Boussinesq modeling for the runup of solitary-like waves on a slope and circular island

This paper presents numerical simulations for the runup of solitary-like waves on a sloping beach and circular island. The solitary-like wave is constructed by introducing an elongation parameter to the wavenumber of the solitary wave. All simulations are performed with a Boussinesq model solving the fully nonlinear and weakly dispersive Boussinesq equations. The numerical model is validated by comparing the computed runup of solitary waves on sloping beach and circular island to the experimental runup data. The propagation of the solitary-like wave in a constant flume and the runup on a sloping plane beach and the circular island are simulated. Initial surface elevation of a solitary-like wave is provided as the initial condition. The waveform of a solitary-like wave with different values of the elongation parameter shows that undular bores and a train of solitary waves could appear in offshore shallow regions. Runup of solitary-like waves on the sloping beach and circular island shares the same decay trends but different powers. Abnormal rear runup only exceeds the front runup for some cases of given nonlinearity parameters and relative wavelength and the waterline diameter of a circular island. The computed ratio of rear-runup/front-runup is less than 1.3.