Abstract
A method using group-induced second-order long waves(GSLW) to represent statistical properties of wave groups with double-peaked spectra is put forward in this paper on the basis of the GSLW theory. the GSLW is regarded as a weighted linear superimposition of the second-order long wave induced by the low peak frequency section and that induced by the high peak frequency section. There is a parabolic relationship between the GSLW and the wave envelope. Then the probability density function and the distribution function of the GSLW amplitude are derived. Thus the formulas for the average time duration and the mean length of runs can be derived. Good agreement between theoretical results and measured values was achieved, as verified with the measured double-peaked spectra in different regions.
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