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This work is based on the application of free surface displacement and
fluctuating wave pressure in an undisturbed water surface. It is shown that the
probability of exceeding wave crest is higher than that of the trough. Using the parameters 1 a and 2 a , it is shown that for a fixed kd the effects of non-linearity decrease on approaching the bottom (sea floor) for which 1
a decreases as ky decreases and 2 a increases as ky decreases. These will be valid for most of the second-order processes in the mechanics of the sea waves.
Keywords: Freed surface displacement, fluctuating wave, undisturbed field, narrow spectrum, wave crest, wave trough.