Local Runup Amplification By Resonant Wave Interactions

TL;DR

This paper investigates how resonant wave interactions can amplify tsunami runup on beaches, revealing phenomena not captured by traditional maximum runup analysis, through numerical simulations of the nonlinear shallow water equations.

Contribution

It demonstrates the existence of resonant regimes between incident wavelength and beach slope, leading to enhanced runup, a phenomenon not previously characterized.

Findings

Resonant interactions cause significant runup amplification.

Energy evolution shows a quasi-periodic state dependent on wavelength.

Dispersion slightly reduces maximum runup but does not alter the overall resonance effects.

Abstract

Until now the analysis of long wave runup on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. One-dimensional numerical simulations in the framework of the Nonlinear Shallow Water Equations (NSWE) are used to investigate the Boundary Value Problem (BVP) for plane and non-trivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the BVP. Resonant phenomena between the incident wavelength and the beach slope are found to occur, which result in enhanced runup of non-leading waves. The evolution of energy reveals the existence of a quasi-periodic state for the case of sinusoidal waves, the energy level of which, as well as the time required to reach that state, depend on the incident wavelength for a given beach slope. Dispersion is found to slightly reduce the value of maximum runup, but not to change the overall picture. Runup amplification occurs for both leading elevation and depression waves.