Motion instabilities in tethered buoy WECs

Theoretical and experimental investigation of yaw
motion instability in a submerged axi-symmetric wave energy
converter is presented. The device is a truncated vertical cylinder
which is taut-moored via three tethers. Assuming linear hydrodynamics,
but retaining non-linear geometry associated with the
tethers, governing equations are derived in 6 degrees of freedom.
Due to the axi-symmetry of the system, there is no hydrodynamic
excitation moment in yaw. However, the yaw governing
equation - correct to second order in buoy motions - reveals
a time-varying restoring moment coefficient. Such systems can
undergo large oscillations given a small initial perturbation,
through the well known Mathieu instability. Targeted regular
wave experiments were used to verify the model predictions on
the onset of yaw motion instability in the first two instability
branches. The yaw motion in a three-tethered system is analogous
to sway motion in a single-tethered device. The yaw instability
and the transverse/sway motion instability both arise due to
coupling with heave. Due to small damping, the instabilities can
be prevalent. The theoretical analysis presented is applicable to
other floating WECs.