Conditions and phase shift of fluid resonance in narrow gaps of bottom mounted caissons

Abstract

This paper studies the viscid and inviscid fluid resonance in gaps of bottom mounted caissons on the basis of the plane wave hypothesis and full wave model. The theoretical analysis and the numerical results demonstrate that the condition for the appearance of fluid resonance in narrow gaps is kh=(2n+1)π (n=0, 1, 2, 3, …), rather than kh=nπ (n=0, 1, 2, 3, …); the transmission peaks in viscid fluid are related to the resonance peaks in the gaps. k and h stand for the wave number and the gap length. The combination of the plane wave hypothesis or the full wave model with the local viscosity model can accurately determine the heights and the locations of the resonance peaks. The upper bound for the appearance of fluid resonance in gaps is 2b/L<1 (2b, grating constant; L, wave length) and the lower bound is h/b≤1. The main reason for the phase shift of the resonance peaks is the inductive factors. The number of resonance peaks in the spectrum curve is dependent on the ratio of the gap length to the grating constant. The heights and the positions of the resonance peaks predicted by the present models agree well with the experimental data.