11:30 AM - 11:45 AM
[ACG47-10] Parameterization of the surface-wave breaking in shallow water for wave-resolving simulations
Keywords:surface wave-resolving numerical model, wave breaking
Wave breaking in shallow water affects not only small-scale processes, such as turbulence near the surface and air-entrainment into the water, but also coastal-scale processes like mean sea level changes (set-up and set-down) and coastal currents (longshore currents and rip currents). Simulating the small-scale processes due to the wave breaking requires numerical models which accurately reproduce the water surface profiles. On the other hand, for the coastal-scale processes, wave-resolving models have been used recently, in which the wave breaking is parameterized under the assumption that the surface does not overturn. One way to parameterize the wave breaking is by explicitly adding energy dissipation effects by the wave breaking into governing equations of the model, using a certain parameter such as surface slope with empirical criteria for wave breaking (e.g., Schäffer et al., 1993). Another way is by introducing ‘shock-capturing schemes’ used for simulating shock wave. The scheme adds numerical viscosity intrinsically without wave breaking criteria and prevents the surface from overturning. Models with this scheme show good agreement with wave tank experiments on wave breaking onset and mean sea level change (e.g., Marchesiello et al., 2020). However, the former approach relies on empirical criteria, while the contribution of the numerical viscosity in the latter is difficult to evaluate.
We have developed a wave resolving model, a sigma-coordinate free-surface nonhydrostatic model, and explicitly added a 4th-order horizontal viscosity to the time evolution equation of the surface elevation without wave breaking criteria to parameterize the wave breaking. For deep water, the wave breaking onset and energy dissipation simulated by our model showed good quantitative agreement with previous experiments (Imamura and Yoshikawa, 2024; JOS fall meeting 2024). In this study, we apply this wave breaking parameterization to shallow water and validate it against wave breaking onset and mean sea level changes.
Two-dimensional (x-z) numerical experiments were conducted based on a wave tank experiment with a 1:35 sloping beach (Bowen and Kirby, 1994). Waves with a wavelength of 3.86 m and height of 0.07 m freely propagated over a model domain whose depth decreased from 0.44 m to 0.13 m.
The results showed that as water depth decreased, the wave height increased, reaching its maximum before rapidly decreasing. The rapid decrease in wave height agrees with the wave breaking, as the location of maximum wave height corresponds well to the wave breaking onset expected from a wave breaking index (Goda, 2010). The mean water level decreased until the wave height peak and then rose after the peak, which is qualitatively consistent with the set-down and the set-up. The decrease in the mean water level corresponds to the analytical solution for the set-down, while the increase in the mean water level remains to be further validated.
The wave breaking parameterization developed in this study enables to represent the wave breaking effects without using empirical criteria as well as to evaluate the numerical viscosity added for parameterization easily. This study suggests that the same approach can be used to parameterize wave breaking in both deep and shallow waters.
We have developed a wave resolving model, a sigma-coordinate free-surface nonhydrostatic model, and explicitly added a 4th-order horizontal viscosity to the time evolution equation of the surface elevation without wave breaking criteria to parameterize the wave breaking. For deep water, the wave breaking onset and energy dissipation simulated by our model showed good quantitative agreement with previous experiments (Imamura and Yoshikawa, 2024; JOS fall meeting 2024). In this study, we apply this wave breaking parameterization to shallow water and validate it against wave breaking onset and mean sea level changes.
Two-dimensional (x-z) numerical experiments were conducted based on a wave tank experiment with a 1:35 sloping beach (Bowen and Kirby, 1994). Waves with a wavelength of 3.86 m and height of 0.07 m freely propagated over a model domain whose depth decreased from 0.44 m to 0.13 m.
The results showed that as water depth decreased, the wave height increased, reaching its maximum before rapidly decreasing. The rapid decrease in wave height agrees with the wave breaking, as the location of maximum wave height corresponds well to the wave breaking onset expected from a wave breaking index (Goda, 2010). The mean water level decreased until the wave height peak and then rose after the peak, which is qualitatively consistent with the set-down and the set-up. The decrease in the mean water level corresponds to the analytical solution for the set-down, while the increase in the mean water level remains to be further validated.
The wave breaking parameterization developed in this study enables to represent the wave breaking effects without using empirical criteria as well as to evaluate the numerical viscosity added for parameterization easily. This study suggests that the same approach can be used to parameterize wave breaking in both deep and shallow waters.