This paper presents a comparative numerical study of the energy dissipation process in the breaking of focused waves by using a potential flow model and a coupled potential/viscous flow model. An empirical eddy viscosity term is introduced to the fully-nonlinear potential (FNP) flow model to account for the breaking wave energy dissipation. The FNP model is further coupled with an incompressible two-phase Navier- Stokes (NS) flow solver through a one-way linkage to generate and propagate focused waves in the domain. Numerical absorbing regions are placed in front of the outlet boundaries to dampen wave reflection. The standalone FNP model and the coupled FNP+NS model are applied to deal with each scenario comparatively. This enables the accurate quantification and comparison of the energy loss of breaking waves calculated by the two numerical models. The velocity field is decomposed into potential component, which is reconstructed from the corresponding free surface elevation computed in the coupled model by using the weakly-nonlinear wave theory, and non-potential rotational component. Detailed analysis of the numerical results shows that: (1) energy loss is closely related to wave steepness, (2) mild rotational motion produced by a non-breaking wave is local in time with a short life-span, (3) strong non-potential motion triggered by wave breaking is not local in time but persists in the flow for dozens of or even many more wave periods.

INTRODUCTION

Wave breaking (white capping) is a transient phenomenon occurring frequently in the propagation of surface gravity water waves in open seas and coastal surf zones. It is of significant importance in coastal and marine engineering due to its capability to produce extreme loadings that can severely damage or completely destroy coastal defence, offshore structure and marine vessel. It also plays an important role in the atmosphere-ocean system by facilitating and enhancing the physical, chemical and biological interactions across the air-sea interface. Breaking is considered as the main sink of the kinematic energy received by ocean waves from winds through complex interactions. It has been shown that wave breaking is also responsible for the momentum, mass and energy exchange between the ocean and the atmosphere (Veron, 2015): it leads to the intensive release of spray into the air, as well as the strong mixing and turbulisation of the upper ocean boundary layer. A recent work of McAllister et al. (2019) shows the significant role played by wave breaking in the formation of rogue waves, which pose a great danger to maritime activities. These aforementioned works demonstrate the importance in the fundamental understanding of wave breaking phenomena.

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