In the original paper, the term “particle density” was erroneously changed during the review process to “particle spacing.” Therefore, all through the paper the text errors should be revised by replacing “spacing” with “density” or “densities.” Revised versions of Figs. 4–8 and 10 are also provided herein. The correct use of the word “spacing” only remains in following four lines in the text: • First paragraph of “Bedload Transport Data” section: “The sediment transport ratio of each case shows that increasing the spacing between the large immobile particles : : : ” • Fourth paragraph of “Holistic Interpretation of the Results” section: “Alternatively, spacing the clusters closer together resulted in the flow patterns interfering with each other and reducing the energy of the turbulence cells.” • Fifth paragraph of “Holistic Interpretation of the Results” section: “(2) at a narrow range of large immobile particle spacings, flow structures build upon each other and amplify their erosive forces.” • Last paragraph of “Conclusions” section: “(2) at a narrow range of large immobile particle spacings, flow structures build upon each other and amplify their erosive forces.” The updated version of the paper may be read with this correction. Inconvenience is regretted.

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A common approach used to mitigate riverbank erosion and maintain watercourse alignments has been through the application of riprap or larger, more stable particles to channel boundaries along reaches of interest. However, very often, these large particles become dislodged from their intended locations (failed erosion measures), becoming part of the bed material composition. In natural systems, large immobile sediments or boulders can also be found, which are often sourced from glacial erratics or colluvial inputs with different spacing and arrangements among them. In lower gradient gravel-bed channels, the impacts that large clasts may impart on river morphologies are uncertain and are studied in this paper. This paper utilizes laboratory experiments to evaluate the effects that varying spacing of large immobile particles in a gravel-bed channel have on sediment transport and bed morphology. The laboratory experiments consist of a series of test cases with a varying spacing of large immobile particles and one base case with no large immobile particles present. In each case, the flume bed was composed of a poorly sorted gravel mixture with a bimodal distribution of sand and gravel meant to be representative of a natural gravel-bed channel. The results of the test cases demonstrated that at a low spacing of large immobile particles, the transported material and the bed material both became coarser. At a medium spacing of large immobile particles, the bed material size and erosion reached a maximum, and the coarser bed material was transported at approximately the same rate as the finer material. Finally, at a high spacing of large immobile particles, the size of the transported material and bed material sizes were similar to that of the base case, and the sediment transport also had the strongest clockwise hysteresis trend, which ultimately led to a net erosion of the gravel-bed channel.

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The aim of this work is the application of a 2D depth-averaged URANS simulation model to study the resonant coupling between standing gravity waves and vortex shedding in shallow water cavity flows. The URANS turbulence modelling approach is adopted for this purpose thanks to the particularities of these turbulent shallow flows: they are characterized by large scale horizontal eddies (2D), which coexist with small-scale 3D turbulence. The proposed model uses a high-resolution WENO-ADER numerical scheme, which allows to accurately resolve the large 2D eddies with a low numerical diffusion and dispersion. The small-scale 3D turbulence cannot be resolved by the 2D depth-averaged URANS, hence it is modelled using a closure relation. Experimental data recorded in straight channels with lateral cavities is considered as benchmark. The ability of the model to predict the resonant gravity waves observed in the experimental setup is assessed. Furthermore, the numerical results are not only analyzed in the physical domain (i.e. space and time) but also in the frequency domain. The study of the spectral characteristics of the time evolution of the water surface and vorticity allows to obtain 2D maps of the seiche amplitude and coupling intensity.@en

Large-Eddy Simulations (LES) are used to investigate the governing processes involved in mass and momentum transfer between the flow in the main channel and symmetrically-distributed lateral bank cavities. In-cavity free-surface velocities, based on laboratory measurements made in an open channel, are used to validate the numerical results. A main vortical structure dominates the in-cavity flow which, despite the shallow nature of the flow, features a remarked three dimensional dynamics. LES results outline the largest velocities through the mouth of the cavity are attained in two thin regions near the bottom-bed and free-surface. In the shear layers established between the main channel and cavities is where the main transfer of turbulent momentum is made between these two flow regions, and the numerical simulations capture well the instantaneous coherent flow structures, e.g. Kelvin-Helmholtz vortices. LES captures a low-frequency standing wave phenomenon even with a rigid-lid approximation adopted at the free-surface boundary. Momentum exchange between cavities and main channel is analysed using the Reynolds Averaged momentum equation in the transverse direction, revealing that the pressure gradient term is the unique contributor to flushing momentum out of the cavities whilst convection and Reynolds normal stress terms are responsible for its entraining into the cavity. Furthermore, sediment deposition areas documented in the laboratory experiments are linked with the simulated hydrodynamics, which correlate with regions of low turbulent kinetic energy and vertical velocities near the bottom of the channel. Overall, the results shed new light into the complex mechanisms involved in mass and momentum transfer; this will aid to design embayments more efficiently regarding sediment transport processes.

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Overbank sedimentation is predominantly due to fine sediments transported under suspension that become trapped and settle in floodplains when high-flow conditions occur in rivers. In a compound channel, the processes of exchanging water and fine sediments between the main channel and floodplains regulate the geomorphological evolution and are crucial for the maintenance of the ecosystem functions of the floodplains. These hydrodynamic and morphodynamic processes depend on variables such as the flow-depth ratio between the water depth in the main channel and the water depth in the floodplain, the width ratio between the width of the main channel and the width of the floodplain, and the floodplain land cover characterized by the type of roughness. This paper examines, by means of laboratory experiments, how these variables are interlinked and how the deposition of sediments in the compound channel is jointly determined by them. The combination of these compound channel characteristics modulates the production of vertically axised large turbulent vortical structures in the mixing interface. Such vortical structures determine the water mass exchange between the main channel and the floodplain, conditioning in turn the transport of sediment particles conveyed in the water, and, therefore, the resulting overbank sedimentation. The existence and pattern of sedimentation are conditioned by both the hydrodynamic variables (the flow-depth ratio and the width ratio) and the floodplain land cover simulated in terms of smooth walls, meadow-type roughness, sparse-wood-type roughness, and dense-wood-type roughness.

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Turbulent shallow flows are characterized by the presence of horizontal large-scale vortices, caused by local variations of the velocity field. Apart from these 2D large vortices, small scale 3D turbulence, mainly produced by the interaction of the flowing water with the solid boundaries, is also present. The energy spectrum of turbulent shallow flows shows the presence of a 2D energy cascade at low wave numbers and a 3D energy cascade at high wave numbers, with a well-defined separation region between them. Horizontal flow movements (e.g. 2D large-scale vortical structures) at low wave numbers mostly determine the hydrodynamic behavior of these flows. Moreover, the generation of standing waves often occurs closely associated to the interaction of 2D horizontal flows with lateral boundaries, this is the case of seiches. To adequately reproduce these phenomena, a mathematical and numerical model able to resolve 2D turbulence is required. We herein show that depth-averaged (DA) unsteady Reynolds averaged Navier Stokes (URANS) models based on the Shallow Water Equations (SWE) are a suitable choice for the resolution of turbulent shallow flows with sufficient accuracy in an affordable computational time. The 3D small-scale vortices are modeled by means of diffusion terms, whereas the 2D large-scales are resolved. A high order numerical scheme is required for the resolution of 2D large eddies. In this work, we design a DA-URANS model based on a high order augmented WENO-ADER scheme. The mathematical model and numerical scheme are validated against observation of complex experiments in an open channel with lateral cavities that involve the presence of resonant phenomena (seiching). The numerical results evidence that the model accurately reproduces both longitudinal and transversal resonant waves and provides an accurate description of the flow field. The high order WENO-ADER scheme combined with a SWE model allows to obtain a powerful, reliable and efficient URANS simulation tool.

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A laboratory study was undertaken to investigate how changes in flow regime and hydrograph shape (number of cycled hydrographs and duration of each hydrograph) together impact bedload transport and resulting bed morphology. Three hydrologic conditions (experiments) representing different levels of urbanization, or analogously different flow regimes, were derived from measured hydrometric field data. Each experiment consisted of a series of hydrographs with equal peak discharge and varying frequency, duration and flashiness. Bedload transport was measured throughout each hydrograph and measurements of bed topography and surface texture were recorded after each hydrograph. The results revealed hysteresis loops in both the total and fractional transport, with more pronounced loops for longer duration hydrographs, corresponding to lower rate of unsteadiness until reaching the peak discharge (pre-urbanization conditions). Shorter duration hydrographs (urban conditions) displayed more time above critical shear stress thresholds leading to higher bedload transport rates and ultimately to more variable hysteresis patterns. Surface textures from photographic methods revealed surface armoring in all experiments, with larger armor ratios for longer duration hydrographs, speculated to be due to vertical sorting and more time for bed rearrangements to occur. The direction of bed surface adjustment was linked to bedload hysteresis, more precisely with clockwise hysteresis (longer hydrographs) typically resulting in bed coarsening. More frequent and shorter duration hydrographs result in greater relative channel adjustments in slope, topographic variability and surface texture.

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