Low-Frequency Phenomena Associated With Vessels Moored at Sea
Authors: Pinkster J.A. 
Published: December 2007

Abstract
The influence of the low-frequency-wave-drifting force on the motions of moored vessels and the loads in the mooring system is demonstrated from results of model tests in irregular waves. The origin of the wave drifting force is discussed and methods for calculating the mean drifting force are reviewed. To facilitate calculation of the low-frequency-wave drifting force on an object in irregular waves, an existing method using the mean drifting force in regular waves is generalized. The results of calculations using the method introduced in this paper are compared with previously published test results. Finally, some remarks are added concerning effects that have not been accounted for in existing calculation methods.

Introduction
A vessel moored at sea in stationary conditions with regard to waves, wind, and current is subjected to forces that tend to shift it from the desired position. For a given vessel and position in the position. For a given vessel and position in the horizontal plane, the motions depend on both the mooring system and the external forces acting on the vessel. In steady conditions, the forces caused by a constant wind and current are constant quantities for a given heading angle of the vessel. The forces caused by a stationary irregular sea are of an irregular nature and may be split into two parts: first-order oscillatory forces with wave 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 linear motions of surge, sway, and heave and the three angular motions of 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 linear oscillatory motions is in the order of the height of the waves.The second-order wave forces, perhaps better known as the wave drifting forces, have been shown to be proportional to the square of the wave height. These forces, though small in magnitude, are the cause of the low-frequency, large-amplitude, horizontal motions sometimes observed in large vessels moored in irregular waves. Tests run in irregular waves in wave tanks of the Netherlands Ship Model Basin revealed a number of properties and effects of the low-frequency-wave properties and effects of the low-frequency-wave drifting force that are discussed here using the results of two test programs.The first of these programs concerns tests run with the model of a 125,000-cu m LNG carrier moored in head seas with an ideal linear mooring system. The second program deals with a 300,000-DWT VLCC moored with a realistic nonlinear bow hawser to a single-buoy mooring in waves, wind, and current coming from different directions.The results of the tests with the LNG carrier are shown in Figs. 1 through 3, while the results of the tests with the 300,000-DWT VLCC are shown in Fig. 4. All results are given in full-scale values. Fig. 1 shows the wave trace and the surge motion of the LNG carrier to a base of time.
SPEJ
P. 487