TABLE OF CONTENTS We are now at the point at which we can set up and solve the equations of motion for a floating body under the influence of small-amplitude waves in an inviscid fluid. However, the results will turn out to be quite unsatisfactory for one mode of motion in particular: rolling. The reason for this is that viscous effects contribute significantly to roll damping. Neglecting these effects will result in predictions which are considerably higher than measured values, particularly near resonance.
The viscous contribution is significant in the case of roll damping simply because the wavemaking contribution is so small for slender (ship-like) bodies. Forced rolling motion generally does not produce much of a disturbance to the fluid; in fact for a semicircular cylinder rolling about its axis, no waves are radiated and so the wavemaking damping is zero. However, we know that some effort is required to produce the motion; the resistance comes from frictional drag on the hull surface. In addition, if the hull has sharp corners (llke a rectangular barge) there will be additional damping due to flow separation and eddy formation. Also, appendages contribute significantly to roll damping, particularly at speed. Thus in order to make reasonable predictions of rolling motion, we need to be able to account for these effects.
Unfortunately, the theoretical prediction of viscous roll damping is beyond the current state-of-the-art for ship-like bodies. The available tools of computational fluid dynamics (CFD) are being applied to the problem, but results...
