Meander dynamics: A nonlinear model without curvature restrictions for flow in open-channel bends

Despite the rapid evolution of computational power, simulation of meander dynamics by means of reduced and computationally less expensive models remains practically relevant for investigation of large-scale and long-term processes, probabilistic predictions, or rapid assessments. Existing meander models are invariantly based on the assumptions of mild curvature and slow curvature variations and fail to explain processes in the high-curvature range. This article proposes a nonlinear model for meander hydrodynamics without curvature restrictions. It provides the distribution of the main flow, the magnitude of the secondary flow, the direction of the bed shear stress, and the curvature-induced additional energy losses. It encompasses existing mild curvature models, remains valid for straight flow, and agrees satisfactorily with experimental data from laboratory experiments under conditions that are more demanding than sharp natural river bends. The proposed model reveals the mechanisms that drive the velocity redistribution in meander bends and their dependence on the river's roughness C_f, the flow depth H, the radius of curvature R, the width B, and bathymetric variations. It identifies C _f^-1H/R as the major control parameter for meander hydrodynamics in general and the relative curvature R/B for sharp curvature effects. Both parameters are small in mildly curved bends but O(1) in sharply curved bends, resulting in significant differences in the flow dynamics. Streamwise curvature variations are negligible in mildly curved bends, but they are the major mechanisms for velocity redistribution in sharp bends. Nonlinear feedback between the main and secondary flow also plays a dominant role in sharp bends: it increases energy losses and reduces the secondary flow, the transverse bed slope, and the velocity redistribution.