Slow drift motions of a floating body in narrow-banded seas.

In an irregular sea, waves of different wave numbers interact non-linearly and give rise to second order forces at the sum and difference frequencies. A moored or dynamically positioned vessel (ship or platform) can be induced to perform slow drift oscillations at the difference frequencies. To study the slow motion in a narrow banded sea, the methods of multiple scales and matched asymptotics were combined. It is first shown in general terms that slow drift motion is accompanied by long waves. The range of applicability of a formula for the wave force by Newman is discussed. An exception to the formula is a long body in beam seas with a small clearance under its keel. Some recent results for this case are presented, exhibiting resonant motion. (A)