On the influence of wave breaking on the height limits of two-dimensional wave groups propagating in uniform intermediate depth water

The empirical non-dimensionalisation of Nelson (1994) for determining wave height limits are critically reviewed using data assembled from recent studies of wave groups propagating in water of constant depth in the laboratory. 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 and strongly-breaking deep water waves. Three-dimensional and more strongly breaking waves in shallower water may yield wave heights higher than those measured during this study. The present study provides more robust and universal characterisation of breaking in transitional water than previously determined by geometric wave observations. Using the same measurement techniques as those of Saket et al. (2017), we have investigated the breaking threshold proposed by Barthelemy et al. (2018) but for different classes of unforced unidirectional wave groups in intermediate water depths. 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 +/- 0.005 with the experimental uncertainty of each data point of +/- 0.020. This threshold is applicable to water depth to wavelength 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.