Nonhydrostatic Quasi-3D Model Coupled with the Dynamic Rough Wall Law for Simulating Flow over a Rough Bed with Submerged Boulders

A reliable depth-integrated model that is suited for capturing the complex flow found with an array of submerged boulders over a permeable rough bed can be an attractive tool for river management. This paper presents a new nonhydrostatic quasi-three-dimensional (3D) calculation method called the general bottom velocity computation of the fourth-degree polynomial equation for vertical distribution of velocity coupled with the dynamic wall law (GBVC4-DWL). The computational domain of the GBVC4-DWL method considers the presence of the boulders, a vortex layer on the bed surface, and a roughness layer under the bed surface. The novelty of this study is that it introduces a dynamic rough wall law for the bottom boundary condition that includes the continuity and momentum equations for vortex and roughness layers to evaluate the nonequilibrium flow induced by the boulders. Comparisons of the results of the present method with previous experimental results and results of previous calculation methods indicate that the present method exhibits considerable improvements in calculating the velocity distribution over a rough bed with isolated submerged boulders.