Numerical investigation of oscillations within a harbor of parabolic bottom induced by water surface disturbances

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.