Knowledge of air-sea exchange processes is important for development of accurate climate model, study of ocean and atmosphere using remote-sensing technology, and prediction of pollutant dispersion on the ocean surface. Also, theoretically, the problem of wind over waves is significant, since the occurrence and effect of air flow separation on the wave dynamics is not fully understood. Here, we consider a robust numerical model to analyze fully nonlinear unsteady air-sea interactions, in particular, that occurring in the inception, growth, and breaking of wind waves. We treat this problem as a flow of two layers of immiscible fluids separated by an interface. Evolution of the interface is determined based on fully nonlinear kinematic and dynamic surface conditions. As application of the current model, we consider time evolution of a periodic wave under the influence of wind. In the case of a small-amplitude wave, it is found that the vortex sheet of the interface merely diffuses into air and water, because of viscosity. In the case of a large-amplitude wave, the vortex sheet gets separated from the interface and rolls up into a distinct vortex structure, resulting in the formation of a recirculation bubble in the trough of the wave (see figure above which shows instantaneous streamlines and vorticity). The air flow separates on the leeward side of the crest and reattaches on the windward side of the next crest. Such air-flow separation and vortical structures over water waves are reminiscent of those observed in recent laboratory and field experiments. Effect of such coherent vortex structures on the growth of interface waves and surface roughness is a topic under investigation.

References

P. Ananthakrishnan, ``Analysis of nonlinear air-sea interactions,'' Proceedings of the Forum on Advances in Numerical Modeling of Free Surface and Interface Fluid Dynamics, ASME Publication FED-Vol. 234, pp.175--182, 1995.

P. Ananthakrishnan, ``Numerical Modeling of Nonlinear Air-Sea Interactions,'', Bulletin of the American Physical Society, Program of the 49th Annual Meeting of the Division of Fluid Dynamics, 1996.