Numerical Model of Wave Run-Up, Overtopping, and Regeneration

TLDR

The paper presents a numerical model of wave run‑up, overtopping, and regeneration. The OTT model solves one‑dimensional nonlinear shallow‑water equations on a sloping bed—including bed shear stress—using a finite‑volume Roe‑type Riemann solver, enabling shoreline‑tracking‑free simulation of wave run‑up, overtopping, and regeneration over obstacles and water‑surface‑piercing structures. The model outperforms empirical formulas in predicting average overtopping rates and event counts for random waves, accurately reproduces dike water depths, and simulates regenerated wave heights, all without requiring a shoreline‑tracking algorithm.

Abstract

A numerical model of wave run-up, overtopping, and regeneration is presented. The model (called OTT) is based on the one-dimensional nonlinear shallow water equations on a sloping bed, including the effects of bed shear stress. These equations are solved using a finite-volume technique incorporating a Roe-type Riemann solver. The main advantage of this approach over previously used finite difference solvers is that no special shoreline-tracking algorithm is required, so that noncontiguous flows can easily be simulated. Hence, this model can be used to simulate the transmission of waves over water surface-piercing obstacles. The numerical scheme and boundary conditions are described, and several existing data sets used to test the ability of the model to simulate wave transformation, run-up, and overtopping. Experiments of random wave (unimodal and bimodal) overtopping, presented here for the first time, indicate that the model performs much better than empirical formulas in predicting average overtopping rates, and that it provides good estimates for the number of overtopping events. Experiments of overtopping of a sea wall by a solitary wave are also presented, including measurements of wave regeneration in lee of the dike. The model does a reasonable job of reproducing the water depths on top of the dike, and performs well in simulating the initial height of the regenerated waves.