A discrete correction scheme for envelope approach of wave group statistics

The existence of empty envelope excursions (EEE) brings error to the envelope approach of wave group statistics, which identifies wave group by envelope upcrossing of a critical level. A group number correction scheme is suggested in this paper to exclude EEE from wave group statistics. To this end, the Ditlevson and Lindgren [J. Sound Vib. 122 (1988) 571] theory about the fraction of empty excursion envelopes (FEEE) is examined to see if it fits for ocean waves. The sea waves are simulated with Monte Carlo method and with P-M and JONSWAP spectrums. The values of FEEE of the simulated waves are investigated and compared with the theory of Ditlevson and Lindgren. The comparison shows that, at the second-order approximation, theoretical predictions of FEEE are close to those derived from simulations. This approximate analytical expression of FEEE is then employed to form a group number correction scheme. Comparisons between numerical and theoretical results of wave group properties show that this correction scheme is quite effective.