We study the shoaling, breaking, and post-breaking of waves, in two dimensions, using a model, i.e., a Numerical Wave Tank, based on coupling a Boundary Element Model, solving potential flow equations, to a Volume Of Fluid model, solving Navier-Stokes equations. We apply the model to calculating the transformation of solitary waves over plane slopes. We compare results to existing laboratory experiments. The agreement is quite good between computations and measurements. Finally, we compute properties of waves breaking over various slopes, such as shape, internal velocities and type of breaking.


As ocean waves approach the shore, they are affected by the decreasing depth, which causes gradual changes in wave celerity, height and shape. These changes are usually referred to as wave shoaling. Very close to shore, shoaling causes wave height to significantly increase and wavelength to decrease; hence, at some point, waves become too steep and break. One usually defines the breaking point (BP) as the location where waves have a vertical tangent on the front face; thus, beyond the BP, waves become unstable, overturn and break. The surfzone extends from the BP to shore, and this is a region of high vorticity, turbulence, and dissipation for the wave flow. For many beaches, cross-shore variations of bathymetry are predominent over longshore variations and, particularly close to shore, it is quite accurate, for all practical purposes, to study wave propagation in two dimensions (2D), in a vertical plane. Comparisons of laboratory experiments with numerical models show that potential flow theory, with fully nonlinear free surface boundary conditions (FNPF), is very accurate for predicting the shape and kinematics of surface waves shoaling over a sloping bottom, up to the BP (e.g., Grilli et al., 1994, 1997; Ohyama et al., 1994; Grilli and Horrillo, 1999).

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