Evolution of arbitrary temporal ocean floor motion-induced surface waves over a trench.

This article focuses on modeling the scattering of surface water waves generated by arbitrary vertical motion of the ocean floor within a trench, accounting for sudden depth changes and ocean compressibility—including static oceanic background compression—under linearized water wave theory. Using Fourier transformation and eigenfunction expansion methods, the study derives frequency-domain solutions for surface displacement and pressure profiles, addressing numerical challenges posed by singularities and oscillations through non-uniform discretization techniques. Time-domain simulations reveal standing wave formations and significant pressure fluctuations within the trench, with effects amplified at greater ocean depths; both two-dimensional and axisymmetric three-dimensional cases are analyzed and compared. The findings highlight the influence of ocean compressibility on wave envelope oscillations and provide a canonical framework for extending tsunami wave propagation models to more realistic bathymetries involving trenches.