Numerical investigation of oscillations within a harbor of parabolic bottom induced by small-scale landslides

Oscillations within a rectangular harbor of parabolic bottom induced by small-scale landslides are investigated numerically based on Boussinesq-type equations and the results are used to reveal the characteristics of the oscillations generated on this type of bottom profile. Relatively, local and small-scale landslides within the harbor may induce obvious transverse oscillations. The predominant transverse components are those with small mode numbers mand nwhen the solid slides start moving from the backwall. The augmentation of the velocity of the slides along the parabolic seafloor may shift the amplitudes of the oscillation components to larger values, which corresponds to the physical understandings of the waves generated by landslides. In comparing the oscillations induced by the slides of constant velocity and those accelerated by gravity force with bottom friction, it is observed that the movements accelerated by gravity force may facilitate the development of certain oscillation modes while those with constant velocity may be in favor of others. While the landslides may not act on an isolated point of the bottom but follow a certain trajectory along the harbor, the transverse oscillations induced by landslides are sensitive to their position of departure both in the cross-harbor direction and in the offshore direction. The numerical result of each transverse eigenfrequency is very close to the theoretical prediction and the spatial structure of each mode may also be well captured by the existing analytical solutions based on shallow water equations. Although longitudinal oscillations may not be steadily generated with landslide movements on a parabolic bottom within the harbor, some patterns of several low-mode ones occur and are also sensitive to the initial location and trajectory of the slides. Wavelet spectra are used to analyze their evolutions and comparisons are made with theoretical predictions.