**5. Conclusions**

In this study, a series of hydraulic model experiments was conducted to analyze the formation and variations of obstacle-induced vortices. These vortices were induced by landslide-generated solitary-like waves propagating over single and composite sets of rectangular and undulating submerged BWs. The induced vortices were further analyzed by PIV techniques using PIVlab, and the correlation between vortex energy and wave energy attenuation induced by different types of submerged BWs was investigated. The results showed that the sum of the relative vortex energy generated behind the composite submerged BW sets is greater than that of the single submerged BW sets. The trend of the estimated total relative vortex energy of the maximum vortices is in agreemen<sup>t</sup> with the sum of the energy attenuation, *KL*, indicating that the attenuated wave energy is related to the induced vortices. Moreover, the total relative vortex energy of the rectangular submerged BW sets is approximately 1.29 (the single set) and 1.27 (the composite set) times larger than that of the undulating submerged BW sets. This shows that the rectangular submerged BW sets have stronger effects on the energy attenuation of the solitary-like wave. The magnitude of the maximum vorticity of the undulating BW sets appears to be larger than that of the rectangular BW sets; however, the total vortex energy is shown to be slightly smaller, owing to the narrower vortex area range. Finally, the induced vortex of the rectangular submerged BW sets is relatively divergent when compared with that of the undulating submerged BW sets, which is relatively concentrated.

**Author Contributions:** Conceptualization, methodology, R.-S.S.; resources, W.-K.W.; formal analysis, C.-Y.L. and R.-S.S.; writing—original draft, C.-Y.L. and R.-S.S.; data curation, C.-Y.L.; writing—review and editing, C.-Y.L. and R.-S.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
