Runup of tsunami waves in U-shaped bays

TL;DR

This paper investigates tsunami wave behavior in U-shaped bays using shallow water theory, revealing conditions for wave shoaling, traveling waves, and significantly increased runup compared to plane beaches.

Contribution

It provides a theoretical analysis of tsunami wave shoaling and runup in U-shaped bays, identifying conditions for traveling waves and quantifying increased runup effects.

Findings

Weak reflection causes significant shoaling effects.

Traveling waves can propagate over large distances without reflection.

Tsunami runup in U-shaped bays exceeds that on plane beaches.

Abstract

The problem of tsunami wave shoaling and runup in U-shaped bays (such as fjords) and underwater canyons is studied in the framework of shallow water theory. The wave shoaling in bays, when the depth varies smoothly along the channel axis, is studied with the use of asymptotic approach. In this case a weak reflection provides significant shoaling effects. The existence of traveling (progressive) waves, propagating in bays, when the water depth changes significantly along the channel axis, is studied. It is shown that traveling waves do exist for certain bay bathymetry configurations and may propagate over large distances without reflection. The tsunami runup in such bays is significantly larger than for a plane beach.