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Pebble clusters are common small-scale morphological features in gravel-bed rivers, occupying as much as 10 per cent of the bed surface. Important links exist between the presence of pebble clusters and the development of flow structures. These links are poorly understood at the three-dimensional level. Particularly neglected has been the effect of clusters on the lateral flow characteristics. A laboratory study was conducted using a hydraulic flume, within which simulated pebble clusters were superimposed onto a plane bed of gravel material. High-resolution three-dimensional flow data were collected above the bed at two different flow depths using an acoustic Doppler velocimeter. The results present evidence of the importance of lateral flow in the development of turbulent flow structure. Narrow regions of high lateral and downstream turbulence intensity exist to both sides of clusters and in a three-dimensional separation zone in their lee. This may indicate the presence of horseshoe-type vortical structures analogous to those identified in less hydraulically rough environments. However, it is likely that these structures are more complicated given the mutual interference of the surrounding medium. The lateral flow was also identified as a key component in the upwelling identified by other authors in the lee of pebble clusters. The results of the vertical flow analysis confirm the hypothesis that six regions with distinct vertical flow characteristics exist above clusters: flow acceleration up the stoss-side of the cluster; recirculation behind the cluster in the wake region; vortex shedding from the pebble crest and shear layer; flow reattachment downstream of the cluster; upwelling of flow downstream of the point of reattachment; and recovery of flow.

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Resilient water supply infrastructure is fundamental for human life and wellbeing (Hallegatte et al., 2019). As adverse impacts of climate change threaten the Sustainable Development Goals (SDGs) (UN, 2021), the need for resilient water supply infrastructure is increasingly important if several SDG targets including clean water and sanitation (SDG 6) are to be met by 2030 (Krueger et al., 2020). However, climate extremes, such as droughts and floods, pose a high risk to water supply infrastructure given their proximity to, and dependency on, water bodies

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A key problem in computational fluid dynamics (CFD) modelling of gravel-bed rivers is the representation of multiscale roughness, which spans the range from grain size, through bedforms, to channel topography. These different elements of roughness do not clearly map onto a model mesh and use of simple grain-scale roughness parameters may create numerical problems. This paper presents CFD simulations for three cases: a plane bed of fine gravel, a plane bed of fine gravel including large, widely-spaced pebble clusters, and a plane gravel bed with smaller, more frequent, protruding elements. The plane bed of fine gravel is modelled using the conventional wall function approach. The plane bed of fine gravel including large, widely-spaced pebble clusters is modelled using the wall function coupled with an explicit high-resolution topographic representation of the pebble clusters. In these cases, the three-dimensional Reynolds-averaged continuity and Navier-Stokes equations are solved using the standard k − ε turbulence model, and model performance is assessed by comparing predicted results with experimental data. For gravel-bed rivers in the field, it is generally impractical to map the bed topography in sufficient detail to enable the use of an explicit high-resolution topography. Accordingly, an alternative model based on double-averaging is developed. Here, the flow calculations are performed by solving the three-dimensional double-averaged continuity and Navier-Stokes equations with the spatiallyaveraged 〈k − ε〉 turbulence model. For the plane bed of fine gravel including large, widely-spaced pebble clusters, the model performance is assessed by comparing the spatially-averaged velocity with the experimental data. The case of a plane gravel bed with smaller, more frequent, protruding elements is represented by a series of idealized hypothetical cases. Here, the spatiallyaveraged velocity and eddy viscosity are used to investigate the applicability of the model, compared with using the explicit highresolution topography. The results show the ability of the model to capture the spatially-averaged flow field and, thus, illustrate its potential for representing flow processes in natural gravel-bed rivers. Finally, practical data requirements for implementing such a model for a field example are given.

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