Understanding of weak turbulence of capillary waves ���

A description of the wind-generated waves on the ocean surface is of vital importance for both engineering and oceanographic purposes. The wavelength of waves in a typical wind sea ranges from 1mm to 100m and rich mechanisms are involved including energy input from wind gravity/capillary wave-wave interactions wave-current-bathymetry interactions and energy dissipation by viscosity and wave breaking. While a complete and accurate modelling of all these multi-scale mechanisms are beyond the physical understanding and computational capability of today the interest of this research is focused on the capillary wave regime which is the dominant part of ocean surface with wavelength less than 17mm. We consider the statistical property in the inertial range of a capillary wavefield under weakly nonlinear interactions. This problem can be generalized to nonlinear dispersive waves in different physical contexts and bears fundamental interests to physicists.