Determining growth rates of wind-driven gravity-capillary waves from the air-sea momentum flux budget

Accurate knowledge of surface wave growth rates by wind plays a critical role in determining the momentum and energy fluxes between the atmosphere and the ocean. Wave growth rates of gravity-capillary waves are calculated based on surface wave spectra and laboratory measurements of total and viscous stress at a wind-driven air-water interface. At the interface the total momentum flux partitions into viscous and wave-induced components. The wave-induced stress is computed via a parameterized wave growth rate, which is proportional to the turbulent stress divided by the wave phase speed squared. The constant of proportionality, beta, is determined under two different assumptions. The first assumption (sheltering assumption) is that the wave growth rate depends on the local turbulent stress, which is a reduced turbulent stress due to the presence of longer waves. In the second assumption (non-sheltering assumption) the turbulent stress is simply equated with the total wind stress. Both assumptions yield simple closed-form expressions for the stress-partitioning ratio. With the sheltering assumption, beta agrees with previous theoretical estimates and is close to the lower bound of previous empirical parameterizations. Without sheltering, beta is significantly lower than previous estimates. Therefore, our results indicate that the growth rate of surface waves is determined by the local turbulent stress rather than the total wind stress.