Effect of Bragg scattering due to bottom undulation on a floating dock

Abstract

A numerical model is developed using the boundary element method to analyze gravity wave transformation by a finite floating dock in the presence of bottom undulation such as trenches, breakwaters and a combination of both in two dimensions. The role of bottom undulation on the sea side of the floating dock has a significant role in wave scattering compared to that of bottom undulation below the dock. The study depicts that Bragg reflection occurs in the case of an array of trenches, breakwaters or a combination of both in the absence of a floating dock. Bragg resonance occurs four times in the case of an array of rectangular breakwaters or a combination of trenches and breakwaters, whilst twice occurs in case of parabolic breakwaters and once occurs in case of triangular breakwaters in water of finite depth. On the other hand, in the case of submerged trenches, Bragg resonance does not occur in deep water. However, in the presence of a floating dock, wave reflection increases in an oscillatory manner with the occurrence of harmonic and sub-harmonic peaks and depressions. Within two consecutive harmonic peaks/depressions, n−1 sub-harmonic peaks/depressions occur in the case of n trenches/breakwaters with floating dock, unlike the occurrence of n−2 sub-harmonic peaks within two consecutive harmonic peaks without the floating dock. Certain changes in phase in the sinusoidal pattern of wave reflection by the floating dock occurs due to the change in the position of the trenches and the breakwaters, whilst the amplitude of wave reflection is independent of the position of the trenches and the breakwaters.