Hasselmann's kinetic equation for wind waves

Summary

Hasselmann's kinetic equation describes how the spectrum of ocean waves changes in time through weak nonlinear interactions among quartets of waves. Klaus Hasselmann derived it in 1962 from the equations of surface gravity waves, under the assumption that the phases of the waves are random. It has the form of a Boltzmann equation in which waves play the role of particles and resonant four-wave interactions play the role of collisions. Together with terms for wind input and wave breaking, it is the core of modern wave forecasting models such as WAM.