Viscous and nonlinear effects on Helmholtz resonance in a gap induced by waves

Abstract

Viscous and nonlinear effects on the gap resonance between a deep-draft hull and a vertical wall are investigated numerically, with particular attention to the low-frequency response, i.e., Helmholtz resonance. Viscous-flow computations indicate that the free-surface response in the gap initially increases and then decreases as the hull draft-to-depth ratio varies from 0.4 to 0.98. Conditions in which there is near complete dissipation and minimal wave reflection (i.e., K_d = 0.99, K_r = 0.07) are identified and the effect of wave height is evaluated. Vorticity contours are used to study the flow field between the hull and boundaries. Significant flow blockage is shown to occur when the hull approaches the bottom boundary, attenuating the gap resonance. In this case, full development of these vortices and water transport into and out of the gap is restricted, leading to increased wave reflection. Numerical simulations for various incident wave heights demonstrate that the Helmholtz resonance still results in substantial wave dissipation (i.e., K_d > 0.89), which is in contrast to the behaviour observed for conventional gap problems. The findings may inform innovative designs for long wave absorbing breakwaters and Oscillating Water Column devices.