The statistics of second order wave forces

A starting point in the statistical analysis of the slow drift motions of moored offshore structures is the determination of the statistical distribution of the second order exciting forces. In the past^2,6 an exponential probability density function has been used, this being the limiting case as the incident seastate becomes infinitely narrow banded. In the present note the second order force distribution is found for a general seastate and a significant deviation from an exponential distribution is found for those seastates which are likely to occur in practice. The statistical theory is based on a heuristic approximation to the second order force, which is shown to be consistent with a frequently used frequency domain approximation which has been suggested by Newman.⁸ Although Roberts² has shown that for very lightly damped systems the response statistics are independent of those of the exciting force, the present results may have a significant effect on the response statistics for higher levels of damping.