Vorticity Dynamics in the Water Below Steep and Breaking Surface Waves

Abstract

This paper provides a new analysis of some aspects of vortical dynamics below surface water waves which are driven either by distant forcing or locally by a sheared turbulent wind. In the first situation, vorticity produced by the shear free condition applied at the surface, remains confined to surface layers as a result of vorticity cancellation in straining regions, even for finite amplitude water waves with significant movement of fluid to and from the surface. This justifies the irrotational flow assumption for finite amplitude water waves. When the waves are generated locally by a wind shear, the mean and fluctuating vorticity generated in the water by the air flow over flat and undulating surfaces is analysed to provide a possible explanation of anomolous turbulent dissipation profiles below waves. We then suggest a new theoretical model for the mean water, air and two-phase velocity fields in quasi-steady breaking waves, building on the work of Banner & Melville (1976) and Longuet-Higgins & Turner (1974). Interactions between finite amplitude three-dimensional waves and mean and fluctuating vortical fields in the water are analysed to differentiate between the mechanisms leading to Langmuir circulation, turbulence amplification by waves and downwards eddy bursting below waves observed by Komori et al. (1993). A previously overlooked mechanism for generation of vorticity in the water flow is identified, that corresponds to the ‘fast’ generation of vorticity by the drift (in contrast to the well-known slow generation by the Stokes drift). This mechanism may explain the observations of rapidly developing streamwise vortices by Veron & Melville (2001).