**4. Summary and Conclusions**

In order to deepen the impact of the downward seepage and the turbulent flow characteristics on the scour geometry around a pier, an experimental measurement of the instantaneous velocity with different percentages of with seepage (10% S and 15% S) and without seepage (NS) have been carried out in four different sections around a pier, for two different diameters (75 and 90 mm).

Upstream of the pier, the streamwise turbulence intensities, with respect of zero seepage, are reduced by 15% in case of the 10% seepage, and by 22% in case of the 15% seepage, respectively. Downstream of the pier, the higher values of vertical turbulence intensities show the presence of wake vortices. Laterally to the pier, the streamwise and vertical turbulence intensities are higher in the seepage runs than without seepage. Upstream of the pier, the positivity of *M30* and *M12* decreases, thus increasing the seepage percentage. Downstream of the pier, decreasing the negativity of *M30* and the positivity of *M03*, respectively, with seepage, shows ejections. Laterally to the pier, the streamwise and vertical turbulence intensities increase by 20%–35% in the seepage runs, resulting in an enhanced in sediment transport.

Upstream of the pier, in the seepage runs, a reduction in TKE-flux confirms the lower erosive capability of the flow. However, the erosive capacity is found to be increased laterally to the pier, by the application of downward seepage. A pronounced effect of seepage has been found on TKE budget. Upstream of the pier, a reduction in the turbulence production, in the case of seepage runs, is in agreemen<sup>t</sup> with a lower turbulence level in the same section. From the turbulence statistics of the flow around the pier, in the seepage runs, it has been observed that they decrease upstream of the pier, which results in a lesser scour depth, while they increase laterally the pier, which results in a wider scour hole and shifting towards the downstream of the scour hole length.

The primary characteristics of the scour hole, like the length and width, were physically measured; and the area and volume were measured by using commercial software Surfer®. Finally, with the help of the experimental results obtained from the laboratory flume, empirical relationships for the prediction of the scour hole characteristics, like length, width, area, and volume, including the downward seepage parameter in terms of the seepage Reynolds number, have been developed. Considering that the laboratory flume is a distorted model of a river, the obtained expression showed a good fit with the estimated values.

**Author Contributions:** B.K. proposed the idea. R.C. did the experiments. R.C., B.K., and P.G. analyzed the results and drafted the manuscript; all of the authors contributed to reviewing and editing the manuscript.

**Funding:** R.C., B.K. and P.G. acknowledge the support by the UNINA-DICEA research project "Experimental and Numerical Fluids Dynamics".

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