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

The scattering of surface water waves generated through an arbitrary temporal motion of a portion of the ocean floor within a trench and from the sudden depth change at the wall of the trench is studied under the assumption of linearized water wave theory and a weakly compressible ocean that includes static oceanic background compression. The Fourier transformation and eigenfunction expansion techniques are deployed to find the surface displacement and pressure profiles with the help of appropriate matching conditions between regions of different depths. The difficulties of numerical computation owing to large oscillations of the displacement potential function around specific frequencies are overcome using adequate non-uniform finer meshing. Apart from the time-domain propagation of tsunami waves away from the origin, standing wave formations are observed within the trench region, supported by significantly large pressure fluctuations in time. These standing waves or the pressure fluctuations are higher when the ocean depth is large. The change in tsunami speed due to sudden depth change is readily visible in the time-domain simulations. Ocean compressibility results in fluctuations in the envelope of the propagating wavefront. Both the two-dimensional and axisymmetric three-dimensional solutions are presented. In comparison, the propagating surface wavefront for the latter case evolves with a sharper slope, which is additionally illustrated by the animation movies.