Nonlinear regimes of tsunami waves generated by a granular collapse

摘要

Tsunami waves induced by landslides are a threat to human activities and safety along coastal areas. In this paper, we characterize experimentally the waves generated by the gravity-driven collapse of a dry granular column into water. Three nonlinear wave regimes are identified depending on the Froude number Fr-f based on the ratio of the velocity of the advancing granular front and the velocity of linear gravity waves in shallow water: transient bores for large Fr-f, solitary waves for intermediate values of Fr-f, and nonlinear transition waves at small Fr-f. The wave amplitude relative to the water depth increases with Fr-f in the three regimes but with different nonlinear scalings, and the relative wavelength is an increasing or decreasing function of Fr-f depending on the wave regime. Two of these wave regimes are rationalized by considering that the advancing granular front acts as a vertical piston pushing the water, while the last one is found to be a transition from shallow-to deep-water conditions. The present modelling contributes to a better understanding of the rich hydrodynamics of the generated waves, with coastal risk assessment as practical applications.