Dispersive effects during long wave run-up on a plane beach

TL;DR

This study compares dispersive and non-dispersive models in simulating long wave run-up on a beach, finding non-dispersive models suffice for maximum run-up height estimation in most cases.

Contribution

It provides a comparative analysis of dispersive and non-dispersive models using experimental data, highlighting when dispersive effects are significant or negligible.

Findings

Dispersive effects are minor for long positive pulses.

Dispersive effects cause wave transformation in sinusoidal and bi-harmonic waves.

Nonlinear shallow water theory is adequate for estimating maximum run-up height.

Abstract

Dispersive effects during long wave run-up on a plane beach are studied. We take an advantage of experimental data collection of different wave types (single pulses, sinusoidal waves, bi-harmonic waves, and frequency modulated wave trains) and simulate their run-up using two models: (i) non-dispersive nonlinear shallow water theory and (ii) dispersive Boussinesq type model based on the modified Peregrine system. It is shown, that for long positive pulses, dispersive effects are not so important and nonlinear shallow water theory can be used. However, for periodic sinusoidal and bi-harmonic pulses of the same period, the dispersive effects result in significant wave transformation during its propagation, but do not have a strong impact on its maximal run-up height. Overall, for maximum wave run-up height, we could not find a preference of dispersive model against the nondispersive one, and, therefore, suggest using nonlinear shallow water model for long wave run-up height estimation.