Temporal and Topographic Source Effects on Tsunami Generation

We present a systematic study of the influence on tsunami waves generated by the uplift of a rectangular plug, of the rise time of the deformation, and of its topographic details (e.g., the presence of a sill). We are motivated by the fact that most simulation codes use an instantaneous deformation of a flat ocean floor as an initial condition of the problem, although Hammack (1973, http://resolver.caltech.edu/CaltechAUTHORS:HAMjfm73) performed pioneering laboratory studies as well as analytical computations featuring variable rise times. Here, we consider three 2-D source shapes, including a flat seafloor, a simple elevated piston, and additional trapezoidal sill on top of it, all with variable rise times, and simulate the resulting waves using the fully nonlinear smooth particle hydrodynamic model graphics processing unit smooth particle hydrodynamic. We validate our results against Hammack's (1973) laboratory measurements and analytical results. We find that a relatively large sill, with height and width of more than half of the local depth and width of the source, has a profound effect on the spatiotemporal structure of the generated free surface wavefield. Specifically, we show that the maximum water surface elevation over the source region is not always the same as the bottom displacement, as assumed in most tsunami propagation models. Next, we obtain simple scaling relationships to predict the maximum height of the generated tsunami over and outside the source, based on the geometry of the sill and the nondimensional bed rise time. Last, we show that inertial effects may lead to an initial free surface displacement over the generation region greater than the maximum vertical displacement of the displaced seabed.