Inundation over land with increasing water depth using self-similarity analysis

ABSTRACT

This paper describes a self-similarity-analysis-based inundation process in which the water depth at the inlet increases as a power function of time. Numerical analyses of the inundation process are conducted to evaluate the feasibility and stability of two types of regimes: inertia-pressure regime and pressure-friction regime. Numerical simulations using the shallow water equations are conducted to investigate the influence of the increments in scaling coefficient and power which determine the temporal variation of the inlet water depth on the inundation process. Both regimes were realized in the numerical simulations, without considering the friction or inertia terms. Based on the linear stability analysis, it was proved that these processes are stable regardless of the increment in the scaling coefficient of the inlet water depth. The early phase of the inundation process is dominated by the scaling coefficient; whereas, eventually the inundation process depended on power.

Keywords:

• Flood modelling
• numerical simulation
• one-dimensional model
• open channel flow
• self-similarity analysis
• unsteady flow

Acknowledgement

We greatly acknowledge Prof. Mohamed Ghidaoui, Dr. Moez Louati and the anonymous reviewers for the suggestions and technical comments, which improved the quality of this manuscript. We would also like to thank Editage (www.editage.com) for proofreading this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.