Numerical simulation of a random sea: a common error and its effect upon wave group statistics

Abstract

A commonly used method of simulating ocean waves from a specified frequency spectrum is shown to be incorrect. The method consists of adding numerous sine curves with random phases; and the error arises from assuming that the amplitudes of these component sine waves are deterministic, when they are in fact random variables. Methods of using random amplitudes are described and only one is found to be satisfactory. In this method the number of random values simulated — and then transformed with an inverse FFT — equals the required number of simulated data points. So simulation in the frequency domain can only give relatively short runs; it is necessary to work in the time domain if arbitrarily long runs are required. Errors in wave group statistics derived from the incorrect simulation method are discussed and related to discrepancies reported between groupiness in simulated data and ocean measurements.