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.
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.