Crest-height statistics in finite water depth. Part 1: The role of the nonlinear interactions in uni-directional seas

• Published in: Ocean engineering 2023-12, Vol.289, p.116369, Article 116369
• Main Authors: Zve, E.S., Swan, C., Hughes, G.O.
• Format: Article
• Language: English
• Subjects: Near-resonant interactions; Nonlinear defocusing; Nonlinear focusing; Nonlinear waves; Wave crest statistics
• ISSN: 0029-8018
• DOI: 10.1016/j.oceaneng.2023.116369

This paper explores the competing nonlinear processes that define the largest crest heights in uni-directional random seas. In deep water, the third-order near-resonant interactions produce a focusing of the free-wave energy and hence larger crest elevations. However, as the effective water depth reduces, theoretical considerations, based upon the assumption that the frequency spectrum is narrow-banded, suggest that this process weakens and below kpd=1.363 (kp being the wavenumber of the spectral peak frequency and d the water depth) energy defocusing occurs. This paper first explores how the near-resonant interactions affect the crest heights arising in broad-banded, non-breaking, uni-directional seas in a wide range of effective water depths. It also quantifies the role of the bound-wave interactions. The numerical calculations conclude that kpd=1.363 indeed defines the boundary between energy focusing and defocusing for realistic jonswap sea-states, irrespective of the spectral bandwidth and steepness. However, for kpd