Run-up amplification of transient long waves

TL;DR

This paper investigates the extreme run-up amplification of long waves on beaches, demonstrating the robustness of resonance effects under spectral perturbations and the influence of wave steepness and beach geometry.

Contribution

It extends existing theories by numerically analyzing resonant run-up amplification for finite beaches and explores the effects of wave steepness and boundary conditions.

Findings

Resonant amplification is robust to spectral perturbations.

Resonance occurs when the incoming wavelength exceeds the distance to the boundary.

Steeper waves lead to higher run-up values.

Abstract

The extreme characteristics of long wave run-up are studied in this paper. First we give a brief overview of the existing theory which is mainly based on the hodograph transformation (Carrier & Greenspan, 1958). Then, using numerical simulations, we build on the work of Stefanakis et al. (2011) for an infinite sloping beach and we find that resonant run-up amplification of monochromatic waves is robust to spectral perturbations of the incoming wave and resonant regimes do exist for certain values of the frequency. In the setting of a finite beach attached to a constant depth region, resonance can only be observed when the incoming wavelength is larger than the distance from the undisturbed shoreline to the seaward boundary. Wavefront steepness is also found to play a role in wave run-up, with steeper waves reaching higher run-up values.