SLENDER-BODY APPROXIMATION FOR SLOWLY-VARYING WAVE LOADS IN MULTIDIRECTIONAL WAVES

Second-order slowly-varying wave forces can, in principle, be obtained from the second-order diffraction potential. However, the theory is c omplicated and relevant computation is very costly. Instead, in this p aper, a very simple second-order slender-body approximation is develop ed, which can be used when inertia effects are important and character istic length scale of the structure is small compared to the wave leng th. In the slender-body approximation, the second-order difference-fre quency inertia force is obtained from the complete description of the second-order acceleration field which includes both temporal and conve ctive terms. Additional second-order contributions due to the axial di vergence correction and fluctuation of the free surface are also inclu ded. The resulting explicit force quadratic transfer functions (QTFs) are obtained for both uni- and multi-directional waves. The slender-bo dy analysis is applied to the computation of slowly-varying pitch mome nts on an articulated loading platform (ALP) and the results agree wel l with the second-order diffraction computation. In particular, the ap proximation method is found to be several orders of magnitude faster t han the second-order diffraction computation. From our numerical resul ts, it is seen that slowly-varying-force spectra are in many cases sen sitive to the wave directional spreading, hence wave directionality ne eds to be considered for the reliable or cost-effective design of futu re compliant offshore platforms.