A Nonhydrostatic Two-Layer Staggered Scheme for Transient Waves due to Anti-Symmetric Seabed Thrust

Abstract

The development of transient waves generated by bottom motion is studied numerically in this work. A nonhydrostatic numerical scheme, based on solving the two-dimensional Euler equations using two-layer approximation for the vertical direction, is implemented. The dispersion relation of this scheme is shown to agree with the analytical dispersion relation over a wide range of [Formula: see text], where [Formula: see text] denotes the wave number and [Formula: see text] the characteristic water depth. To ensure that a good balance between nonlinearity and dispersion is accommodated by the scheme, the propagation of a solitary wave (undisturbed in shape) was simulated. Our next focus was on the simulation of transient waves generated by bottom motion. After conducting a benchmark test against Hammack’s experimental results for downward bottom motion, an anti-symmetric bottom thrust was considered. The resulting transient waves developed different behavior depending on the water depth. Finally, to mimic the December 2004 tsunami, a seabed motion was generated over Aceh bathymetry. This simulation showed that a package of wave trains developed and propagated towards the Aceh coast, and exhibited inter alia the feature of shoreline withdrawal often observed.