Wind waves, a classical example of non-equilibrium wave spectra

For centuries, scientists and sailors have been vexed by how the wind and the sea conspire to create the waves upon the oceans. The ocean wave spectrum was measured in the sixties by Pierson and Moskowitz, however a theory explaining their observations has been lacking. In the first part of the talk, I will review the theoretical attempts, from Kelvin-Helmholtz instability to wave turbulence, with a particular focus on the Phillips-Miles mechanism. The Phillips-Miles approach involves the solution of the hydrodynamic Rayleigh equation at the critical level, which is the height at which the phase speed of the wave is equal to the wind speed. In the second part of the talk, I will present a simple numerical method to treat this problem. Then, I will describe the first steps of a new theoretical approach to treat the wave spectrum.