**4. Conclusions**

This paper presents an experimental study on the temporal development of scour downstream of submerged weirs. Observations show that the dimensions of scour holes downstream of a submerged weir develop very quickly in the initial stage, before progressing at a decreasing rate until the equilibrium is reached. The increase of the flow intensity or overtopping ratio accelerates the scour rate and increases the scour magnitude. Exponential equations were developed to estimate the temporal variation of the scour depth and scour length downstream of the submerged weir. The geometrical similarity of scour holes downstream of the weir was observed in the tests, and an empirical model for describing the temporal evolution of the scour hole profile was developed. A relation between the scour areas and scour dimensions was also proposed. The present study is useful in development of models capable of estimating scour depth downstream of weirs in rivers or coastal areas, for which the overtopping conditions are very common. The proposed equations for scour hole dimensions, profiles, and areal sizes will be good tools for hydraulic engineers in the design of scour countermeasures.

**Author Contributions:** D.G. conceived, designed and performed the experiments; all authors contributed to analysis of the data, writing and discussion of the paper.

**Funding:** This work was funded by the Young Scientists Fund of the National Natural Science Foundation of China (grant number 51709082) and the Fundamental Research Funds for the Central Universities (grant number 2018B13014).

**Acknowledgments:** The first author would like to thank Bruce W. Melville and Jian-Hao Hong for their helpful advice and technical support. The authors would also like to thank The University of Auckland for providing the experimental facilities for this study.

**Conflicts of Interest:** The authors declare no conflicts of interest.
