Formation of Repeating Bar-Flat Bedforms in Ephemeral Gravel Bed Channels: 2. Bridging Mathematical Modelling and Field Observations

Single- and multi-thread gravel-bed ephemeral channels in semi-arid and arid regions have a characteristic repeating, channel-wide pattern of low angle, fine-grained ‘flats’ alternating with steeper, coarse-grained ‘bars’. The genesis of these macroforms, while a topic of ongoing discussion, has not been fully elucidated. We have documented the formation of these macroforms after both artificially homogenising the bed material of a reach of the Nahal Yatir in the northern Negev, Israel, and ensuring its surface was planar. Here, we integrate the empirical data gained from these field experiments with a novel mathematical model. The model we propose, within a one-dimensional framework, is based on the analysis of flow over an initially planar, erodible bed consisting of a bimodal grain size mixture of sediment. We apply linear stability analysis to derive a solution that provides insight into the formational dynamics of these macroforms. Our results indicate that bar-flat patterns may arise from a free-instability mechanism driven by sediment size heterogeneity, provided that the standard deviation of the sediment grain size distribution (GSD) is sufficiently large. Application of the model to a selection of ephemeral channels of the northern Negev suggests that repeating bar-flat patterns are likely to develop during the recession of flash flood hydrographs, specifically when flow conditions approach the critical threshold for bedload transport. Besides providing a possible explanation for the formation of these macroforms, this study also contributes to a broader understanding of geomorphic processes in dryland river systems.