Meander dynamics: A reduced‐order nonlinear model without curvature restrictions for flow and bed morphology

Abstract

AbstractReduced‐order models remain essential tools for meander modeling, especially for processes at large length scales and long time scales, probabilistic simulations, rapid assessments, or when input data are scarce or uncertain. Present reduced‐order meander models consider their dependent variables either as small‐amplitude variations compared to a basic state (linearity) or as varying gradually in a spatial sense (gradual variation). In a prequel, Blanckaert and de Vriend () derived a nonlinear reduced‐order hydrodynamic model without curvature restrictions and showed that linearity or gradual curvature variations assumptions do not hold in strongly curved channels. Moreover, in strongly curved channels, a nonlinear feedback mechanism causes the secondary flow strength to be smaller than its linear mild‐curvature equivalent. In the limit of mild‐amplitude variations and mild curvature, their nonlinear meander flow model simplifies to a well‐known linear formulation. The present paper extends this nonlinear modeling to the bed morphology in strongly curved bends, making use of Exner's sediment conservation principle. Furthermore, the model quantifying the relative influence of the downslope gravitational force is refined by considering nonlinear effects. The coupled nonlinear flow and bed morphology model yields satisfactory results for the bed topography, whereas the corresponding linear model strongly overpredicts the magnitude of the transverse bed slope. Analysis of the forcing mechanisms indicate that this erroneous behavior is caused by an overestimation of the upslope drag force due to the secondary flow.