On the threshold for wave breaking of two-dimensional deep water wave groups in the absence and presence of wind

The threshold for the onset of breaking proposed by Barthelemy et al. (arXiv:1508.06002v1, 2015) has been investigated in the laboratory for unidirectional wave groups in deep water and extended to include different classes of wave groups and moderate wind forcing. Thermal image velocimetry was used to compare measurements of the wave crest point (maximum elevation and also the point of maximum) surface water particle velocity ( $U_{s}$ ) with the wave crest point speed ( $C$ ) determined by an array of closely spaced wave gauges. The crest point surface energy flux ratio $B_{x}=U_{s}/C$ that distinguishes maximum recurrence from marginal breaking was found to be $0.840\pm 0.016$ . Increasing wind forcing from zero to $U_{\unicode[STIX]{x1D706}/4}/C_{0}=1.42$ systematically increased this threshold by 2 %. Increasing the spectral bandwidth (decreasing the Benjamin–Feir index from 0.39 to 0.31) systematically reduced the threshold by 1.5 %.