Quasi-3D modelling of bed shear stresses at high curvature

Single thread meandering rivers exhibit complex planformpatterns in their floodplains, resulting from a complex interaction between flow, bed and bank morphology. The flow through meander bends may be characterized by primary flow in streamwise direction and secondary flow in transverse direction. The secondary flow plays an important role in the redistribution of streamwise momentum and also affects the bed shear stress, which is important for the shaping of the bed topography. Presently, most depth-averaged morphodynamic models adopt a secondary flow parameterization, based on mild curvature assumptions. This yields a linear relation between curvature and secondary flow strength. However, in strongly curved river bends, the secondary flow strength weakens considerably, due to the non-linear interaction of the streamwise and transverse velocity profiles. This interaction does not only affect the redistribution of streamwise momentum, but it is also important for the direction and magnitude of the bed shear stresses. A non-linear quasi-3D hydrodynamic model (i.e. depth averaged plus 3D parameterizations) is presented and used to simulate two sharply curved flume experiments over a horizontal and fully developed bed. The hydrodynamics results are compared to measurements, a three-dimensional hydrodynamic model, a three-dimensional hydrodynamic model with few layers, a linear hydrodynamic model based on mild curvature assumptions, and a depth-averaged model without secondary flow. The non-linear quasi-3D model results show a qualitatively good agreement with measurements and the three dimensional model. The linear quasi-3D model overestimates the angle between the bed shear stress and the depth averaged velocity direction through the bend. Furthermore the linear model fails to capture the increase of bed shear stress magnitude correctly. The depth-averaged model without secondary flow shows no increase of bed shear stress magnitude and no angle between the bed shear stress and the depth averaged velocity direction. Over the horizontal bed the 3D model with a small number of vertical layers underestimates the bed shear stress angle as well as the increase of bed shear stress magnitude. Over the fully developed bed the 3D model with a small number of vertical layers shows an underestimation of the increase of bed shear stress, but shows good agreement for the bed shear stress angle.