Curvature-induced secondary flow in 2D depth-averaged hydro-morphodynamic models: An assessment of different approaches and key factors

Curvature-induced secondary flows are ubiquitous in nature and have long attracted scientist attention. Modelling such kind of secondary flows is not straightforward. While full 3D models fit the purpose at the cost of great computational demand, simplified models often pose concerns about their effectiveness and the representation of key processes. In the present study, helical flow secondary currents are included in a two-dimensional depth-averaged hydro-morphodynamic model on cartesian unstructured meshes. The non-uniform vertical distribution of velocity in streamwise and spanwise directions is accounted for introducing dispersive terms in the shallow water equations, an anisotropic diffusivity tensor in the advection-diffusion equation, and a correction to the direction of bed shear stress and bedload transport. Different approaches available in the literature are recast in similar form and compared to each other in terms of flow field, tracer transport, and bed evolution, using data from laboratory experiments and real-world case studies. The model includes a novel, pure 2D implementation of the non-linear saturation mechanism that limits the growth of secondary flows in relatively sharp bends. A substantial part of the paper is devoted to discuss key factors in secondary flow modelling, including implementation tricks, guidelines to mesh design, the suitability of local and non-local approaches, and the role of bathymetry. The final goal is to provide useful guidelines for 2D hydro- and morphodynamic modelling in river bends.