The simulation of slow-drift motions of offshore structures

Abstract

The large amplitude surge-sway-yaw ‘slow-drift’ motions of a floating body constrained by weak restoring forces in random waves are considered. A multiple time scales approximation is employed to separate the fast time scale associated with the linear motions from the slowly varying motions. The ideal fluid free surface flow is approximated by a perturbation series expansion for small slow-drift velocities and wave-steepness, and is solved around the instantaneous position of the body. The linear zero-speed and forward-speed velocity potentials are solved for arrays of vertical cylinders, using exact interaction theory. The horizontal mean drift forces and the wave-drift damping are obtained, and results for realistic configurations are compared with well-established methods. The surge-sway-yaw equations of the slow-drift motions are solved numerically in the time domain under the influence of short-crested, random waves, including viscous forces. The random wave-signal is generated by the filtering of white Gaussian noise. The slowly-varying forces are obtained using the Newman approximation and efficient summations of time series. The results are compared with full QTF-matrix (Quadratic Transfer Function-matrix) computations of the exciting force. The use of a robust random number generator and the Fast Fourier Transform allows for efficient simulations of long records of the slow-drift motions, and the study of its statistical parameters. The sensitivity upon the simulation length, transients, drag-coefficient and directional spreading are demonstrated.