On the Joint Probability of Wave-Heights and Periods in Intermediate and Shallow Waters

Abstract

In the present paper, a package model is derived, based on a joint probability density function and on a Boussinesq-class numerical wave model. The key task was to produce joint probability density estimates of wave-height and wave period in intermediate and shallow waters given the respective information offshore. This is of paramount importance in the context of design of resilient coastal structures. The approach followed includes an extension of given joint probability density estimate images in deep waters and their decomposition into a manageable data of time series of free surface elevation. These data serve as input to a recently developed wave propagation model of the Boussinesq-class, able to cover the whole range from deep to shallow waters and give the corresponding surface elevation there. The time history of the latter is finally recomposed to produce the associated probability density estimates at any desired point of the nearshore. Additional information concerning the directional energy spreading in shallow waters is obtained. The package model was verified with experimental results proving its validity and ability to produce satisfying results. Finally, characteristic representations of joint probability densities between wave-height and wave period are given, for typical sea bottom slopes and wave incidence.