Overview

Wind-generated waves on the open ocean surface are usually too complex to be described by one regular slowly varying wavetrain, and require more elaborate spectral representations to acount for sea states with a broad band of wavelengths and directions. For infinitesimal waves, there are spectral theories to describe the random sea surface based on linear superposition of many simple wavetrains. The amplitude-spectrum (which contains the amplitudes and phases), or sometimes only the energy spectrum, can be used to convey the information about the complicated geometry and kinematics of the ocean surface. Statistical stationarity is often assumed. A detailed description of such classical treatments can be found in Ochi (1998).

The evolution of gravity-wave spectra is, however, a very dynamical process governed in general by three physical processes: (a) energy input by the wind, (b) energy transfer between the different spectral modes due to nonlinear interaction, and (c) energy dissipation by wave breaking and/or complex interactions with the seabed. Wind input and dissipation are pronounced in windy conditions and in shallow water, whereas nonlinear interaction is always present even outside the storm area and in deep water. Since the early 1960's much fundamental progress has been made on the nonlinear processes in ocean waves, pioneered in particular by Owen M. Phillips, Klaus Hasselmann, and Vladimir E. Zakharov. In recent years the so-called weak-turbulence theory initiated by Zakharov has made a strong impact on the advances of ocean-wave physics. This chapter is intended as an introduction to the weak-turbulence theory with...