Approximation of near-resonant wave motion using a damped harmonic oscillator model

In this work, transient resonant motions excited in linearised scattering interactions are approximated using a simple damped harmonic oscillator model. The scattering interactions considered involve the diffraction of an incident wave-train with a dominant regular time-harmonic component by structures which enclose a portion of the free surface. Provided a single resonant mode only is excited significantly, the fluid oscillation in the vicinity of the structure will primarily be composed of the resonant mode and incident wave mode contributions. The forced damped harmonic oscillator equation is used to predict the fluid motion and, in particular, the elevation of the internal free surface. The predictions are compared to the results from a numerical time-domain solver based on the linearised water-wave equations. It is shown that, given a good estimate of the location of the resonance in the complex frequency plane and a priori knowledge of the form of the incident wave, the model can successfully predict the time-dependent behaviour of the motion. Both two- and three-dimensional scattering problems are considered with a variety of scatterers in each case.