Undular bores and secondary waves -Experiments and hybrid finite-volume modelling

Abstract

Secondary free-surface undulations (Favre waves), appearing for example after the opening of a sluice gate or at the head of a bore, cannot be reproduced by numerical models based on the hydrostatic pressure assumption. The Boussinesq equations take into account the extra pressure gradients but are difficult to integrate due to the high-order derivative terms. The paper describes the physics of wave initiation and proposes a demonstration of the Boussinesq equation based on relatively wider assumptions than usually adopted. A linear stability analysis is developed in finite-difference frame to highlight some potential source of numerical instabilities. These conclusions are transposed in a new hybrid finite-volume / finite-difference scheme, which reveals a better accuracy in period and amplitude when evaluated against experiments.