Nonlinear modeling of mean flow redistribution in curved open channels

Phenomena concerning flow, morphology, and water quality in rivers are often investigated by means of a depth-integrated flow model, coupled to a sediment transport model and a water quality model. In such depth-integrated models, the vertical structure of the flow is represented by a closure submodel, which mainly has to account for the secondary circulation, which (1) redistributes by advection the flow, the boundary shear stresses, the sediment transport, and dissolved and suspended matter, (2) causes the direction of the bed shear stress to deviate from the direction of the depth-averaged velocity and thereby influences the bed topography, and (3) gives rise to additional friction losses as compared with straight uniform flow. The commonly used linear closure submodels are shown to fail in reproducing essential features in moderately to strongly curved flow, because they neglect the feedback between the downstream velocity and the secondary circulation. A nonlinear closure submodel taking this feedback into account is proposed and shown to yield results that compare well with experimental data, even for very strongly curved flow. The feedback effects turn out to be controlled almost exclusively by a single parameter, which enables their parameterization in a relatively simple way. This control parameter also helps to objectively distinguish weak, moderate, and strongly curved flows. The proposed closure submodel has the potential of improving the performance of depth-integrated flow-sediment-water quality models without much extra computational effort.