Modelling roll waves with shallow water equations and turbulent closure

Zhixian Cao*, Penghui Hu, Kaiheng Hu, Gareth Pender, Qingquan Liu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Citations (Scopus)
191 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)161-177
Number of pages17
JournalJournal of Hydraulic Research
Issue number2
Early online date22 Oct 2014
Publication statusPublished - 2015


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

ASJC Scopus subject areas

  • Water Science and Technology
  • Civil and Structural Engineering


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