Probability function of breaking‐limited surface elevation

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Abstract
The effect of wave breaking on the probability function of surface elevation is examined. The surface elevation limited by wave breaking ζb(t) is first related to the original wave elevation ζ(t) and its second derivative ¨ζ(t). An approximate, second‐order, nonlinear, non‐Gaussian model for ζ(t) of arbitrary but moderate bandwidth is presented, and an expression for the probability density function ƒb( ) of ζb(t) is derived. The results show clearly that the effect of wave breaking on the probability density function of surface elevation is to introduce a secondary hump on the positive side of the probability density function, a phenomenon also observed in wind wave tank experiments.

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