Continuous Digital Simulation of the Second-Order Slowly Varying Wave Drift Force

A discussion is given on practical aspects of digital representation in time of the slowly oscillatory second-order wave drift force from a known force spectrum. The emphasis is placed on the computational efficiency and on the suitability of the simulation to a numerical integration of an equation of motion using a variable integration step size, where the force acts as the excitation of motion. The effect of approximating the original spectrum by a white spectrum is discussed. A sensitivity analysis is made to the range of frequencies of the spectra. The force time record is obtained by first generating at equal time intervals a discrete time series which possesses the desired random characteristics, and then by extending the discrete series into a continuously available digital record using a sin(x)/ x-type interpolation. Various numerical tests are illustrated with plots. Superiority of the fast Fourier transform over the cosine series is demonstrated in terms of the spectral contents preservation.