Abstract
Observational evidence indicates that the bubble layer beneath the sea surface may show either an exponential or an inverse-square sound speed profile down to depths greater than 10 m. An exponential profile is consistent with a model of gas transport in which the downward flux is clue to turbulent diffusion and the diffusion coefficient is independent of depth. In this paper, a theoretical model is developed for the inverse-square sound speed (or void fraction) profile, which is also based on turbulent transport but in the presence of a constant stress layer immediately beneath the surface. In such a boundary layer, the diffusion coefficient increases linearly with depth. The new solution, which is based on a Hankel transformation of the diffusion equation, includes the input gas flux explicitly. Expressions are given relating the input gas flux and the transport parameters of the bubble layer to the parameters of the inverse-square profile. By comparing this solution with published experimental data, the wind-speed dependencies of the inverse-square profile parameters, the input gas flux and the coupling coefficient between wind energy and bubble formation are estimated. Future modelling efforts that will be required to establish the link between the hydrodynamic properties of the bubble layer and the ambient noise in the ocean are discussed.