On the Low-Frequency Surge Motions of Vessels Moored in High Seas
Authors: Wichers J.E.W. 
Published: October 2008

ABSTRACT
Moored floating structures for drilling, production and/or storage purposes are being installed in ever increasing water depths and in areas where the environmental conditions are also more severe. As a result of the increased water depth, the elasticity of the mooring system increases.
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. These low-frequency motion components completely dominate the horizontal motions and as a consequence also the mooring, forces. Therefore it is necessary to investigate the low-frequency motions for those situations where greater water depths and more extreme sea conditions occur.
In this paper, results are given of an investigation into the low-frequency surge motions of a large storage tanker moored in a linear system in deep water subject to high head seas. Results of model tests are compared with results of computations. For the computations the term "wave damping" has been introduced. It will be shown that the wave damping significantly influences the low-frequency surge motions. A good agreement between the measured and computed low-frequency surge motions has been found.

INTRODUCTION
Floating structures moored 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, better known as the wave drift 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 of vessels moored at sea.
An example of the Be low-frequency, large-amplitude surge motions in irregular head seas, as measured on a model of a 200,000 DWT VLCC moored in an ideal mooring system, is shown in Figure 1. The results are given as full scale values. The stiffness of this ideal linear mooring system approximately corresponds to the stiffness of single anchor leg moorings usually applied in deep water. The head waves shown in the recording of Figure 1 corresponds to high seas. From Figure 1 it can be seen that the high-frequency surge motions are negligible' small, which means that the surge motions are dominated by the low frequency surge motions.
For this paper computations and model tests were carried out for a series of wave spectra to study the low-frequency motions of a fully loaded 200,000 DWT storage tanker in head seas and for two linear mooring systems.
The series of wave spectra had the following Characteristics: (MATEMATICAL EQUATION AVAILABLE IN FULL PAPER)