Water wave radiation by a heaving submerged horizontal disk very near the free surface

The radiation of water waves by heaving horizontal disk at a shallow submergence depth is considered. The problem is formulated as a Fredholm integral equation. The resonant frequencies originating from the shallow submergence are examined and their locations are computed by a modified Newton’s method. The hydrodynamic coefficients in a neighborhood of a resonance pole are found to be represented by circles in the complex plane. An asymptotic approximation is obtained for small values of the submergence depth. The relationship between the small-submergence first order problem and the dock problem is explored and found to be clearly represented by the added mass and damping coefficients.