Tsunami generated by a granular collapse down a rough inclined plane

In this Letter, we experimentally investigate the collapse of initially dry granular media into water and the subsequent impulse waves. We systematically characterize the influence of the slope angle and the granular material on the initial amplitude of the generated leading wave and the evolution of its amplitude during the propagation. The experiments show that whereas the evolution of the leading wave during the propagation is well predicted by a solution of the linearized Korteweg-de Vries equation, the generation of the wave is more complicated to describe. Our results suggest that the internal properties of the granular media and the interplay with the surrounding fluid are important parameters for the generation of waves at low velocity impacts. Moreover, the amplitude of the leading wave reaches a maximum value at large slope angle. The runout distance of the collapse is also shown to be smaller in the presence of water than under totally dry conditions. This study provides a first insight into tsunamis generated by subaerial landslides at low Froude number. In the last decade, two particularly destructive tsunamis, in the Indian Ocean [1] and in Pacific Ocean [2], have raised the necessity to predict, or at least evaluate the hazards induced by such events for the population and human activities. Although many tsunamis arise from underwater earthquakes [3], some are also induced by submarine and subaerial landslides which can be locally more dangerous as they form near the coast and may exhibit extreme runup [4]. One approach to study tsunamis generated by subaerial landslides relies on the simple configuration of a solid block impacting the water [5, 6]. During a landslide, strong interactions occur between the slide and the generated waves. In this case, estimating real situations requires a deformable slide [7]. Most previous studies focused on the particular case of a Froude number Fr = vs/ √ g H larger than one, i.e. on a slide velocity vs larger than the shallow water wave velocity √ gH (g being the gravity, H the water depth). This configuration is relevant to model geophysical events such as the mega-tsunami of Lituya Bay, Alaska (1958) where the estimated Froude number was about Fr ≃ 3.2 [8]. However, in the simple situation of a cliff collapse, which is expected to happen in the South of France [9], the dynamic would be different as the Froude number becomes smaller than unity. In this situation, an estimate of the interplay between the granular material and the wave is required. Despite important implications on risk control, landslides for a Froude number smaller than one and the generation of the subsequent tsunamis have been poorly investigated. The lack of such studies may be explained by the difficulty of modeling dense flows of granular media despite their major stake in industrial and geophysical applications [10, 11]. Due to these applications, a huge number of studies considered various dense flows of dry granular materials [12–15]. The mechanical properties of the grains are not completely understood but recently, Jop et al. [16] suggested a continuum model, the μ(I)-rheology, to account for the unique properties of dry dense granular flows. This rheology gives a good description in many situations such as a granular collapse [17,18] or granular flows on a pile [16]. However, the addition of water drastically changes the dynamics of granular flows as emphasized by recent studies with partially wet granular media [19–23], suspension of particles [24–26] and underwater granular flows [27, 28]. These studies show the influence of both