A numerical calculation method for flow in the presence of isolatedboulders atop a rough bed by using an enhanced depth integrated model with a non-equilibrium resistance law

摘要

A new calculation method using the non-hydrostatic depth integrated model coupled with nonequilibrium wall law is proposed to calculate flow over rough bed with boulders. The present method has three calculational domains in the vertical direction in order to separate the effects of Large Scale Roughness (LSR) from that of Small Scale Roughness (SSR),namely: a main domain that takes into account the form effect of boulders, a thin vortex layer on the bed surface and a roughness layer under the bed surface as shown in Figure 1. For the main domain between the water surface and the vortex layer, the BVC method (Uchida & Fukuoka 2012), which is a non-hydrostatic depth integrated model, is refined to employ a non-equilibrium wall law. For the non-equilibrium wall law， momentum equations in vortex and roughness layers are derived based on the relationship between the present method and the conventional wall law. Since the present method is physically based and reduces to the conventional wall law for rough bed for the uniform flow condition, we can use same parameters for the conventional equivalent wall law, such as equivalent roughness height. The refined BVC method with non-equilibrium wall law (BVC-NWL) is applied to benchmark experimental results (Papanicolaou et al., 2012) and compared with the BVC method with equilibrium wall law (BVC-EWL) and 2D method.