Parameterizing the surface-wave breaking in wave-resolving simulations

Wave breaking influences both small-scale processes, such as turbulence near the surface and air entrainment, and coastal-scale processes, including mean sea level changes (set-up and set-down) and coastal currents. Recently, wave-resolving models have been employed to simulate coastal-scale dynamics by parameterizing wave breaking under the assumption of a non-overturning free surface. One approach explicitly parameterizes wave breaking effects using empirical breaking criteria specific to the coastal area. Another introduces numerical diffusivity intrinsically through specific numerical schemes, without relying on such criteria. In this study, we introduced a fourth-order diffusivity into the surface elevation evolution equation of a wave-resolving model to explicitly parameterize wave breaking without relying on empirical breaking criteria specific to the coastal area. Laboratory experiments were conducted to validate shallow-water wave breaking. We also evaluated simulation results against an empirical breaker index. To validate deep-water wave breaking, we referenced previous numerical simulations of two-phase flow. Validation results showed that the parameterization successfully captured the onset of wave breaking and the mean water level changes associated with shallow-water wave breaking. For deep-water wave breaking, the parameterization effectively represented the onset of wave breaking and energy dissipation. These results demonstrate that the proposed parameterization captures wave breaking effects without relying on empirical criteria specific to the coastal area and allows straightforward evaluation of added numerical diffusivity, and is applicable to both shallow- and deep-water breaking.