Water wave radiation by a submerged rough disc

Abstract A thin circular body is submerged below the free surface of deep water. The problem is reduced to a hypersingular integral equation over the boundary of the body. Using a perturbation method, the problem is then reformulated by a sequence of simpler hypersingular equations over a flat disc making it well suited for an efficient previously used solution method. The first order approximation is computed and the hydrodynamic force due to heaving radiation motion are presented in terms of the added mass and damping coefficients for a polynomial cap and for a rough disc, modelled by a superposition of sinusoidal surfaces defined by randomly generated parameters. The solution exhibits larger maxima associated with smaller volume of submergence of the body. A slight shift of the damping coefficient maxima to lower frequencies is noticed for the caps. Rough discs with similar statistical properties exhibit different behaviours. Thus, it is the exact specific form of the rough disc that dictates the hydrodynamic force.