Nonlinear regimes of tsunami waves generated by a granular collapse

Tsunami waves generated by subaerial landslides are a threat to human activities along coastal areas, as illustrated by recent events such as the partial flank collapse of Anak Krakatau (2018). To improve our prediction of such events, we consider the collapse of a granular column into water in a quasi-two-dimensional setup. Our experiments reveal three nonlinear wave regimes, depending on the Froude number Frf based on the ratio of the velocity of the advancing granular front at the interface and the velocity of linear gravity waves in shallow water. For large Frf, transient bores are generated, while for intermediate values of Frf quasi-symmetrical solitary-like waves are produced. Finally, nonlinear transition waves are observed at small Frf. The relative wave amplitude increases with the local Froude number in the three regimes with different nonlinear scalings, while the relative wavelength is an increasing or decreasing function of the local Froude number depending on the wave regime. We rationalize these wave regimes using shallow water equations by considering that the advancing granular front acts as a vertical piston pushing the water, and report that nonlinear transition waves are found to be a transition from shallow to deep-water conditions.  The present modeling contributes to a better understanding of the rich hydrodynamics of the impulse waves generated by grains entering into water.