Tsunami wave propagation over an underwater obstacle

Water wave propagation over an uneven seafloor is studied using analytical techniques in application to modeling tsunami wave dynamics on coastlines. A long, solitary wave is modeled as moving over an underwater obstacle situated on a flat seafloor. The obstruction is taken to be symmetric, rectangular, and of finite length. The linear shallow water equations are solved in the frequency domain using the method of Laplace Transforms. The solutions of regions in between the obstacle boundaries are matched together and transformed back to the time domain. The solutions to the equations demonstrate a greater variety of dynamical behavior than for the case of an obstacle of infinite length.