Wave breaking onset of two-dimensional wave groups in uniform intermediate depth water

TL;DR

This study investigates the wave breaking threshold for two-dimensional wave groups in intermediate water depths, confirming a universal parameter value and highlighting the influence of wave grouping on wave height limits.

Contribution

It provides a robust, experimentally validated threshold parameter for wave breaking applicable across various water depths, improving understanding of wave behavior in transitional waters.

Findings

Threshold parameter B_x = 0.835 ± 0.005 for wave breaking.

Wave grouping can produce waves 30% taller than Nelson's limit.

Universal applicability of the breaking threshold across water depths.

Abstract

Using the same measurement techniques as those of Saket et al. (2017), we have investigated the breaking threshold proposed by Barthelemy et al. (arXiv:1508.06002v1, 2015b) but for different classes of unforced unidirectional wave groups in intermediate water depths in the laboratory. The threshold parameter $B_x = U_s/C$ (where $U_s$ is the horizontal surface water particle velocity at the wave crest and $C$ is the wave crest point speed) which distinguishes breaking from non-breaking waves was found to be 0.835 $\pm$ 0.005 with the experimental uncertainty of each data point of $\pm$ 0.020. This threshold is applicable to water depth to wave length ratios as low as 0.2 including the deep water conditions investigated by Saket et al. (2017). No dependence on peak spectral wavenumber was found at the scales achievable in a large-scale laboratory. The present study provides more robust and universal characterisation of breaking in transitional water than the empirical non-dimensionalisation of Nelson (1994). The limiting wave height to water depth ratios of marginally breaking deep and intermediate water waves remain within 10 % of Nelson's values. However, it is shown that the effect of wave grouping can produce waves in shallower water that are at least 30 % greater in height than the limit proposed by Nelson (1994). The present study supports use of limits based on McCowan (1894) and Miche (1944) for coastal engineering design for marginal breaking waves. Three-dimensional and more strongly breaking waves in shallower water may yield wave heights higher than those measured during this study.