**5. Conclusions**

In this study, the V-shaped undulating bottom can be regarded as the combination of two parts of oblique bottom undulations relative to the incident waves. The spatial distributions of the wave heights in the focusing areas owning to Bragg resonance of regular wave-bottom interactions are symmetric about the center of the V-shaped undulating bottom, and the largest wave height is distributed along the *x*-axis of symmetry. From these two aspects of spatial distributions and quantitative analysis, it is found that when *α* is about 162.24◦, obvious focusing areas and focal points appear, and the focusing intensity at this angle is the strongest. By optimizing *α*, the wave-focusing effect is improved. When 145◦ < *α* < 180◦, the wave amplitude increase at the focal points can reach more than 1.81 times of the initial incident wave amplitude, which is higher than that of the focal points when *α* = 180◦. In particular, when *α* = 162.24◦, the wave-focusing effect is the best and the maximum amplitude increases by 2.87 times of the initial incident wave amplitude. When *α* < 145◦, the maximum amplitude increase of the focal points is less than that of *α* = 180◦. When *α* = 90◦, the maximum amplitude of the focal points is unchanged, i.e., wave energy focusing does not occur.

Therefore, the V-shaped undulating bottom at the angle of 162.24◦ is selected to study the random wave-bottom interactions characteristics. It is found that there is a good linear relationship between *H*smax/*H*s0 and *BFI*, which combines wave steepness and spectrum width. For *BFI*, in the range of 0.15–1.0, the values of *H*smax/*H*s0 linearly increase with the increase of *BFI*.

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**Author Contributions:** Formal analysis, J.S.; investigation, S.X.; methodology: J.T.; software, H.Z., J.T. and J.S.; validation, S.X.; writing—original draft preparation, H.Z.; writing—review and editing, A.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research is supported financially by the National Key Research and Development Program of China (2020YFD0900701) and the National Natural Science Foundation of China (U1706230).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

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