Validated theoretical model of wind-wave evolution

The current model temporally and spatially describes the entire wind-wave evolution, from initial ripples to steady state. This model has no adjustable parameters and it was validated against extensive experimental measurements performed in our lab. Two distinct theoretical approaches currently exist: The Miles’ approach that is linear, deterministic and is based on shear-flow instability. The Phillips’ approach which is nonlinear and stochastic, wave excitation is attributed to pressure fluctuations in the airflow. There is no model so far that attempts to describe the entire evolution process. Experiments in our lab on excitation of waves by impulsively applied wind show that the process consists of four distinct stages; the wave field is stochastic with multiple length scales. Our quasi-linear theory is based on the solution of the coupled Orr-Sommerfeld equations; each harmonic grows exponentially. Unlike other studies, we account for co-existence of all unstable harmonics resulting in the expected surface elevation. Breaking imposes limit on the maximum wave steepness; the fetch limits the maximum growth duration.

The multi-stage process of evolution in time and in space of characteristic amplitudes and of dominant frequencies is predicted by the suggested theory.