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.

Stochastic-deterministic modeling of bed load transport in shallow water flow over erodible slope: Linear stability analysis and numerical simulation

“…However, numerical simulations of free surface instabilities in frictional flows down inclined planes have shown that a non-negligible eddy viscosity ν is required to avoid the development of unphysical short wavelength instabilities as well as to reproduce the non-linear steady-state shape of roll waves [11,15,18,64]. In this study the main role of the eddy viscosity is to prevent the development of discontinuities in the free surface, which allows us to evaluate the free surface slope in the presence of jumps and steps of the bed elevation.…”

“…In this study the main role of the eddy viscosity is to prevent the development of discontinuities in the free surface, which allows us to evaluate the free surface slope in the presence of jumps and steps of the bed elevation. A rough estimation of the eddy viscosity is given by ν ≈ ν t h τ b /ρ with the non-dimensional parameter ν t in the range of 4 ≤ ν t ≤ 18 [18].…”

A Method of Chained Analytical Wave Structures for Large Scale Stratified Two-Phase Pipe Flows

“…al. [5], including k − ε turbulent closures to their Riemann solver + MUSCL method. They report good agreement with the experimental data of Brock's [3] after the k − ε extension.…”

Preface Special Issue “Advances in Numerical Modelling of Hydrodynamics”

“…Developments in numerical methods and computing power continue to grow, to cite just a few (Caviedes-Voullième and , Sanders et al 2010, Dawson et al 2013, Cao et al 2015, George 2011, Smith and Liang 2013, Lacasta et al 2013, Zhou et al 2013, Donat et al 2014, Zanotti et al 2015, Delis et al 2011, Juez et al 2014, Jian et al 2015, Ran et al 2015, Murillo and Garcia-Navarro 2010, Marsooli and Wu 2015, Swartenbroekx et al 2013, Guan et al 2014, Kim et al 2014. This growth has opened-up opportunities to increase the accuracy, robustness and computational complexity of latest simulation models, and to address issues of practical relevance for modelling hydrodynamic processes.…”