Higher-order gap resonance between two identical fixed barges: a study on the effect of water depth

Nonlinear piston-mode fluid resonance in the gap formed by two identical fixed barges in close proximity is investigated using a two-dimensional (2D) fully nonlinear numerical wave tank (NWT). To delve into the effect of water depth on higher-order resonances in the gap, consistent models are employed to describe the incident waves and wave-structure interactions for finite and shallow water depths. In contrast to previous studies, strong 4th- and 5th-order nonlinear gap resonances are observed under the action of shallow-water waves, resulting in significant higher-harmonic responses that are comparable to the corresponding 1st and 2nd harmonics. For a given wave height, those waves are found to be more critical than the finite-depth waves which are capable of evoking 2nd- or 3rd-order gap resonance. Highly oscillatory behavior is observed at the trough under the action of shallow-water waves. This is ascribed to the higher-harmonic diffraction effects, breaking the `perfect cancellation' between the incident-wave harmonics which should otherwise produce smooth and flatter wave trough. Unlike what a linear diffraction theory will predict, the gap response does not behave completely in a quasi-static manner under long cnoidal waves, and the higher harmonics generally show larger phase differences to the corresponding incident-wave components until the resonance occurs. The present study suggests that the water-depth effect and higher harmonics should be consistently accounted for in the design and analysis of side-by-side marine operations in coastal environments involving piston-mode gap responses.