Added Mass and Damping of Rectangular Bodies Close to the Free Surface

A submerged two-dimensional rectangle in calm water with infinite depth is studied. The rectangle is oscillating in a heave motion. Negative added mass and sharp peaks in the damping and added-mass coefficients have been found when the submergence is small and the width of the shallow region on top of the rectangle is large. Resonant standing waves will occur in this area. A linear theory is developed to provide a relatively simple explanation of the occurrence of negative added mass for submerged bodies. The vertical hydrodynamic force is associated only with the flow in the shallow region, and the resulting pressure which acts on the top face of the rectangle. The results from this theory are compared with numerical results from the Frank method. The importance of the interaction effect between the top and the bottom of the body, which is neglected in the present theory, is discussed.