Wave evolution induced by moving bottom topography via the Dirichlet–Neumann operator

Bed motion can cause the free surface of initially still water to deform and eventually evolve into a train of solitons. This study conducts long-duration numerical simulations of such initial-disturbance waves using a fully nonlinear potential flow model solved by the Dirichlet–Neumann operator (DNO) method. Comparative validation tests against Hammack's experimental data and Boussinesq model simulations demonstrate the superior accuracy of the DNO predictions. The nondissipative numerical scheme is verified through a reversibility check. Whereas wave crests propagate at a constant velocity, their amplitudes exhibit dynamic variations before stabilization. Herein, the nonconstant amplitude characteristics of soliton solutions are effectively reconstructed through an inverse scattering transform within a fully nonlinear potential flow framework. As a powerful tool for solving fully nonlinear potential flow problems, the DNO method establishes fundamental research paradigms for elucidating the physical mechanisms of tsunami generation by submarine earthquakes.