Vessels moored at sea will undergo low-frequency motions due to wind, current and waves. Computer programs are being developed to predict theoretically the motions of such vessels, particularly the motions in the horizontal plane, which consist of a high-frequency part (oscillations with periods corresponding to those of waves) and a low-frequency part. In these theoretical approaches only potential damping is taken into account; viscous damping, which substantially influences the low-frequency phenomena, is not included. Moreover, the damping of moored structures in resonance conditions seems to be influenced by additional damping caused by the waves. Both viscous and wave damping have to be determine experimentally. At the Netherlands Ship Model Basin model tests have been carried out to determine the low-frequency hydrodynamic coefficients of a VLCC and a LNG carrier in surge direction in calm water and in regular waves. The measured data are compared with theoretical results obtained-using a computer program based on three-dimensional linear potential theory.


A vessel moored at sea is subjected to forces that tend to shift it from the desired position. For a given vessel and position in the horizontal plane, 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, whose frequencies equal the frequencies present in the spectrum of the irregular waves. These are the translatory motions surge, sway and heave and the angular motions roll; pitch and yaw. In general, the first-order wave forces are proportional to the wave height, as are the ensuing motions. The magnitude of the translatory motions is in the order of the height of the waves.

The second-order wave forces, better known as the wave drifting forces, have been shown to be proportional to the square of the wave height (ref.[1], [2] and [3]). These forces, though small in magnitude, are the cause of the low-frequency, large-amplitude, horizontal motions sometimes observed during model tests and on prototype vessels moored at sea. An example of these low-frequency, large-amplitude surge motions, in irregular head seas as measured on a model of a 125,000 cu m LNG carrier moored with an ideal linear mooring system, is shown in Fig. 1. The results are given as full scale values. This paper concerns only the low-frequency longitudinal surge phenomena in still water and in head waves of a VLCC and a LNG carrier moored in relatively deep water.

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