Joint Distribution of Wave Heights and Wavelengths and Distribution of Wave Steepness

A joint probability density is derived for wavelengths and wave heights. It is asymmetric and depends only on the spectral bandwidth edefined by Cartwright and Longuet-Higgins (1956). After that a theoretical probability density for wave steepness is obtained. It tends to Rayleigh distribution as e→ 0. A comparison between theoretical steepness distribution and laboratory experiment result shows good agreement.