Estimation of mean spectral directions in random seas

A method for obtaining the directional spectrum, on assuming that the frequencies of the elementary waves are all different from one another, is reproposed in a form suitable for applications to sea states near a coast. The method is applied to an interval of 10 h during which the sea state remained basically steady state off the beach at Reggio Calabria (East coast of the Straits of Messina). It is shown that the directional spectrum converges as the length of the time series data grows. A numerical simulation of a 10 h sea state confirms that the directional spectrum converges as the length of the time series grows, and the convergence is on to the known directional spectrum used to make the numerical simulation. Through the numerical simulation, it is proved that the method, generally, is suitable for applications even with short time series of wind waves (duration of about 100 Tp). Finally, it is shown that the method is not necessarily inadequate even with short records of multimodal sea states with different modal directions, modal amplitude ratios and intermodal distances.