Harbor Oscillations Induced by Nonlinear Transient Long Waves

Abstract

The process of the excitation of harbors and bays by transient nonlinear long waves is investigated both theoretically and experimentally. A numerical method employing finite element techniques is used to solve the weakly nonlinear‐dispersive‐dissipative equations of motion for variable depth applied to this problem. Several dissipative effects also are included. The open sea conditions are simulated using a time varying radiative boundary condition imposed at a finite distance from the harbor entrance. Experiments are conducted using continuous waves incident upon a narrow constant depth rectangular harbor; the results show that, for the lowest resonant mode, convective nonlinearities could be neglected and a linear dissipative solution is sufficient to describe the wave dynamics inside the harbor. For higher resonant modes nonlinear convective effects must be included. Using transient waves, good agreement is obtained between the experimental and theoretical results for a rectangular harbor with a linearly sloping bottom and a constant depth harbor with a trapezoidal planform. The theoretical method is applied to Hilo Bay, Hawaii, to investigate its response to incoming long waves.