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According to Philips, in 1985, to obtain the whitecap fraction, one can refer to an average bubble persistence time $\tau_{bub}$ to obtain $W$:  \begin{equation}  W = \int_{0}^{\infty}\tau _{bub}c\Lambda(c)dc,  \end{equation} where $\{tau}_{bub}$ $\tau_{bub}$  is the bubble persistence time, $\Lambda(c)$ is the Philips parameter and $c$ is the forward speed of the beaking wave crest.