Wave Force Predictions from Nonlinear Random Sea Simulations

ABSTRACT A nonlinear interaction matrix is introduced which may be used with a fast Fourier transform algorithm to simulate by digital computer nonlinear random seas correct to second order in an ocean of finite depth. The second order corrections to the linear first order wave spectrum are-computed and may be added to the linear spectral components in the frequency domain. The time sequence of the random nonlinear waves is efficiently obtained by an inversion of the fast Fourier transformalgorithm from frequency to time. This nonlinear random sea time sequence may then be filtered by the linear digital filter method modified by a vertical coordinate stretching function in order to compute the kinematic fields required in the Morison equation to predict horizontal pressure force on a vertical piling. Pressure force spectra and normalized cumulative probability distributions are computed from the pressure force realizations which were computed by filtering simulated nonlinear random sea realizations. The simulated results are compared with the measured pressure force spectra and normalized cumulative probability distributions recorded by Wave Force Project II at the 55.3 ft. dynamometer elevation of an instrumented drilling platform during Hurricane Carla in the Gulf of Mexico. INTRODUCTION As the design of offshore permanent pile supported structures moves beyond the four hundred foot bottom contour into regions of greater depth and as the mathematical models which describe the compliant nature of the pile-soil interaction become more sophisticated, the requirement to perform dynamic analyses of these structures becomes more critical. Foster [1], Edge and Meyer [2], Borgman [3], Malhotra and Penzien [4, 5], Nath and Harleman [6], Plate and Nath [7], Selna and Cho [8], Mansour and Millman [9], Berge and Penzien [10], Muga and Wilson [11], interazios, have presented models for the dynamic response of permanent pilesupported structures to random forces. Therandom forces used in these studies were either the superposition of linear Fourier components with random phase angles which were uniformly distributed between (-?,?) or a strictly periodic Stokian wave of finite amplitude. The purpose of this study is to provide a nonlinear random time sequence realization of a surface gravity wave spectrum in an ocean of finite depth and to utilize this realization as a forcing function to a digital linear filter to obtain the kinematic fields required to predict pressure forces. The emphasis will be on the simulation of a random time sequence vice the determination of the invariant statistics of random realizations. PROBLEM FORMULATION Hasselmann [12] and Tick [13] (cf. Kinsman [14] have given solutions to the boundary value problem for random surface gravity waves correct to second order in water of finite depth. These solutions assume that the spectral representation of the velocity potential and the instantaneous free surface elevation may be perturbed according to the following perturbation expansions.