A balanced treatment of secondary currents, turbulence and dispersion in a depth-integrated hydrodynamic and bed deformation model for channel bends

This work deals with the formulation and numerical implementation of a two-dimensional mathematical and numerical model describing open channel hydrodynamics, sediment and/or scalar transport and riverbed evolution in curved channels. It is shown that a well balanced 2D model can predict flow features, sediment and scalar concentration, and bed elevation with an accuracy that is suitable for practical river engineering. The term “balanced” implies that important physical processes are modeled with a similar degree of complexity and exhaustiveness. The starting point of the model formulation is the assumption of self-similarity of vertical velocity profiles (horizontal velocities in the longitudinal and transverse directions), that are scaled by shear velocity and streamline curvature, both resolved by the model. The former is scaled by a bed-resistance coefficient that must be estimated or calibrated – as usual – on a application-specific basis, and the latter is computed by a new, grid-based but grid orientation independent, scheme that acts on the discrete solution. All processes, including bottom shear, momentum dispersion, scalar dispersion, turbulent diffusion, bed load, and suspended load, are modeled using physically based, averaged values of empirical or semi-empirical constants, and consistently with the assumed velocity profiles (and bed-generated turbulence). Bed deformation modeling can be implemented with either an equilibrium or non-equilibrium formulation of the Exner equation, depending on the adaptation length scale, which must be taken under consideration if significantly larger than the length scale of the spatial discretization. The governing equations are solved by high-resolution, unstructured-grid Godunov method, which is elsewhere tested and shown to be reliable and second-order accurate. Application of the model to laboratory test cases, using standard parameter values and previously reported bed-resistance coefficients, gives results comparable to many 2D and 3D models previously applied to the same cases, most part of which benefit from case-specific parameter tuning. There are obviously intrinsic limits to the descriptive ability of 2D models in river modeling, but the results of this study point to the utility and cost-effectiveness of a well-designed 2D model.