Moored floating structures for drilling, production-storage-offloading or other purposes are being installed in ever increasing water depths and in areas where the environmental conditions are also more severe. Such structures, moored permanently in high seas, have to survive safely the most severe weather conditions. Therefore of importance to understand the mechanisms which govern the motions and the mooring forces of these facilities.

In deep water the mooring systems inevitably have soft elasticity characteristics. With the increase in the elasticity of the mooring, the low frequency horizontal motions induced by low frequency second order wave drift forces also become larger. The low frequency resonant motion components completely dominate the horizontal motions and, consequently, also the mooring forces. In order to predict the amplitudes of the low frequency resonant motions the magnitude of the second order wave drift forces and the values of the low frequency hydrodynamic damping must be known.

The low frequency hydrodynamic potential damping due to the radiated waves is negligibly small. In general the low frequency damping is determined by viscous effects and a damping caused by the presence of waves. The last mentioned damping is called the wave damping. Dependent on the wave spectra the wave damping can significantly dominate the viscous damping contributions.

In this paper results are given of a study of the origin of the wave damping. For this purpose the second order wave drift forces acting on the moored vessel in head waves have been expanded to the low frequency surge displacement and surge velocity. The wave damping can be defined by taking into account the dependence on velocity of the second order wave drift forces. To verify the results, model experiments were carried out in which the velocity dependent second order wave drift forces were determined.


Floating structures mooored at sea are subjected to forces that tend to shift them from their desired position. For a given vessel the motions depend both on the mooring system and on the external forces acting on the vessel. The forces on the vessel caused by an irregular sea are of an irregular nature and may be split into two parts:

  • first order oscillatory forces with wave frequency and,

  • second order slowly varying forces with frequencies much lower than the wave frequency.

The first order oscillatory wave forces on a vessel cause the well-known ship motions, with frequencies equal to the frequencies present in the spectrum of the irregular waves.

The second order wave forces, also known as the wave drift forces, have been shown to be proportional to the square of the wave height, while the frequencies correspond to the frequencies present in the spectrum of the wave groups in the irregular waves, [1].

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