Nonlinear harmonics of gap fluid resonance with floating body motions

Abstract

Resonant response of water waves in a narrow gap, the so-called gap resonance, is a hydrodynamic phenomenon with practical applications. When coupled to body motions, the physics becomes rather complicated, involving body motions, fluid resonance and damping that determines the response amplitude. Gap resonances between two identical elongated bodies, with one held fixed and the other floating, are investigated experimentally for unidirectional waves with broadside incidence. Transient wave groups with different maximum surface elevations are generated, to examine the nonlinear physics. Sub- and super-harmonics, which can be substantially larger than the linear component, are observed in the responses. When going from the diffraction problem (both bodies fixed) to the coupled problem (allowing one body to move), the gap responses are significantly amplified, i.e. by a factor of 2. The first resonant mode that dominates the diffraction problem disappears in the coupled problem. A new resonant mode, which is shown to arise from body motions, is excited inside the gap through nonlinear processes. This mode features a double-humped ‘camel-back’ shape, leading to remarkably large responses. The floating body is observed to oscillate in sway with significant amplitudes at two distinct natural frequencies that are far apart. This is of great interest for the design of mooring lines connecting the two bodies, as it appears to cause resonances at the wave frequencies in addition to the low frequencies. A semi-analytical model is developed to investigate the multiple natural frequencies in sway, yielding further insight into gap resonances.