Grain Size Sorting and Steady Bars Formation in Straight Channels—Part 2: Linear Theory

Abstract This is the second of two papers aimed to investigate grain sorting patterns associated with the formation of steady alternate bars in gravel‐bed rivers. Part 1 presented the analysis of a series of tailored experiments, performed in a mobile bed laboratory flume with fixed, straight banks. The results showed that a consistent pattern of grain size distribution emerges in conjunction with the bed topography upon reaching the final equilibrium configuration, nearly independent of the flow discharge and channel width. In this second part, a two‐dimensional morphodynamic model is formulated to interpret the experimental observations. The model is solved through a linear analysis, which allows the description of the spatial structure of the flow field, channel bed, and bed surface texture at equilibrium. The model accurately reproduces the sorting pattern associated with bar development, as it captures the gradual coarsening upstream of the bar head and finer particles accumulating on the lee side. The sorting pattern is governed by the balance between the selective transport of sediment grains in the streamwise direction and the gravitational effect due to lateral bed slope. The model's outcomes crucially depend on the formulation adopted to describe the effect of lateral bed slope on the direction of sediment transport. Specifically, the good agreement between theory and laboratory data is verified when the effect of lateral hiding on particle direction is neglected. The results suggest the need for a general formulation, supported by dedicated laboratory and numerical experiments, to better understand grain mechanics on arbitrarily sloping beds.