, whereas networks of quartz-sulfide veins and veinlets with subordinate disseminated sulfides are present in rigid psammitic beds in interbedded pelite-psammite horizons. While the wide distribution of finely disseminated sulfides point to the rather pervasive fluid flow along grain-scale permeabilities during recrystallization of mineral fabrics, the formation of fractures and resultant dilatancy in psammitic units created hydraulic gradients and focused fluid flow into the psammite horizons. High-grade ore shoots are controlled by the combination and interplay of two main factors, namely lithological contacts and subtle deflections of bedding of the highly-strained, subvertical metaturbidites. The mineralized corridor of the Twin Hills deposit is largely confined to imbricated and/or tightly folded packages of interbedded pelites-psammites within the otherwise pelite-dominated sequence. It is these units that promoted fracturing, fluid flow and the development of fine-scale vein networks as a result of pronounced strain partitioning between pelitic units (ductile) and interbedded psammites (brittle) during regional deformation. Ore shoots of higher-grade mineralization (>1.5 g/t Au) follow these main lithological contacts, but are laterally confined to subtle (5–15°) clockwise deflections of bedding (dilational jogs) from its regional east-northeast trends. Outside these deflections, gold mineralization is patchy and only sub-economic. The structural and lithological controls of the Twin Hills mineralization closely resemble those of orogenic gold deposits, whereas the fine-grained and dispersed texture of gold and associated sulfide mineralization are more reminiscent of disseminated gold deposits. We suggest that the Twin Hills deposit is an example of a hypozonal orogenic gold deposit formed under peak metamorphic amphibolite conditions.

Turbulence modelling for depth-averaged velocity and boundary shear stress of a dense rigid grass bed open channel

Abstract The present research focusses on a comparison of experimental and numerical approaches for flow over fixed artificial rigid grass bed channels. Various flow parameters like longitudinal velocity, depth-averaged velocity (DAV), boundary shear stress (BSS) and secondary current are analysed and compared with seven numerical models: standard, realizable and renormalization group (RNG) k–ε models and standard, shear stress transport (SST), generalized k–ω (GEKO) and Baseline (BSL) k–ω models. To evaluate the strength of the seven applied models, the error analysis has been performed. It is found that the RNG k–ε and SST k–ω models provided better results for both the DAV and BSS prediction, but the RNG k–ε model is found to be the most suitable for predicting the DAV and the SST k–ω model for BSS as compared to the other models. For the longitudinal velocity profiles, both the RNG k–ε and SST k–ω models are found to provide good agreement with experimental results at the centre of the channel, whereas the SST k–ω model is more accurate near the wall. Overall, the SST k–ω model has predicted the results with good accuracy for all the flow parameters considered in the present study.

Melt rates in the kilometer-size grounding zone of Petermann Glacier, Greenland, before and during a retreat

Warming of the ocean waters surrounding Greenland plays a major role in driving glacier retreat and the contribution of glaciers to sea level rise. The melt rate at the junction of the ocean with grounded ice-or grounding line-is, however, not well known. Here, we employ a time series of satellite radar interferometry data from the German TanDEM-X mission, the Italian COSMO-SkyMed constellation, and the Finnish ICEYE constellation to document the grounding line migration and basal melt rates of Petermann Glacier, a major marine-based glacier of Northwest Greenland. We find that the grounding line migrates at tidal frequencies over a kilometer-wide (2 to 6 km) grounding zone, which is one order of magnitude larger than expected for grounding lines on a rigid bed. The highest ice shelf melt rates are recorded within the grounding zone with values from 60 ± 13 to 80 ± 15 m/y along laterally confined channels. As the grounding line retreated by 3.8 km in 2016 to 2022, it carved a cavity about 204 m in height where melt rates increased from 40 ± 11 m/y in 2016 to 2019 to 60 ± 15 m/y in 2020 to 2021. In 2022, the cavity remained open during the entire tidal cycle. Such high melt rates concentrated in kilometer-wide grounding zones contrast with the traditional plume model of grounding line melt which predicts zero melt. High rates of simulated basal melting in grounded glacier ice in numerical models will increase the glacier sensitivity to ocean warming and potentially double projections of sea level rise.

Fatigue of a cylindrical shell lying on a rigid bed

In the extractive industries of the oil and gas industry, multi-span pipelines with lodgement-type supports are widely used. In the contact area of the pipeline with the support, contact stresses arise, created by the internal pressure of the pipeline, weight and wind load, and which can change during operation depending on the load. The assessment of the service life of such pipeline structures is an urgent technical and economic problems, which allows not only to prevent man-made and environmental disasters, but also to save material. This paper presents a method for calculating the fatigue of a steel cylindrical shell that is in contact with a rigid or elastic support of the lodgement type. Shell fatigue analysis is performed for contact stresses, which are determined by solving the corresponding contact problem. When calculating the fatigue of the shell, the linear damage summation hypothesis and the modified model of cyclic degradation of the material were used.

A finite element method for partially erodible bed evolution coupled with multiphase flows

This paper introduces a continuous finite element model for two phase flows coupled with evolving bedforms. The method extends the positive definite non-oscillatory finite element algorithm (NFEM) capabilities to predict sediment transport, multiphase flow, and evolution of the resulting interfaces limiting fluids, erodible sediment layers and non-erodible strata. Free surface hydrodynamics is simulated by the integration of the governing equations for incompressible multiphase flows, including the advection and reinitialization of a phase function to update the interface location. Sign preservation of the algorithm is essential both for fluid interface tracking procedure and for the landform tracking. In the first case, the property avoids unphysical overshoots along the free surface. In the second case, a positive definite thickness of the erodible layer of sediment is mandatory to account for interaction between evolving cohesionless sediment layers and rigid beds. To compute sediment layer thickness, the method incorporates a conservation law to balance evolution of the bed position with sediment mass flux, including a general template for saturated flux calculation. The framework permits the simulation from bed load dominant transport to saltation dominant transport. Fluid/terrain interface is explicitly captured by a surface tracking methodology whereby the mesh is adapted to the bedform. Numerical experiments explore several saturated sediment flow formulae for interactive evolution of dune/atmosphere system, as well as stringent dam-break type problems on channels with dry beds and partially and totally erodible beds.

Numerical study on flow pattern in meandering channels: The effect of hydraulic conditions and meander geometry

Natural rivers are one of the main sources of water and energy for humans. The design and management of exploitation of natural rivers systems will require a complete understanding of flow and sediment transport mechanics. Meanders are one of the most common types of rivers in nature, which have a very complex flow. The three-dimensional (3D) and complex characteristics of flow in meanderings bring up the necessity of investigating the flow pattern in this channel with 3D numerical models. This study aimed to investigate the flow pattern and predict the erosion and sedimentation site in the meandering. Also, the effect of the Froude number (Fr), the ratio of width-to-depth ([Formula: see text]/[Formula: see text] and meander angle parameters on the flow field are investigated. In this study, the turbulent flow pattern in a sine-generated channel and the angle of 50∘ with a rectangular section with width = 40 cm and the rigid bed is studied using the 3D mathematical model SSIIM1.1. The primary and secondary flow patterns were studied using the turbulence models of [Formula: see text]-[Formula: see text] and SST [Formula: see text]-[Formula: see text]. Comparison of numerical models and experimental results showed that the flow pattern is predicted well by both turbulence models of turbulence. But in some cases, the SST [Formula: see text]-[Formula: see text] model has provided closer results to the experimental results. The results show that the shear stress pattern depends on the changes in the Fr. But, the secondary flow pattern does not change much by changing the Fr. Also, changes in the [Formula: see text]/[Formula: see text] ratio affect the secondary flow pattern and shear stress pattern, so that for [Formula: see text]/[Formula: see text], a small rotary cell is made in addition to the main rotary cell near the outer coast. The results also show that the flow pattern and shear stress depend on the channel angle.

Nová interpretace fosilního záznamu v metamorfovaných horninách u Koberov (krkonošsko-jizerské krystalinikum, geopark UNESCO Český ráj, Česká republika)

The belt of dark carbonaceous rocks (shale and metamorphic limestone) near Koberovy (Krkonoše-Jizerské Mts. Crystalline Complex) is historically considered a record of the Silurian marine environment, due to the findings of poorly preserved but abundant fossils. Prantl (1948) considered them to be graptolites and, based on existing knowledge, classified the rocks as Silurian. Chlupáč (e.g. 1989) was of a similar opinion. However, later, the same author (Chlupáč 1993) re-interpreted all the remnants of the fauna found as traces of the activity of organisms, thus extending a possible stratigraphic interpretation to virtually entire Phanerozoic. Two different types of Koberovy fossils (two samples) were donated to me by prof. Chlupáč shortly before his death. These are two plates of graphitic calcareous shale, the metamorphism of which is revealed on foliation planes (parallel to bedding) for example by the presence of metamorphic minerals such as white mica (muscovite) and chlorite. The first of these has almost straight to slightly curved “strings” on the surface – probably the original bedding plane – in the left part (oriented according to Fig. 1A), which are dark under normal light; however, surface minerals have a pronounced luster, therefore under a particular illumination, the “strings” appear as light lines. The width of the lines is almost constant, about 0.6 mm. Another group of lines occurs in the centre of the sample. These show a “loop” pattern which can be compared to the double “e” in cursive writing. The width of these lines is around 0.6 mm again, with random fluctuations to lower values. A similar and final biogenic structure is in the top right of the Figure 1A. These are three semi-arcs, the estimated half of which is missing on the sample, probably representing an original 3-D spiral-like structure. Width of this structure is on average slightly larger than the previous two structures: it reaches about 0.8–1.0 mm. The second finding is preserved similarly: on the photograph (Fig. 1B), reflected light is used to highlight the dark fossil on the gray carbonaceous slate background. This sample contains four crescent-shaped segments, two in the “D” position and the remaining two in the “C” position. The next segment has an irregular oval shape and the last is a dashed line. The size of the structures is about 30 mm. Chlupáč (1993) withdrew from the original opinion that these poorly-preserved fossils are graptolites (Prantl 1948, Chlupáč 1953). Instead, he offered an interpretation that these were trace fossils. However, we cannot agree with this view for following reasons: 1. Ichnofossils, which have a similar contour as the spiral structures of the first finding, belong in particular to the ichnogenera Gordia Emmons, 1844 and Spirodesmos Andree, 1920. These fossils are surface grazing traces preserved in hyporelief or epirelief. Such ichnofossils have a small conservation potential during regional metamorphism, with movements and chemical transformations on the foliation planes. No rich relief-ichnofauna has been found in regional metamorphic rocks worldwide. 2. On the other hand, ichnofossils, which have the character of full reliefs, can be preserved even in high-grade metamorphic rocks (staurolite isograd in Jeseníky Mts., Chlupáč 1987a). However, they do not appear on the foliation planes, but are preserved within the rigid beds (quartzite) and are usually best observed in vertical fractures of the rock. The preservation of Gordia ichnofossil in a sequence of rhythmically alternating layers of black calcareous shales and graphitic crystalline limestones (sometimes dolomitic) is hard to imagine. For instance, even in completely unmetamorphosed rocks, surface ichnofossils and trace fossils of shallow tiers do not tend to persist; the limestone environment is specific and largely restrictive for the preservation of ichnofossils; see Savrda et al. (2012).

Extraction of hexavalent chromium from wastewater using novel rotating zigzag contactor

ABSTRACT HIGEE (an acronym of high gravity) devices have attracted considerable attention among the researchers due to its immense process intensification capability. In order to achieve desired process efficiency this technology replaces terrestrial acceleration by centrifugal one (typically 1000g) which can be attained by rotating a specially shaped rigid bed. This study focuses on liquid–liquid extraction of hexavalent chromium [Cr(VI)] from wastewater using aliquat-336 as an extractant inside a novel rotating zigzag contactor (RZC). Extraction efficiency of RZC were observed with the variation in pH (2–10), rotational speed (300–1100rpm), aqueous phase (0.4–1.2 L-min−1) and organic phase (0.05–0.15 L-min−1) flow rate, feed (25–200 mg-L−1) and extractant (0.5–1.25 vol%) concentration. The results obtained from this study showed a significant improvement in extraction efficiency (85–99%) with the variation in rotational speed (300–1100rpm). It was observed that the efficiency increased with rotational speed, total flow rate and the organic phase flow rates but decreased with the feed concentration and pH of the aqueous solution. Comparison with some conventional contactors reveals that the extraction efficiency obtained in RZC was nearly 40–50% higher under the same operating conditions.

Numerical simulation of early stages of scour around a submarine pipeline using a two-phase flow model

Current-induced scour around a submarine pipeline during onset and tunnel erosion are investigated in both clear-water and live-bed regimes using an Eulerian–Eulerian two-phase model for sediment transport. The Hybrid Fictitious Domain-Immersed Boundary (HFD-IB) method is adopted to simulate the pipeline structure. The model is validated against two published experimental data: (1) flow past a pipeline near a rigid bed and (2) scour around a pipeline over a sand-bed, showing favorable results for the flow and scour patterns around the pipe. The driving mechanisms of the onset and tunnel erosion are investigated by examining the detailed fluid–sediment interactions around the pipe in both regimes. The driving mechanisms for the onset and tunnel erosion are found similar in both regimes, except their time and magnitude scales. The onset is triggered by the piping mechanism induced by the upstream–downstream pressure gradient beneath the pipe. Meanwhile, the jet flow is the driving mechanism for the tunnel erosion. The simulated live-bed condition shows a higher upstream–downstream pressure gradient beneath the pipe, faster piping mechanism, more intense jet flow velocity and sediment flux compared to the clear-water condition. The model well capture these underlying mechanisms, suggesting its promising capability as a predictive tool for scouring.

Utilization of Geogrid and Water Cushion to Reduce the Impact of Nappe Flow and Scouring on the Downstream Side of a Levee

Water overflowing from a levee generates scour holes on the toe, which progresses towards the backward crest of the levee and results in nappe flow generation. The direct collision of nappe flow on the downstream area causes levee failure. It is important to introduce a novel countermeasure against scouring caused by nappe flow. Hence, the present study utilized a new technique to reduce scouring due to nappe flow by introducing a combination of pooled water and geogrids. Herein, laboratory experiments were conducted with the three cases for rigid bed (R), named as NR, G1R, G2R (N, G1 and G2 represent no geogrid, geogrid 1 and geogrid 2, respectively), and moveable bed (M), named as NM (nothing moveable), G1M (geogrid 1 moveable), G2M (geogrid 2 moveable), to elucidate the effect of dimensionless pooled water depth (DP*), overtopping depth (DC*) and the aperture size of geogrids (d*) on flow structure and scouring. The results showed that the scour depth was reduced by around 17–31% during the NM cases, 57–78% during the G1M cases and 100% during the G2M cases by increasing the DP* from 0.3 to 0.45. Hence, the combination of geogrids with pooled water (G1M, G2M) performed a vital role in suppressing the scouring, but the results of G2M were more advantageous in terms of scouring countermeasures.

Experimental investigation of flow pattern at 180° bend with rigid bed in effect of twin convergent bridge piers

The generation of vortices in sharp bends of rivers is a well-known phenomenon. However, their influence on the bridge pier has not been investigated deeply. This study studies the flow pattern around the twin convergent bridge pier in a sharp bend by an experimental approach. The test facility includes a channel located at Advanced Hydraulic Laboratory, Persian Gulf University, with a 1 m width and 2 m central radius. The flow 3D velocity is measured along the bend by an ADV velocimeter. It is realized that the most important vortex from a sediment transport point of view is located adjacent to a pier in a plane just parallel to the flow direction. Furthermore, it could be concluded that the pier influencing range has an approximate dimension of 10 times pier diameter in a plane parallel to flow and 3 timer pier diameters in the vertical plane. Results and discussions are presented throughout the paper.

Hydraulic Jump on a Partially Vegetated Bed

AbstractHydraulic jump may form when a supercritical flow runs over a vegetated bottom and change the downstream flow hydraulics and fluid properties after air‐water mixing and energy dissipation at the flow transition. Unlike the abundant literature on hydraulic jump characteristics on engineered or natural sediment rough beds, few studies of vegetation roughness effects have been reported. New experiments were conducted by creating hydraulic jumps with identical inflow Froude numbers on a smooth bed, fully and partly grated rough beds, and partially vegetated grate‐rough beds covered with artificial plants of different densities. The free‐surface dynamics and air‐water flow properties were investigated with primary focus on the interaction between the flow and flexible vegetation barrier/roughness, in addition to the effects of Froude number and inflow roughness conditions. The characteristic jump and jump roller lengths were found shortened as the jump roller was deflected over the vegetation layer. The flow structure modification was observed with a steepening of the roller free‐surface profile and enhanced surface wave propagation, especially when the flow experienced an invert roughness discontinuity at the toe. An increasing bubble detection frequency was obtained in nonvegetated channels when the bed was roughened, but additional vegetation on the rough invert caused reduction in the bubble frequency and cross‐sectional mean air concentration by inducing roller deflection and air bubble detrainment. The results indicated that the effects of perturbing artificial flexible vegetation with relatively large plant height could be different from uniformly distributed rigid bed roughness elements and complicated by the time‐varying flow‐vegetation interaction.

Interaction between breaking-induced vortices and near-bed structures. Part 1. Experimental and theoretical investigation

The present work describes the vortex–vortex interactions observed during laboratory experiments, where a single regular water wave is allowed to travel over a discontinuous rigid bed promoting the generation of both near-bed and surface vortices. While near-bed vortices are generated by the flow separation occurring at the bed discontinuity, surface vortices are induced by the wave breaking in conjunction with a breaking-induced jet. A ‘backward breaking’ (previously observed in the case of solitary waves) occurs at the air–water interface downstream of the discontinuity and generates a surface anticlockwise vortex that interacts with the near-bed clockwise vortex. With the vortex–vortex interaction influenced by many physical mechanisms, a point-vortex model, by which vortices evolve under both self-advection (in relation to both free surface and seabed) and mutual interaction, has been implemented to separately investigate the vortex- and wave-induced dynamics. The available data indicate that both self-advection and mutual interaction are the governing mechanisms for the downward motion of the surface vortex, with the effect of the breaking-induced jet being negligible. The same two mechanisms, combined with the mean flow, are responsible for the almost horizontal and oscillating path of the near-bed vortex. The investigation of the vortex paths allow us to group the performed tests into three distinct classes, each characterized by a specific range of wave nonlinearity. The time evolution of the main variables characterizing the vortices (e.g. circulation, kinetic energy, enstrophy, radius) and their maximum values increase with the wave nonlinearity, such dependences being described by synthetic best-fit formulas.

Hydraulics of flow over full-cycle cosine and rectangular sharp-crested weirs

Laboratory experiments were carried out to investigate the hydraulic characteristics of full-cycle cosine and rectangular sharp-crested weirs in free flow condition. The head–discharge relationships of full-cycle cosine weirs were determined theoretically and the discharge coefficients were correlated with weir geometry for both rigid and erodible bed conditions. The proposed model showed higher discharge coefficients in full-cycle cosine weirs in comparison with rectangular sharp-crested weirs. The three-dimensional velocity profiles of full-cycle cosine and rectangular weirs were measured by an acoustic Doppler velocimeter probe. The effects of weir geometry on mean flow and local erosion upstream of the weirs were studied for two sediment sizes of 0.7 mm and 1.2 mm. The time-averaged velocity profiles exhibited strong three-dimensional flow in full-cycle cosine weirs. The strength of the upper eddy in the crest location of full-cycle cosine weirs decreased by increasing the weir gap opening and the jet stream deflected upward due to uneven eddy sizes. The maximum streamwise velocity of cosine weirs increased by four times the average velocity at the crest level of the weir and the transverse velocity profiles captured strong vortices in the vertical plane closest to the weir. The effect of weir gap opening of full-cycle cosine weirs on the total scour volume was studied for two sediment sizes. It was found that the scour volume in the upstream region of cosine weirs was higher than the scour volume formed upstream of a rectangular weir with the same opening.