Abstract
A new numerical method for calculating the interaction of steep (nonlinear)ocean waves with large coastal or offshore structures of arbitrary shape is described. The evolution of the flow, and in particular the loads on the structure and the runup around it, are obtained by a time-stepping procedure in which the flow at each time step is calculated by an integral equation method based on Green's theorem.
A few comparisons are made with available solutions and results are presented for a typical design wave in shallow water. The method is capable of predicting forces caused by steep waves accurately and without prohibitive computer effort.
Introduction
The prediction of wave forces on large offshore structures on the basis of linear diffraction theory, which is formally valid for small-amplitude sinusoidal waves, is now an established part of offshore design procedure. Reviews of the approaches generally used have been given by Hogben etal.,1 Isaacson,2 and Sarpkaya and Isaacson.3
To account more realistically for the effect of large wave heights, research recently has been directed primarily toward developing a second approximation based on the Stokes expansion procedure. However, such an approach is of practical value only under restricted conditions, as in the case of anundisturbed wave train described by Stokes second-order theory. In particular, nonlinear wave effects are expected to be of greatest importance for steep shallower waves, and these are precisely the conditions in which a Stokes second-order solution becomes invalid.
A numerical solution to the complete boundary value problem without any wave height perturbation procedure is clearly desirable. The approach outlined here is described in detail by Isaacson.4 In this method, the wave diffraction is treated as a transient problem with known initial conditions corresponding to still water in the vicinity of the structure and a prescribed incident wave form approaching the structure. The development of the flow then can be obtained by a time-stepping procedure, in which the velocity potential of the flow at any one instant is obtained by an integral equation method basedon Green's theorem.
Comparison with known diffraction solutions can be made only for relatively restricted situations. A few such comparisons have been carried out and arequite favorable. Results also are presented for a typical design wave in shallow water, and these are found to differ significantly from linear theory predictions.
Second-order Long Period Wave Forces on an Offshore Structure in Shallow Water (1st report)
