Runup Characteristics of Symmetrical Solitary Tsunami Waves of “Unknown” Shapes

Abstract

The problem of tsunami wave runup on a beach is discussed in the framework of the rigorous solutions of the nonlinear shallow-water theory. We present an analysis of the runup characteristics for various shapes of the incoming symmetrical solitary tsunami waves. It will be demonstrated that the extreme (maximal) wave characteristics on a beach (runup and draw-down heights, runup and draw-down velocities and breaking parameter) are weakly dependent on the shape of incident wave if the definition of the “significant” wavelength 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 runup of the solitary pulses. They can be directly applicable for tsunami warning because in many cases the shape of the incident tsunami wave is unknown.