Computations of Wave Drift Forces

ABSTRACT This paper presents results from computations of drift forces upon different bodies in regular waves. An original fluid finite-element computer model is used to derive the hydrodynamic characteristics. Three formulations of the second-order steady forces are tested on a sphere, a rectangular box, and a 200 000 dwt tanker. INTRODUCTION With the development of offshore floating systems, wave-drift forces have become a critical factor in the design of positioning and mooring systems, in which they are responsible for the so-called slow-drift oscillations and resulting peak mooring loads. Slow-drift oscillations appear in irregular waves. In regular waves only steady drift forces occur. However slow-drift and steady drift forces are very similar in nature, and the former may be approximated, if the latter are known for a sufficient range of wave period. The first part of this paper shows how the body motion and velocity of the flow may be derived for an arbitrary body in regular waves. Different formulation of the drift forces are introduced. The second part shows numerical results obtained for various bodies. These results are discussed. A description of IFP's radiation-diffraction model TRITON is given in the Appendix. THEORETICAL FORMULATION (Available in full paper) RESULTS OF NUMERICAL TESTS Floating sphere Kudou considered the case of a half-immersed sphere floating in water of infinite depth, and was able to derive the drift force analytically. He also presented results from model tests. Since TRITON allows no infinite depth, a fictitious bottom was taken at one wave-length underneath the sphere bottom. In this case both Fl and F2 were computed. It can be seen that Fl and F2 agree well, both together, and with Kudou's analytical derivations. However convergence of F2 appears to be much slower than F1's at kR=1, which corresponds to the heave natural period (Fig. 4). The peak in the drift force is slightly shifted toward the higher frequencies (kR=1.2), showing that both diffraction and radiation intervene in this peak value. Note that it is higher (Cd=.85) than the asymptotic value of the drift force as the frequency goes to infinity (Cd=.67). This is a typical three dimensional effect. Floating box Reference is made to the paper presented by Det Norske Veritas, which treats the case of a box (90 m × 90 m × 40 m) floating in water of infinite depth. This case allows comparisons to be made between FI and F3. Good agreement is found between FI and F3 and with DNV's results (Figures 5 and 6). Numerical tests performed on other bodies, especially ships and barges, have shown however, that Fl has slightly better stability than F3 in the vicinity of roll natural periods. This phenomenon is linked to the fact that linearized theory over-estimates the roll motion, taking no account of viscous effects.