Landslide tsunamis propagating along a plane beach

Abstract

A forced two-horizontal-dimension analytical model is developed to investigate the distinguishing physical features of landslide-induced tsunamis generated and propagating on a plane beach. The analytical solution is employed to study the wave field at small times after the landslide motion starts. At larger times, the occurrence of transient edge waves travelling along the shoreline is demonstrated, showing the differences with the transient waves propagating over a bottom of constant depth. Results are satisfactorily compared with available experimental data. Finally, the validity of non-forced numerical models is discussed

Hydro-acoustic frequencies of the weakly compressible mild-slope equation

“…Since HA waves are generated at different depths as the slide moves down the incline, energy is transmitted to them at several frequencies and modes. In this case, the trapped low-frequency HA component could be significant and longshore HA waves could be used to predict incoming edge waves propagating along a beach (Sammarco & Renzi 2008). This intriguing research hypothesis is being considered in ongoing work.…”

“…Water is in the region x > 0, the shoreline is at x = 0. The planebeach geometry has important practical applications in tsunami models (Mei et al 2005;Sammarco & Renzi 2008). It is also particularly interesting as it allows one to obtain an exact analytical solution in terms of integrals of Bessel functions.…”

The hydrodynamics of landslide tsunamis: current analytical models and future research directions

“…Such an initial condition was then to be implemented in tsunami propagation and inundation models. Later, Sammarco and Renzi (2008) demonstrated that no analytical proof of the validity of the hot-start approach could be given, suggesting that such simplified models be used only for quick runup assessment. Indeed, Liu et al (2003) were among the first to recognise the importance of including the time history of the seafloor deformation in landslide tsunami modelling.…”

“…The numerical results of Lynett and Liu (2005) highlighted the need to develop an appropriate analytical two-horizontal-dimension (2HD) model to explain such dynamics. Following the suggestion of Lynett and Liu (2005), Sammarco and Renzi (2008), Renzi and Sammarco (2010) and Renzi and Sammarco (2012) developed fully 2HD analytical models of landslide tsunami generation and propagation along a plane beach and around a conical island, induced by a sliding solid block. By using the forced linear shallow water equation, Sammarco and Renzi (2008) derived the analytical form of both the offshore component and the transient edge waves travelling along the shoreline of a plane beach.…”

“…Indeed, modelling landslide tsunamis is intrinsically challenging as it involves a time-dependent bottom deformation in the same region where the waves are generated and propagate. In this paper, we shall review the analytical models of Sammarco and Renzi (2008), Renzi and Sammarco (2010) and Renzi and Sammarco (2012), which have become benchmark models for numerical codes (Romano et al 2013;Dias et al 2014;Stefanakis et al 2014) and statistical emulations (Sarri et al 2012) of landslide tsunamis. Analytical models provide an invaluable tool in the science of tsunami modelling, for they allow one to obtain a sound physical understanding of the wave dynamics and to carry out parametric investigations on the influence of the system main parameters on the maximum wave runup.…”