Theoretical and experimental analysis of tethered buoy instability in gravity waves

The motion of a tethered spherical buoy subjected to incident regular waves was measured in a wave tank. Transverse instability was observed when the period of the wave generated was close to one-half of the natural period of the buoy. The transverse instability confirmed as Mathieu type was predominant at the surface but diminished with increase in the depth of submergence. The stable and unstable zones were determined on the Mathieu's instability diagram. Experimental results were in agreement with the predicted zone of instability for a two degree of freedom oscillation problem of Mathieu type which has a periodically varying spring constant.