The speed, breaking onset and energy dissipation of 3D deep-water waves

Abstract

This thesis presents a 3D laboratory study of directional deep-water wave groups; addressing wave breaking onset, the speed of highly steepened waves and whitecaps, energy dissipation rates and geometric characteristics of whitecaps.

The energy convergence breaking onset threshold parameter δ(t) of Song & Banner (2002) was not a robust indicator of progression to breaking for all tested conditions. However, systematic behaviour for increases to initial energy beyond maximum non-breaking wave conditions show δ(t) is weakly dependent on imposed directionality, while complex dissimilarity is measured between bimodal and chirped wave groups types.

The disparity between measurements of broken wave speeds of approximately 0.8c0 (Rapp and Melville, 1990), where c0 is the linear equivalent wave speed, and the Stokes’ theoretical wave speed at maximal steepness of approximately 1.10c0 (Longuet-Higgins, 1975) is resolved. The mechanism identified concerns the wave crest as, whether it proceeds to breaking or not, it leans backwards and slows to approximately 0.85c0 prior to reaching maximal steepness. If the wave proceeds to break the resultant white-capping begins at approximately this slowed rate before decelerating.

The dimensionless energy loss rates of Duncan (1981, 1983) and Phillips (1985) were measured for these directionally forced breaking waves. The results are consistent with existing unidirectional normalisations for the range of field-derived loss rates and the dissipation rate models of Romero et al. (2012). The waves are the first published for directionally forced waves and show systematic divergence from the unidirectional case, where wave convergence increases the dimensionless loss rates.

The measured characteristic patterns of whitecaps are the first published directionally forced wave groups exhibiting laterally oscillating crescentic breaking lobes (Su, 1982a). Breaking width and swept area show a strong dependence of directional convergence. The average swept length of individual breakers shows less dependence on imposed directionality. Imposed wave directionality does not initiate or cause changes to the number of breaking-events in multiple-break sequences.

The specialised equipment used to support this investigation is discussed, including development and implementation of a bottom-cantilevered segmented directional wave generator and the application of LiDAR sensing methodology for non-breaking wave measurements.