Numerical modelling of tsunami propagation in idealised converging water body geometries

Abstract

Tsunamis have caused many severe natural disasters in human history, such as in 2018 at Palu City located in a narrow bay resulting in over 4340 fatalities. The tsunami propagation characteristics are greatly affected by the water body geometry. For converging geometries such as fjords, bays and estuaries, the interaction between incident tsunamis and lateral boundaries has not been extensively studied. Therefore, the propagation of approximately linear, Stokes, cnoidal and solitary waves are studied numerically in converging, uniform depth water bodies with side angles of 7.5°, 15°, 30° and 45°. Both curved (without sidewall reflection) and straight wave sources (involving sidewall reflection) are used. SWASH, an open-source numerical wave propagation model based on the non-hydrostatic non-linear shallow water equations, is used. For a curved wave source, the wave heights H closely follow Green’s law and doubled as the water body width converged to 25% of the original width. However, for wide geometries with a straight wave source, due to reflections from the converging walls, Greens law is inappropriate to predict H. Wave energy can be concentrated on the sides or laterally transferred from stem wave growth and interaction, producing much larger H than predicted by Greens law. The water body width relative to the water depth h is found to have a significant effect on this transformation. Solitary wave amplitudes from 0.100 to 0.623 times h are simulated. An equation is derived for the solitary wave amplitude in a converging water body and an empirical equation is proposed for the prediction of the stem angle. A method for evaluating wave amplification at sidewalls is further presented and compared with the simulation results of this study. Finally, the application of this method is illustrated with an example inspired by the 2018 Palu Bay event. These findings enhance the physical understanding of the effect of the converging water body geometry on tsunami propagation and improve tsunami prediction and hazard assessment.