Oceanic propagation of a potential tsunami from the La Palma Island

Abstract

[1] The likelihood of a large scale tsunami from the La Palma Island is considered small by most. Nevertheless, the potential catastrophic consequences call for attention. Here we report on numerical simulations of a tsunami that might result from the extreme case of a flank collapse of the Cumbre Vieja volcano at the La Palma Island, done by combining a multimaterial model for the wave generation with Boussinesq models for the far-field propagation. Our simulations show that the slide speed is close to critical, effectively generating an initial wave of several hundred meters height. Our main focus is the wave propagation which is genuinely dispersive. In the far-field, propagation becomes increasingly complex due to the combined effects of dispersion, refraction, and interference in the direction of propagation. Constructive interference of the trailing waves are found to decrease the decay of the maximum amplitude with distance compared to classical asymptotic theory at transatlantic distances. Thus, the commonly used hydrostatic models fail to describe the propagation. Consequences of the La Palma scenario would be largest at the Canary Islands, but our findings also suggests that the whole central Atlantic would face grave consequences. However, the largest surface elevations are smaller than the most pessimistic reports found in literature. We also find undular bores towards the shorelines of America.

On the effect of the water body geometry on landslide–tsunamis: Physical insight from laboratory tests and 2D to 3D wave parameter transformation

“…Kranzer and Keller (1959) showed analytically that the wave amplitude decays differently in 2D, with x -1/3 to x -1/2 , compared to 3D, with r -1 . Similar analytical results are shown by Løvholt et al (2008). They found a 2D wave height decay ranging from x -1/3 (for a monopolelike source) to x -2/3 (for a dipole-like source).…”

“…The celerity of the onshore waves is smaller as they are travelling in reduced effective water depth and are more dispersive. These onshore waves are trapped which significantly affects their propagation behaviour as discussed in detail in Appendix C.Frequency dispersion and the associated physical processes, such as an apparent energy transfer between successive wave crests, are important because this may (temporarily) 23 enhance trailing waves (Løvholt et al, 2008;Di Risio et al, 2009b). As a consequence, successive wave crests may exceed the primary wave magnitude as was observed in Fig.…”

“…In 3D, the corresponding wave height decays were found as r -5/6 to r -7/6 . Løvholt et al (2008) also compared these 3D decays with…”

“…Generic model studies systematically vary parameters (slide properties, hill slope angle, water depth) which may be estimated a priori for real-world events, and express the unknown wave parameters (amplitude, height, period) as a function of these parameters. The resulting empirical equations can be very efficient in predicting future events (Heller et al, 2009), and are often the most straightforward method if time is limited.At the very least, such equations can help to determine whether or not a prototype specific numerical (Løvholt et al, 2008;Abadie et al, 2012) or physical (Davidson and Whalin, 1974;Fuchs et al, 2011) model study is required. These latter methods are both considerably more expensive and time consuming than applying generic empirical equations.…”

“…At the very least, such equations can help to determine whether or not a prototype specific numerical (Løvholt et al, 2008;Abadie et al, 2012) or physical (Davidson and Whalin, 1974;Fuchs et al, 2011) model study is required. These latter methods are both considerably more expensive and time consuming than applying generic empirical equations.…”