Numerical simulation of roll waves using shallow water equations with consideration of Boussinesq’s coefficient

Hidekazu Shirai, Takashi Hosoda, Naoya Kanazawa

Monday 29 june 2015

14:50 - 15:05h at Amazon (level 1)

Themes: (T) Water engineering, (ST) River and coastal engineering

Parallel session: 2C. Coastal engineering

Roll waves are unsteady open channel flows which can be seen in steep open channels. Many researchers have been studied these phenomena experimentally and theoretically to clarify the hydraulic characteristics of them, specially wave profiles. According to Dressler (1949) mathematical theory, which is derived from shallow water equations by assuming that Boussinesq’s coefficient is 1.0, the wave profiles are determined by discharge, channel slope and wave celerity. Later, Ishihara et al.(1954) and Iwagaki & Iwasa (1955) extended this theory to deal with both turbulence and laminar water flows by Boussinesq’s coefficient equal to 1.05-1.2. However, using this extended theory, wave profiles are uniquely determined without relation to wave celerity. In this study, the derivation of the theory was reviewed and compared with Dressler’s theory, in order to understand the origin of this difference from Dressler’s theory. Numerical simulation of roll waves were also conducted. It was found that wave profiles are not unique and that roll waves have various wavelength and wave height in numerical results regardless of Boussinesq’s coefficient. Finally, comparison of Dressler’s theory and the numerical simulation results show that the wave profiles presented by Ishihara et al. and Iwagaki & Iwasa’s theory can be obtained under the limited situation.