Under consideration for publication in J. Fluid Mech. 1 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 stochastic excitation by wave incoherent random atmospheric pressure fluctuations unrelated to wave amplitude (Eckart 1953; Phillips 1957) and the second instability arising from wave induced coherent atmospheric pressure fluctuations proportional to wave amplitude (Helmholtz 1868; Kelvin 1871; Jeffreys 1925; Miles 1957). Incoherent wave independent forcing produces growth of surface height variance linear in time while coherent forcing proportional to wave amplitude produces exponential growth. While observed wave developments can be fit to these forms, and despite broad 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 theory and field observations of wave growth has proved elusive. Accepting that the dominant contribution to wave growth results from an at least statistical proportionality and coherency in phase lag between atmospheric pressure fluctuations and surface elevation, at issue is the mechanism by which this relationship is produced and maintained. Mechanisms previousl