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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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Wave and Roller Transformation Over Barred Bathymetry
Abstract The cross‐shore transformation of breaking‐wave roller momentum and energy on observed barred surfzone bathymetry is investigated with a two‐phase Reynolds Averaged Navier Stokes model driven with measured incident waves. Modeled wave spectra, wave heights, and wave‐driven increases in the mean water level (setup) agree well with field observations along transects extending from 5‐m water depth to the shoreline. Consistent with prior results the roller forcing contributes 50%–60% to the setup, whereas the advective terms contribute ∼20%, with the contribution of bottom stress largest (up to 20%) for shallow sandbar crest depths. The model simulations suggest that an energy‐flux balance between wave dissipation, roller energy, and roller dissipation is accurate. However, as little as 70% of the modeled wave energy ultimately dissipated by breaking was first transferred from the wave to the roller. Furthermore, of the energy transferred to the roller, 15%–25% is dissipated by turbulence in the water column below the roller, with the majority of energy dissipated in the aerated region or near the roller‐surface interface. The contributions of turbulence to the momentum balance are sensitive to the parameterized turbulent anisotropy, which observations suggest increases with increasing turbulence intensity. Here, modeled turbulent kinetic energy dissipation decreases with increasing depth of the sandbar crest, possibly reflecting a change from plunging (on the steeper offshore slope of the bar) to spilling breakers (over the flatter bar crest and trough). Thus, using a variable roller front slope in the roller‐wave energy flux balance may account for these variations in breaker type.
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- Award ID(s):
- 2318785
- PAR ID:
- 10504816
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Journal of Geophysical Research: Oceans
- Volume:
- 129
- Issue:
- 5
- ISSN:
- 2169-9275
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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