Numerical modeling of flow processes over gravelly surfaces using structured grids and a numerical porosity treatment

Abstract

This article describes the development and validation of a method for representing the complex surface topography of gravel bed rivers in high‐resolution three‐dimensional computational fluid dynamic models. This is based on a regular structured grid and the application of a porosity modification to the mass conservation equation in which fully blocked cells are assigned a porosity of zero, fully unblocked cells are assigned a porosity of one, and partly blocked cells are assigned a porosity of between 0 and 1, according to the percentage of the cell volume that is blocked. The model retains an equilibrium wall function and an RNG‐type two‐equation turbulence model. The model is combined with a 0.002 m resolution digital elevation model of a flume‐based, water‐worked, gravel bed surface, acquired using two‐media digital photogrammetry and with surface elevations that are precise to ±0.001 m. The model is validated by comparison with velocity data measured using a three‐component acoustic Doppler velocimeter (ADV). Model validation demonstrates a significantly improved level of agreement than in previous studies, notably in relation to shear at the bed, although the resolution of model predictions was significantly higher than the ADV measurements, making model assessment in the presence of strong shear especially difficult. A series of simulations to assess model sensitivity to bed topographic and roughness representation were undertaken. These demonstrated inherent limitations in the prediction of 3‐D flow fields in gravel bed rivers without high‐resolution topographic representation. They also showed that model predictions of downstream flux were more sensitive to topographic smoothing that to changes in the roughness parameterization, reflecting the importance of both mass conservation (i.e., blockage) and momentum conservation effects at the grain and bed form scale. Model predictions allowed visualization of the structure of form‐flow interactions at high resolution. In particular, the most protruding bed particles exerted a critical control on the turbulent kinetic energy maxima typically observed at about 20% of the flow depth above the bed.