Numerical and experimental analysis of shallow turbulent flow over complex roughness beds

ABSTRACT

A set of shallow-water equations (SWEs) based on a $\hat{k}-\hat{\epsilon }$ Reynold stress model is established to simulate the turbulent flows over a complex roughness bed. The fundamental equations are discretized by the second-order finite-difference method (FDM), in which spatial and temporal discretization are conducted by staggered-grid and leap-frog schemes, respectively. The turbulent model in this study stems from the standard $\hat{k}-\hat{\epsilon }$ model, but is enhanced by replacing the conventional vertical production with a more rigorous and precise generation derived from the energy spectrum and turbulence scales. To verify its effectiveness, the model is applied to compute the turbulence in complex flow surroundings (including a rough bed) in an abrupt bend and in a natural waterway. The comparison of the model results against experimental data and other numerical results shows the robustness and accuracy of the present model in describing hydrodynamic characteristics, especially turbulence features on the complex roughness bottom.

KEYWORDS:

• Energy spectrum
• roughness bed
• SWE model
• shallow flows
• turbulent flows

Acknowledgements

Dr. Xiekang Wang and Dr. Xianye Wang kindly provided the 3D experimental data in Section 3.1. The authors are also grateful to Dr. Luis Cea for the data in Section 3.2.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Matteo Rubinato http://orcid.org/0000-0002-8446-4448

Ehsan Kazemi http://orcid.org/0000-0002-1780-1846

Jaan H. Pu http://orcid.org/0000-0002-3944-8801

Additional information

Funding

This work was supported by the National Key Research and Development Program of China [grant number 2016YFE0122500], the National Key Basic Research Program of China [973 program, grant numbers 2013CB036401 and 2013CB036402], China Postdoctoral Science Foundation [grant number 2016M591184] and Program of Introducing Talents of Discipline to Universities [grant number BC2018038].