On alpha stable distribution of wind driven water surface wave slope

TL;DR

This paper introduces an alpha-stable distribution model for wind-driven water surface slopes, providing a new probabilistic framework that better captures the non-Gaussian behavior observed in experimental data.

Contribution

It presents a novel alpha-stable distribution formulation for water surface slopes and compares its effectiveness with existing models using laboratory data.

Findings

Alpha-stable model fits experimental slope data well.

Compared models show the alpha-stable distribution captures non-Gaussian features.

The approach offers a new probabilistic tool for surface wave analysis.

Abstract

We propose a new formulation of the probability distribution function of wind driven water surface slope with an $\alpha$-stable distribution probability. The mathematical formulation of the probability distribution function is given under an integral formulation. Application to represent the probability of time slope data from laboratory experiments is carried out with satisfactory results. We compare also the $\alpha$-stable model of the water surface slopes with the Gram-Charlier development and the non-Gaussian model of Liu et al\cite{Liu}. Discussions and conclusions are conducted on the basis of the data fit results and the model analysis comparison.