On the joint distribution of wave periods and amplitudes in a random wave field

Abstract A theoretical probability density is derived for the joint distribution of wave periods and amplitudes which has the following properties: (1) the distribution is asymmetric, in accordance with observation; (2) it depends only on three lowest moments m0, m1, m2 of the spectral density function. It is therefore independent of the fourth moment m4, which previously was used to define the spectral width (Cavanié et al. 1976). In the present model the width is defined by the lower-order parameter v = (m0m2/m21 - 1)½. The distribution agrees quite well with wave data taken in the North Atlantic (Chakrabarti & Cooley 1977) and with other data from the Sea of Japan (Goda 1978). Among the features predicted is that the total distri­bution of wave heights is slightly non-Rayleigh, and that the interquartile range of the conditional wave period distribution tends to zero as the wave amplitude diminishes. The analytic expressions are simpler than those derived previously, and may be useful in handling real statistical data.