Tsunami runup on a sloping beach. Issue 1 (12th January 2020) - Chugunov, Vladimir A.; Fomin, Sergei A.; Noland, William; Sagdiev, Bayazit R.
Abstract : The purpose of this article is to propose the quasilinear theory of tsunami runup and run‐down on beach profiles of varying complexity. We begin with the one‐dimensional nonlinear shallow water wave equations, which we consider over a piecewise‐linear beach of various geometries along with several intuitive initial and boundary conditions. The primary obstacle in solving this problem is the moving boundary associated with the shoreline motion. To avoid this difficulty, we replace the moving boundary with a stationary boundary by applying a transformation to the spatial variable of our computational domain. A characteristic feature of any tsunami problem is the smallness of the parameter ϵ = η 0 / h 0 where η 0 is the characteristic amplitude of the wave and h 0 is the characteristic depth of the ocean. The presence of this small parameter enables us to effectively linearize the problem using the method of perturbations, which leads to an analytical solution via an integral transformation. This analytical solution assumes that there is no wave breaking. Our solution is then shown to predict the shoreline motion analytically with good accuracy.