ON THE MOTION OF A SMALL TWO-DIMENSIONAL BODY SUBMERGED BENEATH SURFACE WAVES.

The classical hydrodynamical problem of a body submerged beneath a free surface is considered. The flow is two-dimensional and the cross-section of the body and its motion are arbitrary. In the limit as a typical body dimension becomes small compared with its depth the method of matched asymptotic expansions becomes applicable and expressions for the forces and moment experienced by the body can be found. Several cases are considered in detail where the body is permitted to move in response to the forces and moment. We also find the additional forces, due to the free surface, experienced by a lifting body - a body about which there is a circulation.