Freak waves caused by reflection

Abstract

We study the temporal distribution of wave energy in a wave field that is generated by the reflection of a wave spectrum from a vertical wall. Weakly nonlinear wave fields over finite, constant depth are considered, and the reflection induces large correlations between different wave components of the wave field. The nonlinear time evolution of such an inhomogeneous random wave field is studied by means of an equation developed by Crawford, Saffman and Yuen in 1980. We show that, depending on the spectrum and the water depth, there is a significant increase in the probability of freak waves, whose height is more than twice the significant wave height, created by the reflection off the wall.