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We revisit the classical but as yet unresolved problem of predicting the strength of breaking 2-D and 3-D gravity water waves, as quantified by the amount of wave energy dissipated per breaking event. Following Duncan ( J. Fluid Mech. , vol. 126, 1983, pp. 507–520), the wave energy dissipation rate per unit length of breaking crest may be related to the fifth moment of the wave speed and the non-dimensional breaking strength parameter $$b$$ . We use a finite-volume Navier–Stokes solver with large-eddy simulation resolution and volume-of-fluid surface reconstruction (Derakhti & Kirby, J. Fluid Mech. , vol. 761, 2014 a , pp. 464–506; J. Fluid Mech. , vol. 790, 2016, pp. 553–581) to simulate nonlinear wave evolution, with a strong focus on breaking onset and postbreaking behaviour for representative cases of wave packets with breaking due to dispersive focusing and modulational instability. The present study uses these results to investigate the relationship between the breaking strength parameter $$b$$ and the breaking onset parameter $$B$$ proposed recently by Barthelemy et al. ( J. Fluid Mech. , vol. 841, 2018, pp. 463–488). The latter, formed from the local energy flux normalized by the local energy density and the local crest speed, simplifies, on the wave surface, to the ratio of fluid speed to crest speed. Following a wave crest, when $$B$$ exceeds a generic threshold value at the wave crest (Barthelemy et al. 2018), breaking is imminent. We find a robust relationship between the breaking strength parameter $$b$$ and the rate of change of breaking onset parameter $$\text{d}B/\text{d}t$$ at the wave crest, as it transitions through the generic breaking onset threshold ( $$B\sim 0.85$$ ), scaled by the local period of the breaking wave. This result significantly refines previous efforts to express $$b$$ in terms of a wave packet steepness parameter, which is difficult to define robustly and which does not provide a generically accurate forecast of the energy dissipated by breaking.
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Laboratory studies of Lagrangian transport by breaking surface waves
While it has long been recognized that Lagrangian drift at the ocean surface plays a critical role in the kinematics and dynamics of upper ocean processes, only recently has the contribution of wave breaking to this drift begun to be investigated through direct numerical simulations (Deike et al. , J. Fluid Mech. , vol. 829, 2017, pp. 364–391; Pizzo et al. , J. Phys. Oceanogr. , vol. 49(4), 2019, pp. 983–992). In this work, laboratory measurements of the surface Lagrangian transport due to focusing deep-water non-breaking and breaking waves are presented. It is found that wave breaking greatly enhances mass transport, compared to non-breaking focusing wave packets. These results are in agreement with the direct numerical simulations of Deike et al. ( J. Fluid Mech. , vol. 829, 2017, pp. 364–391), and the increased transport due to breaking agrees with their scaling argument. In particular, the transport at the surface scales with $$S$$ , the linear prediction of the maximum slope at focusing, while the surface transport due to non-breaking waves scales with $$S^{2}$$ , in agreement with the classical Stokes prediction.
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- Award ID(s):
- 1634289
- PAR ID:
- 10130718
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 876
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2019.544
