wave breaking

In coastal areas, wave dissipation and non-linear wave-wave interaction are dominant processes.In order to obtain a correct prediction of both the total wave energy and its distribution over the wave spectrum at locations in the coastal region, numerical wave prediction models should include an adequate description of wave propagation, non-linear wave-wave interaction, and wave breaking. All of these aspects have been included in the Boussinesq-type wave model TRITON.

Wave breaking is modelled in TRITON through the use of an eddy viscosity model, which  guarantees energy dissipation. The property of momentum conservation is retained by the present implementation. The eddy viscosity coefficient is modelled algebraically, using the physical ideas behind the surface roller concept. This coefficient is assumed to scale linearly with the thickness of the roller, which is present as soon as the wave steepness exceeds a certain threshold value.

One-dimensional model results have been presented by Van Gent and Doorn (Coastal Dynamics Conference 2001) and compared with measurement data for different wave spectra on a shallow foreshore. These results demonstrated that the combination of the eddy viscosity concept and the surface roller is able to accurately predict the global effect of complicated wave energy dissipation in applications of practical interest.

The one-dimensional concept of the eddy-viscosity model has been extended to two dimensions. The performance of the implemented 2D wave-breaking model has been investigated using part of an extensive data set of waves propagating over a shoal on a beach (Van Gent et al., 2001). A snapshot of the surface elevation for a regular wave field is shown in Figure 1. The breaker model has been validated for long- and short-crested waves, either regular or irregular, using different values for the wave steepness and wave height, and even different water depths and angles of incidence. For one single test, the measured and computed significant wave height and mean wave period at locations along three rays are shown in Figure 2. The outcome of the two-dimensional validation study shows that the breaker model is suitable for the rather extreme conditions considered.

Recently, measures have been taken to overcome stability problems. Smoothing of breaker characteristics has led to more reliable results and a more stable integration procedure. Furthermore, a threshold for the eddy viscosity has been introduced. The explicit time integration scheme in Triton requires a relatively small time step. The choice of the time step is critical, since a very large value causes an underestimation of the energy dissipation, and a very small value leads to unacceptably high computational time. In the future the critical mass of the choice of the time step will be relaxed by integrating the breaker term in a (semi-) implicit way.

more information

For more information, please contact Jacco Groeneweg or Mart Borsboom.