Water waves generated by underwater landslides

Abstract

Water waves generated by underwater landslides threaten coastal communities near heads of fjords, near heads of underwater canyons, near river deltas, and on volcanic islands. This work provides a thorough analysis of water waves generated by two-dimensional underwater landslides using experimental, theoretical, and computational means. Water wave amplitudes generated by an underwater landslide are a function of the landslide length, the initial landslide submergence, the incline angle measured from horizontal, the characteristic distance of landslide motion, the characteristic duration of landslide motion, and the landslide rate of deformation. Nondimensional wavemaker curves constructed from the aforementioned parameters allow water wave amplitudes to be predicted. These wavemaker curves apply broadly to water waves generated by unsteady motion of a submerged object provided the motion is governed by only one characteristic distance scale and one characteristic time scale. Water wave amplitude predictions can be used for hazard mitigation studies. An analytical solution of underwater landslide center of mass position in time provides the characteristic distance and time scales of landslide motion. Two-dimensional experimental results on a 45 degree incline confirm the existence of wavemaker curves for solid block landslides as a function of nondimensional geometrical quantities and what is called the Hammack number. The Hammack number is the correct nondimensional time for water wave generation problems. Water wave amplitudes generated by solid block landslides can be predicted from the wavemaker curves if the center of mass motion is known. The analytical solution reproduces the center of mass motion of solid block and granular material landslides. Experimental results of granular material landslides on a 45 degree incline show that landslide deformation reduces water wave amplitudes. Therefore, water waves generated by solid block landslides provide an upper bound on water waves generated by geometrically and kinematically similar deforming landslides. A criterion for the generation of linear water waves is given along with criteria for deep (or long) wave propagation down a constant depth channel. Simulations of water waves generated by underwater landslides were conducted with an inviscid fluid dynamics code. The waves simulated by the code agree reasonably well with experimental results.