Analytical and numerical investigation on the energy of free and locked tsunami waves generated by a submarine landslide

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Submarine landslides are capable of causing locally catastrophic tsunamis. Landslide parameters, particularly those related to the landslide motion, are highly uncertain in a real landslide tsunami event. To date, a practical method for effectively and efficiently modeling the landslide tsunami generation process is still lacking. To gain insight into the landslide tsunami generation mechanism, we employed a combination of analytical derivation and numerical computation. From the wave energy perspective, we found the locked wave component of a landslide tsunami to be as important as the free wave component. Thus, the locked wave component cannot be neglected. We showed that for a geophysically relevant submarine landslide speed, the locked wave component has a deceivingly small wave amplitude with large flow velocities. Thus, careful attention must be paid to flow velocities when modeling landslide tsunamis. For a submarine landslide forcing water waves at a constant speed, we found that the total wave energy first evolves from zero to a peak value, before decreasing to an asymptotic value. These two distinct energy values and the corresponding wave generation times may serve as conservative estimates in predictive studies, in which precise information on the landslide dynamics is impossible to obtain. Finally, we used the 1998 Papua New Guinea landslide tsunami as an example to demonstrate how the findings in this study aid in the modeling effort for a real event.