Flow modelling in gravel-bed rivers: rethinking the bottom boundary condition
A key problem in computational fluid dynamics (CFD) modelling of gravel-bed rivers is the representation of multi-scale roughness, which spans the range from grain size, through bedforms, to channel topography. These different elements of roughness do not clearly map onto a model mesh and use of simple grain-scale roughness parameters may create numerical problems. This paper presents CFD simulations for three cases: a plane bed of fine gravel, a plane bed of fine gravel including large, widely-spaced pebble clusters, and a plane gravel bed with smaller, more frequent, protruding elements. The plane bed of fine gravel is modelled using the conventional wall function approach. The plane bed of fine gravel including large, widely-spaced pebble clusters is modelled using the wall function coupled with an explicit high-resolution topographic representation of the pebble clusters. In these cases, the three-dimensional Reynolds-averaged continuity and Navier–Stokes equations are solved using the standard k − e turbulence model, and model performance is assessed by comparing predicted results with experimental data. For gravel-bed rivers in the field, it is generally impractical to map the bed topography in sufficient detail to enable the use of an explicit high-resolution topography. Accordingly, an alternative model based on double-averaging is developed. Here, the flow calculations are performed by solving the three-dimensional double-averaged continuity and Navier-Stokes equations with the spatially-averaged 〈k − e〉 turbulence model. For the plane bed of fine gravel including large, widely-spaced pebble clusters, the model performance is assessed by comparing the spatially-averaged velocity with the experimental data. The case of a plane gravel bed with smaller, more frequent, protruding elements is represented by a series of idealized hypothetical cases. Here, the spatially-averaged velocity and eddy viscosity are used to investigate the applicability of the model, compared with using the explicit high-resolution topography. The results show the ability of the model to capture the spatially-averaged flow field and, thus, illustrate its potential for representing flow processes in natural gravel-bed rivers. Finally, practical data requirements for implementing such a model for a field example are given.