Analytical Approach for Long Wave Solution to an Arbitrarily Varying Topography

Abstract

An investigation of the effects of bottom topography on the run-up height of vertical structures in protecting from destructive oceanic long waves, such as tsunamis, was conducted by using an analytical solution derived from the continuity and momentum equations. Because the solution of the governing equation is expressed as a Bessel function in cases where the water depth varies linearly, the present solution was obtained by assuming the water depth as a series of constant slopes. The present solution was verified by comparing with an analytical solution derived previously. The reflection of waves and the effects of bottom topography on the run-up height of vertical structures that partially reflect waves were investigated.