Run-up characterstics of symmetrical solitary tsunami waves of unknown shapes

TL;DR

This paper analyzes how the shape of symmetrical solitary tsunami waves affects their run-up on beaches, deriving universal formulas that are useful for tsunami warning systems when wave shapes are unknown.

Contribution

It provides universal analytical expressions for tsunami wave run-up characteristics that are weakly dependent on wave shape, aiding in tsunami prediction.

Findings

Extreme wave characteristics are weakly dependent on wave shape.

Derived universal formulas for run-up and draw-down heights and velocities.

Applicable for tsunami warning when wave shape is unknown.

Abstract

The problem of tsunami wave run-up on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. We present an analysis of the run-up characteristics for various shapes of the incoming symmetrical solitary tsunami waves. It will be demonstrated that the extreme (maximal) wave characteristics on a beach (run-up and draw-down heights, run-up and draw-down velocities and breaking parameter) are weakly dependent on the shape of incident wave if the definition of the significant wave length determined on the 2/3 level of the maximum height is used. The universal analytical expressions for the extreme wave characteristics are derived for the run-up of the solitary pulses. They can be directly applicable for tsunami warning because in many case the shape of the incident tsunami wave is unknown.