The stochastic parametric mechanism for generation of surface water waves by wind

Theoretical understanding of the generation and growth of wind driven surface water waves has been based on two distinct mechanisms; the first being excitation by wave incoherent random atmospheric pressure fluctuations and the second shear instability arising from wave coherent atmospheric pressure fluctuations. Incoherent forcing produces growth rates linear in time while coherent forcing produces growth rates exponential in time. While observed wave developments can be fit using a sum of a linear and an exponential growth rate, and despite agreement on the underlying physical process of momentum transfer from the atmospheric boundary layer shear flow to the water waves by atmospheric pressure fluctuations, quantitative agreement between theoretical predictions and field observations of wave growth has proven elusive. Accepting that the largest contribution to wave growth proceeds from an at least statistically coherent phase lag between atmospheric pressure fluctuations and surface elevation, at issue is how this favorable mean phase relationship is produced and maintained. In this work an alternative mechanism is proposed that unites the wave incoherent atmospheric forcing process, with its essentially turbulent character and linear growth rate, with the wave coherent atmospheric forcing with its exponential growth rate. The mechanism produces exponential growth and is an example of the universal instability arising from the essential nonnormality of time-dependent flows.