The impact of air-flow separation on the drag of the sea surface

An approach that allows assessment of the impact of air-flow separation (AFS) from wave breaking fronts on the sea-surface drag is presented. Wave breaking fronts are modelled by the discontinuities of the sea-surface slope. It is assumed that the dynamics of the AFS from wave breaking crests is similar to that from the backward facing step. The form drag supported by an individual breaker is described by the action of the pressure drop distributed along the forward face of the breaking front. The total stress due to the AFS is obtained as a sum of contributions from breaking fronts of different scales. Outside the breaking fronts the drag of the sea surface is supported by the viscous surface stress and the wave-induced stress. To calculate the stress due to the AFS and the wave-induced stress a physical model of the wind-wave spectrum is used. Together with the model of the air flow described in terms of surface stresses it forms a self-consistent dynamical system for the sea surface-atmosphere where the air flow and wind waves are strongly coupled. Model calculations of the drag coefficient agree with measurements. It is shown that the dimensionless Charnock parameter (roughness length normalized on the square of the friction velocity and the acceleration of gravity) increases with the increase of the wind speed in agreement with field measurements. The stress due to the AFS normalized on the square of the friction velocity is proportional to the cube of wind speed. At low winds the viscous surface stress dominates the drag. The role of the form drag, which is the sum of the stress due to the AFS and the wave-induced stress, is negligible. At moderate and high winds the form drag dominates. At wind speeds higher than 10 m s(-1) the stress supported by the AFS becomes comparable to the wave-induced stress and supports up to 50% of the total stress.