A numerical wave tank based on the coupling of a Boundary Element model, solving tully nonlinear potential flow equations, and a Volume Of Fluid model solving Navier-Stokes equations is developed and used to calculate transformation of shoaling and breaking waves in nearshore areas.
The Boundary Element Method (BEM) has proved very efficient for calculating the propagation and shoaling of ocean waves over arbitrary bottom topography, up to overturning of a wave (e.g., Grilli et al., 1994, 1997, 1998; Grilli and Horrillo, 1997, 1998). In such computations, fully nonlinear potential flow theory is typically solved in a Boundary Integral formulation based on free space Green's function, coupled to a higher-order time updating of both the boundary geometry and potential. Such numerical models are often referred to in the literature as numericalwave tanks (NWT) because they simulate the functionality of laboratory tanks, i.e., wave generation, propagation and radiation/absorption (see below). Many laboratory experiments have shown that computations in NWTs based on potential flow equations are very accurate in predicting both the shape and kinematics of surface waves shoaling over a sloping bottom, up to the breaking point (for which waves have a vertical tangent on the front face), and slightly beyond, up to the instant of impact of a breaker jet on the free surface. Further than this, however, the method breaks down due to the violation of governing equations. Their principle is to absorb energy from incident waves, at the extremity of the NWT, before they start overturning, through a combination of surface pressure and lateral active absorption ("absorbing pistons", AP). Without an AB, periodic waves shoaling up a slope would normally lead to a succession of breakers at the top of the slope, of which only the first one would be calculated in the NWT.