Experiments on generation of surface waves by an underwater moving bottom

Abstract

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal highpass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

Near- and far-field tsunami waves, displaced water volume, potential energy and velocity flow rates by a stochastic submarine earthquake source model

“…Linear wave theory indicates that seismic displacement by stochastic source models and tsunami generation can 40 constructively interfere (Geist 2015). Jamin et al (2015) computed theoretically the kinetic energy and the free surface elevation by an underwater moving bottom using the linear water wave theory and showed that the theoretical results displayed very good agreement with the experimental data. Nonlinear effects become significant and dominant as tsunami enters the run-up phase, see (Lynett and Liu 2002;Glimsdal et al 2007;Løvholt et al 2012;Samaras et al 2015).…”

“…maximum amplification, see Ramadan et al 2011). This solution is accurate if the depth of the water, h, is much greater than the amplitudes of and ζ (sea floor uplift) and η (free surface elevation) and if the wavelength of the leading wave of the incoming tsunamis is very 50 long in comparison with the local water depth, which is usually true for most tsunamis triggered by submarine earthquakes, slumps and slides, see (Todorovska and Trifunac 2001;Trifunac et al 2002;Todorovska et al 2002;Trifunac et al 2003;Hayir 2006;Jamin et al 2015). All these studies neglected the nonlinear terms in the boundary conditions to study the generation of the tsunami waves using the transform methods.…”

“…The linear water wave theory has been developed as a fundamental theory in questions of stability for both near-35 and far-field problem in the open ocean which provides an ample understanding of the physical characteristics of the tsunami, see (Jamin et al 2015;Kervella et al 2007;Saito and Furumura 2009;Saito T 2013;Constantin and Germain 2012;. Additionally, one of the notable consequences of the linear theory is that the height distribution at the surface is not always identical to the bottom, see (Jamin et al 2015) and (Saito 2013).…”

“…Additionally, one of the notable consequences of the linear theory is that the height distribution at the surface is not always identical to the bottom, see (Jamin et al 2015) and (Saito 2013). Linear wave theory indicates that seismic displacement by stochastic source models and tsunami generation can 40 constructively interfere (Geist 2015).…”

“…Saito (2013) derived analytical solutions for the velocity distributions in the sea to visualize the tsunami generation process. Jamin et al (2015) performed combined measurements of the free-surface deformation and the fluid velocity field based on the role of the bottom kinematics. Uniform slip dislocations will not accurately simulate details of the local tsunami wavefield and are largely 25 insufficient to account for local tsunami amplitude variations caused by the combined effect of earthquake source complexity and inhomogeneous fault and earth structure in subduction zones.…”