Tsunami waves generated by submarine landslides of variable volume: analytical solutions for a basin of variable depth

I Didenkulova,N Zahibo,E Pelinovsky,I Nikolkina

doi:10.5194/nhess-10-2407-2010

Abstract

Abstract. Tsunami wave generation by submarine landslides of a variable volume in a basin of variable depth is studied within the shallow-water theory. The problem of landslide induced tsunami wave generation and propagation is studied analytically for two specific convex bottom profiles (h ~ x4/3 and h ~ x4). In these cases the basic equations can be reduced to the constant-coefficient wave equation with the forcing determined by the landslide motion. For certain conditions on the landslide characteristics (speed and volume per unit cross-section) the wave field can be described explicitly. It is represented by one forced wave propagating with the speed of the landslide and following its offshore direction, and two free waves propagating in opposite directions with the wave celerity. For the case of a near-resonant motion of the landslide along the power bottom profile h ~ xγ the dynamics of the waves propagating offshore is studied using the asymptotic approach. If the landslide is moving in the fully resonant regime the explicit formula for the amplitude of the wave can be derived. It is demonstrated that generally tsunami wave amplitude varies non-monotonically with distance.

Highlights

The landslide motion is recognized as an important source of tsunami wave generation, since it is the second most frequent tsunami source after earthquakes responsible for about 10% of all tsunami waves (Gusiakov, 2009).At least, two special workshops specialized on this problem should be mentioned (Keating et al, 2000; Yalciner et al, 2003).For example, an underwater landslide on 17 July 1998 caused the destructive Papua New Guinea tsunami, when the 15-m wave at the coast devastated three villages and took more than 2200 lives (McSaveney et al, 2000; Synolakis et al, 2002)
This effect of variable volume of the landslide has never been analyzed in the problem of tsunami wave generation and the given study is focused on this problem
The tsunami wave generation by submarine landslides of a variable volume moving with a variable speed in a basin of variable depth is studied analytically

Summary

Introduction

The landslide motion is recognized as an important source of tsunami wave generation, since it is the second most frequent tsunami source after earthquakes responsible for about 10% of all tsunami waves (Gusiakov, 2009). Didenkulova et al.: Tsunami waves generated by submarine landslides of the erosion processes in avalanches, so that the deposited mass in the runout zone can be much larger than the initial mass in the starting zone This effect of variable volume of the landslide has never been analyzed in the problem of tsunami wave generation and the given study is focused on this problem. It was shown that in the case of bottom profile h ∼ x4/3 (h is the water depth and x is coordinate directed offshore) the wave equation with an external force can be simplified and the same methods as for a constant depth basin can be applied It was found later in (Didenkulova et al, 2009) that this bottom profile can be interpreted as a “non-reflecting” one.

Basic model

Findings

Conclusions