Theoretical study of drift of small rigid floating objects in wave fields

Small floating objects do not alter the ocean wave characteristics. They are passively driven by waves. This is a theoretical study of the drift pattern of a small floating object in a monochromatic wave field. Small amplitude and deepwater conditions are assumed. Extension to intermediate water depth is straightforward, The effect of added mass and drag coefficients of the object, as well as the presence of wave reflection, is investigated. It is found that approximate analytic solutions exist for the two special cases where either the added mass coefficient or the drag coefficient vanishes. In general, the long-term motion of the floating object is oscillatory with the wave frequency but superimposed with a net drift. For the case when the drag coefficient vanishes, the net drift depends on the initial condition. Both forward and backward drifts are possible. For realistic added mass and drag coefficients, the motion is retarded. Sensitive dependence on the initial condition is still present. If a reflective wave is present, the motion of the object can be arrested. The higher the reflection, the more likely it is to trap the floating object. The critical reflection coefficient to trap the object is dependent on the added mass and the drag coefficient of the object.