The influence of bandwidth on the energetics of intermediate to deep water laboratory breaking waves

Abstract

An experimental investigation of two-dimensional dispersively focused laboratory breaking waves is presented. We describe the bandwidth effect on breaking wave energetics, including spectral energy evolution, characteristic group velocity, energy dissipation and its rate, and breaking strength parameter, b. To evaluate the role of bandwidth, three definitions of wave group steepness are adopted where Ss and Sn are bandwidth-dependent and Sp remains constant when bandwidth is changed. Our data show two regimes of spectral energy evolution in breaking wave groups, with both regimes bandwidth-dependent: energy dissipation and gain occur at f > 0.95fp ( fp is the peak frequency) and f < 0.95fp, respectively. The characteristic group velocity, which is used in energy dissipation calculations, increases by up to 7% after wave breaking, being larger for higher bandwidth breaking waves. An unambiguous bandwidth dependence is found between Sp and both the fractional and absolute wave energy dissipation. Wave groups of larger bandwidth break at a lower value of Sp and consequently lose relatively more energy. The energy dissipation rate depends on the breaking duration which itself is bandwidth dependent. Consequently, no clear bandwidth effect is observed in energy dissipation rate when compared with either Sp or Ss. However, there is a systematic bandwidth dependence in the variation of b when parameterised in terms of Sp, with their relationship becoming increasingly nonlinear as bandwidth increases. When parameterised with Ss, b shows a markedly reduced bandwidth dependence. Finally, the numerical breaking onset and relationship between b and Ss in the numerical study of Derakhti & Kirby (J. Fluid Mech., vol. 790, 2016, pp. 553–581) is validated experimentally