Resonance of Long Wave Runup on South China Sea’s Piecewise Topographies

Abstract

Solving the linear shallow water equations on a profile of four segments and matching the solutions on the turning points, runup of periodic long waves is obtained analytically. The resonant phenomena appear when periodic long waves propagate on piecewise topographies. According to the propagation path of tsunami waves, several profiles in the South China Sea are picked up. The topographies can be simplified to a four-segments profile which comprises a horizontal deep seabed, a continental foundation, a continental slope and a continental shelf from the trench to the shore. The runup amplification are calculated both analytically and numerically. Resonant phenomena appear and the values of runup are quite large at the resonant frequencies.