Modeling wave runup with depth-integrated equations

In this paper, a moving boundary technique is developed to investigate wave runup and rundown with depth-integrated equations. Highly nonlinear and weakly dispersive equations are solved using a high-order finite difference scheme. An eddy viscosity model is adopted for wave breaking so as to investigate breaking wave runup. The moving boundary technique utilizes linear extrapolation through the wet-dry boundary and into the dry region. Nonbreaking and breaking solitary wave runup is accurately predicted by the proposed model, yielding a validation of both the wave breaking parameterization and the moving boundary technique. Two-dimensional wave runup in a parabolic basin and around a conical island is investigated, and agreement with published data is excellent. Finally, the propagation and runup of a solitary wave in a trapezoidal channel is examined.