Influence of submerged annular rippled breakwater on hydrodynamic performance of column floating pier

Based on linear potential flow theory, a mathematical model of the interactions between a floating pier with a submerged annular rippled breakwater and linear monochromatic waves was established. The fluid domain was divided into four regions: an exterior region, a mild-slope region, a gap region, and an interior region. The modified mild slope equation (MMSE) was used to establish the velocity potential expression of the mild-slope region, where the rippled breakwater was located. The matched eigenfunction expansion method (MEEM) was then used to derive the semi-analytical solution of the diffraction and radiation problem of the floating pier under linear monochromatic waves. After the accuracy of the mathematical model was ensured by comparison with other results and convergence analysis, the effects of the amplitudes and lengths of the ripples, the distance between the floating pier and the breakwater, and the number of ripples of the submerged annular rippled breakwater was analyzed. The results showed that the increase in the ripple amplitude and number aggravated the fluctuations of the wave excitation forces and the hydrodynamic coefficients of the floating pier as the wavenumber and ripple length varied. The wave excitation force and hydrodynamic coefficient of the floating pier changed periodically with the increase in the distance between the breakwater and the floating pier. This period was only related to the wavenumber, which was slightly larger than half the wavelength. The valley value and the corresponding position of the valley that appeared with this periodic change were affected by the ripple amplitude and length of the submerged annular rippled breakwater.