This paper is concerned with the development and application of the hydrodynamic theory required to provide theoretical predictions of low frequency damping. This necessitates development of forward speed dependent expressions for the mean second order forces and an improved diffraction potential algorithm. The predictions of the resulting generalized strip theory implementation are compared with published data at intermediate steps of the full calculation and the final low frequency damping predictions compared with the experimental findings of Wichers. Assessment of the applicability of the proposed presented procedure, its generalization and other methods of investigating the low frequency phenomenon are discussed.


The oil industry has been applying large safety factors in the designing of mooring lines. This factor coupled with the need to go into ever increasing water depths means the costs of providing moorings increases significantly. Overpredication of horizontal excursions of a moored structure may also exclude some of-the mooring options available to the designer. Therefore, the need exists for improved mooring design related analyses.

Mooring system forces are induced by the high (wave) frequency first order motions and the large amplitude (zeroth order) slowly varying low frequency mot ions. Although the low second order frequency forces are small, they are sufficient to excite the complaint mooring system's low frequency resonance. Hence dynamic magnification may produce very large forces in the mooring system.

The second order forces are proportional to the wave amplitude squared and theoretical calculation of both the mean and slowly varying drift force components is possible. For large displacement structures 3D diffraction theory is generally used1,2,3,4* although exact evaluation of the slowly varying drift force requires determination of the second order velocity potential. So far no complete solution to the 3D second order velocity potential has been achieved because of the requirement to satisfy inhomogeneous free surface boundary conditions. Hence different approximations have been adopted1, 2, 5 although Sun and Gu6 claimed solution of the slowly varying second order potential by singularity distribution. However, the singularity used is the same as the first order solution, which obviously does not satisfy the second order free surface and bottom conditions simultaneously. Moreover the radiation condition assumed to open to debate.

In addition to predicting the low frequency wave excitation force, values of the motion dependent damping and added mass coefficients are required to estimate the amplitude of the low frequency motion correctly. The low frequency added mass coefficient can be evaluated by three or two dimensional source distribution techniques. However the low frequency radiation damping predicted by linear potential theory is vanishingly small. Damping due to viscous or higher order effects must be included to improve the modeling although the ITTC Ocean Engineering Committee agreed that low frequency damping is a poorly understood phenomenon. In this paper a theoretical treatise of low frequency damping, inspired by Wicher's studies, is considered.

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