Analytical solution of oblique wave interacting with a periodic array of specific caissons connected with partially immersed thin walls (comb-type)

Abstract

This paper presents a three-dimensional (3D) analytical solution for oblique wave interaction with a periodic array of specific caissons connected with partially immersed thin walls (comb-type caisson). A periodic boundary condition of the velocity potential along the longitudinal direction of the breakwaters is adopted in the analytical solution. The unknown coefficients of series solutions of velocity potentials are determined using the matched eigenfunction expansion method. Formulae for hydrodynamic quantities, including reflection and transmission coefficients, wave forces and free surface elevations, are presented. The convergence of the analytical solution is examined. The present analytical solution in special cases agree well with previous results. Effects of wave parameters and structural geometry parameters on the hydrodynamic quantities of the comb-type caisson breakwater are investigated. The variations of the hydrodynamic quantities versus the main influencing factors (namely, relative wave chamber width, side plate location, immersed depth of side plate, length of side plate, incident wave angle and wave number) are presented. The abrupt changes of the hydrodynamic quantities caused by interactions among multiple reflected and transmitted waves are clarified. The present 3D analytical solution can be employed to determine the optimal configuration of comb-type caisson breakwaters in preliminary design due to its high computing efficiency.