Fully Nonlinear Potential Flow Simulations of Wave Shoaling Over Slopes: Spilling Breaker Model and Integral Wave Properties

Abstract

A spilling breaker model (SBM) is implemented in an existing two-dimensional (2D) numerical wave tank (NWT), based on fully nonlinear potential flow (FNPF) theory and the boundary element method (BEM), in which an absorbing surface pressure is specified over the crest of impending breaking waves (detected based on a maximum front slope criterion) to simulate the power dissipated during breaking. The latter is calibrated to match that of a hydraulic jump of parameters identical to local wave properties (height, celerity,. . .). Although this model is not aimed at being fully physical in the surfzone, it allows more accurately simulating properties of fully nonlinear shoaling waves than standard empirical absorbing beaches (AB). After assessing the convergence with the discretization of 2D-NWT results for strongly nonlinear shoaling waves, simulations are first validated based on laboratory experiments for non-breaking and breaking waves, shoaling up a mild slope; a good agreement is found between both. The NWT is then used to compute fully nonlinear local (height, celerity, asymmetry) and integral (mean-water-level, radiation stress) properties of periodic waves shoaling over mild slopes. Discrepancies with standard results of wave theories are discussed in light of fully nonlinear effects modeled in the NWT. While only periodic waves are considered here, the SBM could be applied to shoaling irregular waves, for which the breaking point location will constantly vary, which would be advantageous compared to an AB fixed in space. For such cases, besides its more physical energy absorption, the SBM would allow better preventing wave overturning that may occur far from shore due to nonlinear wave-wave interactions and otherwise interrupt the FNPF-NWT simulations.

A Unified Breaking Onset Criterion for Surface Gravity Water Waves in Arbitrary Depth

“…Grilli et al (1997) showed that the model could accurately predict breaking crest elevations, breaker index, and breaker types for solitary waves of various incident height propagating over mild to steep slopes. Finally, Grilli et al (2019) show that the model also accurately simulates the shoaling and propagation of periodic waves over a bar similar to that considered here. B9-r 97.2 1.43 0.7 2 10 0.57 0.08 0 0 Blenkinsopp and Chaplin (2007) Note.…”

Comparing methods of modeling depth-induced breaking of irregular waves with a fully nonlinear potential flow approach

“…The implementation and validation of wave breaking dissipation methods have been presented for the fully nonlinear potential flow solver whispers3D in the case of two dimensional waves. Among the various breaking models presented in the literature, three existing dissipation methods were implemented here: HJ and HJf, based on the analogy between a breaking wave and a hydraulic jump (Guignard and Grilli, 2001;Grilli et al, 2019), and an eddy viscosity-like formulation of the dissipation (Kennedy et al, 2000). Three initiation criteria for wave breaking were also compared.…”

“…(3). The first method (denoted HJ in the following) uses an analogy with a hydraulic jump propagating over a flat bottom to estimate a pressure term D = −P surf /ρ, with ρ the water density (Guignard and Grilli, 2001;Grilli et al, 2019). The zone where the pressure is applied extends on both sides of the breaking wave crest between x f and x b (see Figure 1…”

“…Following the detection of the onset of wave breaking, several different dissipation mechanisms can be applied by adding a term to the dynamic free surface boundary condition. Over the specified spatial extent of wave breaking, the wave energy dissipation can be calculated using a surface roller model (Schäffer et al, 1993), a vorticity model (Svendsen et al, 1978), an eddy viscosity model (Kennedy et al, 2000;Kurnia and van Groesen, 2014;Papoutsellis et al, 2018bPapoutsellis et al, , 2019, or by analogy with a hydraulic jump (Guignard and Grilli, 2001;Grilli et al, 2019;Papoutsellis et al, 2019). These mechanisms require parameterizing both the definition of the onset of wave breaking and the intensity and spatial extent of the applied dissipation.…”

Modelling of depth-induced wave breaking in a fully nonlinear free-surface potential flow model

“…The term introduced in the FSBC is computed by solving a differential equation derived by requiring that momentum is conserved as the waves break over a flat bottom. The second method, EHJ, is the implementation of the dissipative term proposed by Guignard and Grilli (2001) and Grilli et al (2019). This term is constructed such that it produces negative work proportional to the work done by a hydraulic jump with wave characteristics similar to those of the breaking wave.…”