Modeling of impulse waves generated by a viscous collapse in water

Abstract

The generation of tsunamis by landslides has been the object of a lot of studies, focusing in particular on the wave maximum amplitude η0,max to quantitatively assess the damage which these events may cause. The literature has long identified that this amplitude η0,max is correlated to a Froude number F rmax proportional to a maximum slide front velocity ẋf,max . Yet, the dynamics of the slide needs to be determined from initial conditions to allow prediction of the maximum amplitude η0,max. Based on a canonical initial configuration, the aim of the present work is thus to better understand the transient physics connecting the landslide to the wave growth leading to the prediction of the wave maximum amplitude. In particular, the collapse of a Newtonian slide from air to water is considered here, investigating the role of two key ingredients: the slide inertia and viscous dissipation. The parameter space is systematically varied beyond laboratory and geophysical estimations to gain understanding on the fundamental process of wave formation, with 2D threephase numerical simulations using Basilisk. Results show that the column collapse of a Newtonian slide allows to capture most of the physics of wave formation, and the correlation between η0,max and the Froude number F rmax ∝ ẋf,max is recovered. A dynamical model of collapse reveals how the interplay between inertia and dissipation controls the slide dynamics through a Reynolds number Re(t) which, in turn, determines the kinematics of slide-water interface as quantified by the Froude number F r(t). A simple model based on an idealised evolution of the collapse dynamics and volume conservation allows to explicitly determine F rmax and η0,max from the initial condition. This model allows to capture results obtained from the numerical simulations and in accordance with empirical correlations usually found in the literature.

From granular collapses to shallow water waves: A predictive model for tsunami generation

“…However, so far a unifying model relating the wave amplitude to the initial geometry of the column and the water depth remains elusive. Such an attempt was made recently through the study of the collapse of a Newtonian viscous fluid into a water layer [47]. Nevertheless, this configuration is closer to a dam-break problem and does not account for the granular nature of the landslide.…”