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Time-domain second-order wave interactions with floating offshore structures Ng, Joseph Y.


Over the past decade, numerical modelling of nonlinear wave-structure interaction problems has been an important topic of ocean engineering research, with practical applications relating to load and response predictions for large floating structures subjected to steep waves. With the increasing need to incorporate more accurate analyses of wave effects into existing offshore design procedures, the emphasis of recent hydrodynamic research has been on the development of numerical solutions to a wide variety of nonlinear wave-structure interaction problems. In particular, the present theoretical work considers the second-order wave radiation and combined diffraction-radiation problems in both two and three dimensions for the case of large floating offshore structures of arbitrary shape. The mathematical formulation of the corresponding initial-boundary value problem can be derived on the basis of potential flow theory. A recent time-domain approach is extended to simulate second-order hydrodynamic effects involving large floating structures which cannot be obtained by the conventional linear hydrodynamic theory. The method involves the application of Taylor series expansions and the use of Stokes perturbation procedure to establish the corresponding first- and second-order boundary value problems with respect to a time-independent fluid domain. A time-stepping scheme together with a suitable iterative procedure are used to solve the coupled fluid-structure governing equations, and an integral equation method based on Green's theorem is used to obtain the wave field at each time step. In relation to conventional nonlinear methods, the present method provides a relatively algebraically straightforward and computationally effective numerical algorithm for treating the second-order free surface flow problems. The method is used to study the second-order wave radiation problem in two and three dimensions, in which surface-piercing structures of arbitrary shape undergo forced sinusoidal motions in otherwise still water. The method is illustrated by numerical results obtained from two semi-submerged circular and rectangular cylinder sections and a truncated surface-piercing circular cylinder. The second-order oscillatory force component due to second-order wave potential, for both the two-dimensional vertical plane case and the general three-dimensional case, contributes significantly in the evaluation of the total hydrodynamic forces. Although the second-order problems have been studied quite extensively in the context of wave diffraction and radiation separately, results for the nonlinear diffraction-radiation problem are rather scarce. This combined problem involves the equations of motion of the structure as well as nonlinear interactions between the incident, diffracted and radiated wave components. The present method is subsequently extended to simulate second-order wave interactions with large floating structures in two and three dimensions, and is illustrated by applying respectively to the cases of a semi-submerged circular cylinder and of a floating truncated circular cylinder. Numerical computations presented relate to the transient motion of a freely-floating cylinder with a specified initial vertical displacement, and the diffraction-radiation of Stokes second-order waves by a moored floating cylinder. In general, numerical results indicate significant second-order hydrodynamic effects in the forces and motions of large floating structures subjected to regular waves, as well as in the corresponding free surface profiles and wave amplitudes.

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