Second-Order Directional Seas and Associated Wave Forces

Most methods for wave force computation incorporate either the nonlinearities of the ocean surface for a single fundamental component or the random and/or directional characteristics using superposition of linear wave components. One exception is the intuitive "hybrid" method, which combines elements of linear and nonlinear waves. This paper describes and applies a method correct to the second order in wave height for calculating waves and wave forces caused by a directional wave spectrum on an offshore structure.Starting with a prescribed linear spectrum of directional waves, a set of random phases is generated and the second-order spectrum computed with phases defined by all contributing pairs of first-order components. Thus, with one realization of the spectrum complete up to the second order, the wave profile and water particle kinematics can be profile and water particle kinematics can be simulated in the time domain. The wave forces also are computed in the time domain, taking full account of their nonlinear and directional properties. The resulting wave forces at any level vary in direction and magnitude. The total wave forces summed over all piling of a structure are less than those for a unidirectional train of waves with the same one-dimensional spectrum.Several examples are presented to illustrate reductions in maximum wave forces caused by the directional distribution of waves. We found that for a single piling the maximum force decreases by a factor ranging from 1.0 to 0.61 as the directional spread increases from unidirectional to uniformity over a half plane. For a four-pile group on a square array of 300-ft (91.4-m) spacing, the corresponding decrease in the factor is 1.0 to 0.51 for a Bretschneider spectrum with a peak period of approximately 12 seconds. The results of this complete model are compared with the more intuitive and approximate hybrid method and are found to agree quite well. Force spectra are presented and discussed for the inline and transverse directions. Introduction The nonlinearity, randomness, and directionality of a real sea preclude a simple but realistic determination of wave loading on a single- or multiple-pile group. Presently, there are two essentially different but complementary methods for computing wave loadings. One method represents nonlinearities of a single wave composed of a characteristic fundamental period and its higher harmonics. A number period and its higher harmonics. A number of such theories have been-developed. Dalrymple extended the stream function approach of Dean, to waves on a shear current. Some of these theories adequately account for the nonlinearities; however, they avoid the random and directional characteristics of the sea surface. The second method uses the principle of linear superposition of an infinite principle of linear superposition of an infinite number of waves with given frequencies, amplitudes, and directions of propagation but independent phases; the total energy is distributed over a phases; the total energy is distributed over a continuum of frequencies and directions. In this manner, a three-dimensional Gaussian sea can be represented fully. However, ignoring the nonlinearities makes the random Gaussian model unrealistic - especially for large waves. SPEJ P. 129