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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 m and n when 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. [ABSTRACT FROM AUTHOR]

Oscillations within a rectangular harbor of constant slope induced by submerged sliding masses are investigated numerically based on Boussinesq-type equations and results are used to reveal the characteristics of the generated oscillations. The numerical result of each transverse eigenfrequency is very close to the theoretical prediction and the spatial structure of each mode of the oscillations may also be well captured by the existing analytical solutions based on shallow water equations. The investigation shows that relatively small-scale sliding masses whose width is small compared with the harbor width may induce obvious transverse oscillations. The predominant transverse components are those with small mode numbers when the solid slides start moving from the backwall. 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 very low transverse oscillation modes while those with constant velocity may also be in favor of the higher ones. The augmentation of the sliding velocity along the constant slope may shift the amplitudes of the oscillation components to smaller values, which corresponds to the physical understandings of the waves generated by underwater sliding masses or landslides. While the sliding masses may not act on an isolated point of the bottom but follow a certain trajectory along the harbor, the transverse oscillations induced by them are sensitive to their position of departure in both the cross-harbor direction and the offshore direction. Longitudinal oscillations may be induced by relatively large sliding masses of harbor width on a constant slope within the harbor. Although the longitudinal oscillations may not reach a steady state without forcing terms at the entrance of the harbor, some patterns of several low-mode ones occur and wavelet spectra are used to analyze their evolutions and comparisons are made with theoretical predictions. It is revealed that the longitudinal oscillations are also sensitive to the moving velocity and initial location of the sliding masses. [ABSTRACT FROM AUTHOR]

Oscillations within a rectangular harbor of parabolic bottom induced by water surface disturbances are investigated numerically based on Boussinesq equations and results are used to reveal the characteristics of the oscillations generated by disturbances of this type. The similarities and differences compared with those generated by a movable seafloor are also discussed. Relatively local and small-scale water surface disturbances may induce obvious transverse oscillations with little trace of longitudinal ones. The predominant transverse components are those with small alongshore mode number m and no node in the offshore direction. The augmentation of the rapidity of depth variation of the parabolic bottom may shift the resonant frequencies to larger values. These transverse modes are sensitive to the initial position of water surface disturbances. The spatial structure of each mode is well captured by the existing analytical solution based on shallow water equations. Although longitudinal oscillations may not be steadily generated with water surface disturbances, some patterns of several low-mode ones occur and are also sensitive to the position of the disturbances. Wavelet spectra are used to analyze their evolutions and comparisons are made with theoretical predictions for the three principle longitudinal modes. [ABSTRACT FROM AUTHOR]