**7. Conclusions**

This study presents an experimental study of the temporal evolution of the propeller jet flow within a developing scour hole around a vertical quay wall. The asymptotic scour profiles under the condition of four wall clearances ( *X* w = <sup>1</sup>*D*p, 2 *<sup>D</sup>*p, 3 *<sup>D</sup>*p, and 4 *D*p) were compared with their counterpart without any confinement; the results highlight the crucial role of the presence of the quay wall in shaping the final scour hole. The flow patterns within the asymptotic scour hole for the same four wall clearance cases were also compared to examine the vortex scouring mechanisms. In the small wall clearance cases ( *X* w = <sup>1</sup>*D*p, 2 *D*p), where the wall e ffect is more pronounced, a vortex system comprising three vortices was observed with the primary vortex being responsible for the scouring action. With increasing wall clearances and thus decreasing wall e ffects, the former three-vortices system transforms into a single vortex residing in the scour hole at *X* w = <sup>3</sup>*D*p; when *X* w = <sup>4</sup>*D*p, the single vortex further diminishes. This transformation provides an explanation for the observed inverse relationship between the scour depth and wall clearance in the case of the closed type quay. Moreover, similarities and di fferences were discussed with respect to the vortical structure in the case of the closed quay and that of the open quay. Such comparison elucidates the distinct influence of di fferent quay types on the formation of flow patterns and the resulting scour profiles, which furnishes a laboratory reference for the maintenance work of quay structure in terms of propeller induced scour damage.

To investigate the evolution of the vortex system and its interaction with the developing scour hole, the temporal development of the flow patterns at a typical case of *X* w = <sup>2</sup>*D*p was discussed. The results highlight the significant di fference in the vortex scouring mechanism at the initial instant with a flatbed and that in the presence of a developing scour hole. During the scouring process, although the shear layer structure associated with the propeller jet streams seems to remain steady over time, the vortex system undergoes a considerable change, for which the relative dominance of each individual vortex was analyzed in terms of their circulation developments. As the scour process develops, the near-bed vortex (V3) gradually overwhelms its two counterparts (V1 and V2) and exhibits a positive correlation with the increasing scour depth. In addition, the energy spectra analysis was conducted to examine the turbulent energy cascade and its implication for the associated scouring process. The −5/3 law was confirmed for the energy spectra at the centers of all the three vortices throughout the entire scouring process, indicating an asymptotic balance between turbulence production and dissipation within large-scale eddies associated with the vortex system. Furthermore, a comparison of the overall spectra over the entire frequency band of the three vortices reveals that the turbulent kinetic energy associated with the scour-driving vortex (V3) gradually decreases as the scour hole evolves. This phenomenon, to some extent, links the energy transfer from the turbulence dissipation to the scour excavating action.

Finally, the near-bed flow characteristics (i.e., AKE, TKE, RSS), which are indicative of erosive flow mechanisms, are discussed. The results show that the near-bed TKE gradually decreases with the development of the scour hole, confirming the inference from the energy spectra analysis. Meanwhile, the near-bed AKE appears to be enhanced when the vortex is stabilized by the presence of a large scour hole. The increase of AKE and decrease of TKE with time shows that less energy is transferred from the mean to turbulent flow fields, which is the reason the scouring process progressively diminishes. The RSS distribution, on the other hand, undergoes an insignificant change during the scouring process, indicating its comparatively less important role in a ffecting scour.

**Author Contributions:** Conceptualization, M.W., N.-S.C. and Y.-M.C.; Data curation, M.W.; Formal analysis, M.W.; Supervision, N.-S.C. and Y.-M.C.; Writing–original draft, M.W.; Writing–review & editing, M.W., N.-S.C. and Y.-M.C. and F.Y.

**Funding:** The National Key Research and Development Program of China (2016YFC0402302; 2017YFC1502504).

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