Spectral description of migrating bed forms and sediment transport

This paper considers the problem of spatiotemporal bed topography evolution and sediment transport estimation in rivers with migrating bed forms of different types and sizes, in statistical equilibrium conditions. Instead of resorting to bed form classification, we propose to evaluate the evolution of multiscale bed topography as the integral of unit contributions defined through a space-time Fourier decomposition of bed elevations. Using joint 2-D spectra in the frequency and wave number domain, a functional relationship between the length scales and the timescales in which migrating bed forms are decomposed is proposed and developed into a dimensionless expression for scale-dependent convection velocities. This formulation highlights the violation of Taylor's hypothesis for migrating bed forms, confirming statistically that larger bed forms travel slower as compared to smaller bed forms. This phenomenological description leads to a spectral extension of the Simons et al. (1965) formula for sediment transport to incorporate a range of multiscale migrating features. Both the scaling of convection velocities and the spectral estimate of sediment transport rate were validated through extensive bed elevation data from laboratory experiments conducted at the St. Anthony Falls Laboratory, for a range of Froude numbers 0.2<Fr<0.5, under varying discharge and bed material composition.