Tsunamis - harbor oscillations induced by nonlinear transient long waves

摘要

The process of excitation of harbors and bays by transient nonlinear long waves is investigated theoretically and experimentally. In addition, nonlinear shallow water waves generated in a closed rectangular basin by the motion of the basin are also examined.ududTwo numerical methods based on finite element techniques are used to solve the weakly nonlinear-dispersive-dissipative equations of motion and are applied to the basin excitation problem and the transient harbor oscillation problem, respectively. In the latter case, the open sea conditions are simulated by including a radiative boundary condition in time at a finite distance from the harbor entrance. Various dissipative effects are also included. In addition to the numerical results, analytical solutions are presented to investigate certain particular aspects of basin and harbor oscillations (e.g., the effects of viscous dissipation in a harbor with simple geometry).ududExperiments conducted in the closed rectangular basin indicate that for a continuous excitation at or near a resonant mode of oscillation the linear theory becomes inadequate and the nonlinear-dispersive-dissipative theory must be used. For a transient excitation the validity of the linear theory depends on the value of the Stokes parameter. Indeed, some features not predicted by the linear theory can be directly inferred from the magnitude of this parameter.ududExperiments on the continuous wave induced oscillations of a narrow rectangular harbor with constant depth show that at the first resonant mode convective nonlinearities can be neglected and a linear dissipative solution is sufficient to describe the waves inside the harbor. At the second resonant mode which corresponds to a longer harbor relative to the length of the incident wave, nonlinear convective effects become important and must be incorporated into the numerical model. Also the characteristics of various sources of dissipation which reduce resonance in the harbor are investigated experimentally. The sources considered include, among others, laminar boundary friction, leakage losses underneath the harbor walls, and energy dissipation due to flow separation at the entrance of the harbor.ududThe good agreement obtained between the experiments and the nonlinear numerical model developed in this study suggests that this model could be used with some confidence to predict the response characteristics of prototype harbors. As an example, the results of this study have been applied to the response of Ofunato Bay (Japan) to the tsunami generated by the Tokachi-Oki earthquake of May 16, 1968. The model has been used to investigate the effects of convective nonlinearities on the bay oscillations and also to determine the efficiency of the breakwater which was built to reduce the effects of tsunamis at Ofunato.