# Analytic theory of a wind-driven sea

### Analytic theory of a wind-driven sea

Series: Program in Applied Mathematics Colloquium
Location: Math 501
Presenter: Vladimir Zakharov, Department of Mathematics, University of Arizona

A self-sustained analytic theory of a wind-driven sea is presented. It is shown that the wave field can be separated into two ensembles: the Hasselmann sea that consists of long waves with frequency $\omega<\omega_H$, $\omega_H \sim 4-5 \omega_p$ ($\omega_p$ is the frequency of the spectral peak), and the Phillips sea with shorter waves. In the Hasselmann sea, which contains up to 95 \% of wave energy, a resonant nonlinear interaction dominates over generation of wave energy by wind. White-cap dissipation in the Hasselmann sea in negligibly small. The resonant interaction forms a flux of energy into the Phillips sea, which plays a role of a universal sink of energy. This theory is supported by massive numerical experiments and explains the majority of pertinent experimental facts accumulated in physical oceanography.