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 $S_s$ and $S_n$ are bandwidth-dependent and $S_p$ 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 $f > 0.95f_p$ ( $f_p$ is the peak frequency) and $f < 0.95f_p$ , 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 $S_p$ and both the fractional and absolute wave energy dissipation. Wave groups of larger bandwidth break at a lower value of $S_p$ 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 $S_p$ or $S_s$ . However, there is a systematic bandwidth dependence in the variation of $b$ when parameterised in terms of $S_p$ , with their relationship becoming increasingly nonlinear as bandwidth increases. When parameterised with $S_s$ , $b$ shows a markedly reduced bandwidth dependence. Finally, the numerical breaking onset and relationship between $b$ and $S_s$ in the numerical study of Derakhti & Kirby (J. Fluid Mech., vol. 790, 2016, pp. 553–581) is validated experimentally.

A Comparison of Laboratory and Field Measurements of Whitecap Foam Evolution From Breaking Waves

“…Indeed, the recent work of Cao et al. (2023) explicitly show that the fractional energy loss in laboratory breaking waves is bandwidth dependent, but that this bandwidth dependence greatly diminishes when considering the energy dissipation rate per unit crest length. Cao et al.…”

“…From the data presented in Table S12 in Supporting Information S1 for ϵ l , no clear bandwidth effect is evident. Indeed, the recent work of Cao et al (2023) explicitly show that the fractional energy loss in laboratory breaking waves is bandwidth dependent, but that this bandwidth dependence greatly diminishes when considering the energy dissipation rate per unit crest length. Cao et al (2023) did not explicitly examine the effect of bandwidth on ϵ A .…”

“…Much of what is known about the physics of breaking waves has been determined through careful laboratory experiments that have measured quantities such as energy dissipation and fluid turbulence, breaking speed and duration, Lagrangian mass transport, air entrainment, bubble plume depth, evolving foam area and the role of surfactants in foam stabilization (e.g., Callaghan et al., 2016; Cao et al., 2023; Deane et al., 2016; Deane & Stokes, 2002; Duncan, 1981; Lamarre & Melville, 1991; Lenain et al., 2019; Rapp & Melville, 1990; Sinnis et al., 2021; Tian et al., 2010). The laboratory experiments allow for: (a) the properties of incipient breaking waves to be carefully controlled, (b) the precise placement of instrumentation to collect accurate measurements of surface and sub‐surface flow properties, and (c) the careful manipulation of water chemistry.…”