A σ -coordinate transport model coupled with rotational boussinesq-type equations

This paper describes a σ -coordinate scalar transport model coupled with a Boussinesq-type hydrodynamic model. The Boussinesq model has the ability to calculate both three-dimensional velocity distributions and the water surface motion. To capture ‘dispersion’ processes in open channel flow, horizontal vorticity effects induced by a bottom shear stress are included in the Boussinesq model. Thus, a reasonable representation of vertical flow structure can be captured in shallow and wavy flow fields. To solve the coupled Boussinesq and scalar transport system, a finite-volume method, based on a Godunov-type scheme with the HLL Riemann solver, is employed. Basic advection and advection–diffusion numerical tests in a non-rectangular domain were carried out and the computed results show good agreement with analytic solutions. With quantitative comparisons of dispersion experiments in an open channel, it is verified that the proposed coupled model is appropriate for both near and far field scalar transport predictions. From numerical simulations in the surf zone, physically reasonable results showing expected vertical variation are obtained.