Modelling roll waves with shallow water equations and turbulent closure

ABSTRACT

A physically enhanced model is proposed for roll waves based on the shallow water equations and k−ϵ turbulence closure along with a modification component. It is tested against measured data on periodic permanent roll waves, and the impact of turbulence is demonstrated to be essential. It is revealed that a regular inlet perturbation may lead to periodic permanent or natural roll waves, when its period is shorter or longer than a critical value inherent to a specified normal flow. While a larger amplitude or shorter period of a regular inlet perturbation is conducive to the formation of periodic permanent roll waves, their period remains the same as that of the perturbation, while their amplitude increases with the perturbation period and is independent of the perturbation amplitude. An irregular inlet perturbation favours the formation of natural roll waves, so does a larger amplitude of the perturbation.

Keywords:

• k−ϵ turbulence model
• natural roll waves
• periodic permanent roll waves
• shallow water equations
• turbulent Reynolds stress