On alpha stable distribution of wind driven water surface wave slope.

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. [J. Phys. Oceanogr. 27, 782 (1997)]. Discussions and conclusions are conducted on the basis of the data fit results and the model analysis comparison.