On the wave field due to a moving body performing oscillations in the vicinity of the critical frequency

A two-dimensional submerged body translating under a free surface with stea dy velocity U while performing small oscillations with frequency omega is c onsidered. It has been known for a long time that for a single source the s olution becomes unbounded at the critical frequency, which is given by tau = U omega/g = 1/4 where g is the acceleration of gravity. It was therefore believed that also the motion due to an oscillating body was unbounded at t his frequency. It has, however, in the last few years been shown that this motion is bounded for tau = 1/4. In this paper previous results are discuss ed, and the strong variation of the forces with respect to omega close to t au = 1/4 is examined. Recently a mathematical argument was given that the m otion at the critical frequency is bounded for bodies with nonzero cross-se ction area. It is proved that also the motion generated by a thin foil with zero cross-section area. is bounded at tau = 1/4.