Quantification of river bedform variability and complexity is important for sediment transport modeling as well as for characterization of river morphology. Alluvial bedforms are shown to exhibit highly nonlinear dynamics across a range of scales, affect local bed roughness, and vary with local hydraulic, hydrologic, and geomorphic properties. This paper examines sediment sorting on the crest and trough of gravel bedforms and relates it to bed elevation statistics. The data analysed here are the spatial and temporal series of bed elevation, grain size distribution of surface and subsurface bed materials, and sediment transport rates from flume experiments. We describe surface topography through bedform variability in height and wavelength and multiscale analysis of bed elevations as a function of discharge. We further relate bedform migration to preferential distribution of coarse and fine sediments on the troughs and crests, respectively, measuring directly surface and subsurface grain size distributions, and indirectly the small scale roughness variations as estimated from high resolution topographic scans.
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The paper describes the derivation of a depth-averaged, two-dimensional form of the sediment balance equation, suitable to study the morphodynamics of movable sediment beds even when the flow depth attains values comparable to bed irregularities. This equation is derived by double-averaging in time and in space the instantaneous three-dimensional sediment balance equation. For this, a proper phase function is introduced, which depends on the statistics of bed topography. The structure of the macroscopic volumetric sediment discharge vector resulting from the averaging procedure is discussed for the case of dominant bedload transport. The theoretical framework developed within the paper sets the stage for a proper parametrization of the physical processes acting at spatial scales smaller than those usually resolved by depthaveraged numerical models.
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