A Model of Strongly Forced Wind Waves

Abstract

A model of surface waves generated on deep water by strong winds is proposed. A two-layer approximation is adopted, in which a shallow turbulent layer overlies the lower, infinitely deep layer. The dynamics of the upper layer, which is directly exposed to the wind, are nonlinear and coupled to the linear dynamics in the deep fluid. The authors demonstrate that in such a system there exist steady wave solutions characterized by confined regions of wave breaking alternating with relatively long intervals where the wave profiles change monotonically. In the former regions the flow is decelerated; in the latter it is accelerated. The regions of breaking are akin to hydraulic jumps of finite width necessary to join the smooth ''interior'' flows and have periodic waves. In contrast to classical hydraulic jumps, the strongly forced waves lose both energy and momentum across the jumps. The flow in the upper layer is driven by the balance between the wind stress at the surface, the turbulent drag applied at the layer interface, and the wave drag induced at the layer interface by quasi-steady breaking waves. Propagating in the downwind direction, the strongly forced waves significantly modify the flow in both layers, lead to enhanced turbulence, and reduce the speed of the near-surface flow. According to this model, a large fraction of the work done by the surface wind stress on the ocean in high winds may go directly into wave breaking and surface turbulence.

The equilibrium dynamics and statistics of gravity–capillary waves

“…In anticipation of this possibility, in Fedorov & Melville (2009) we developed a two-layer model of the strongly forced surface layer, with a thin turbulent boundary layer over the underlying irrotational waves. This model leads to instabilities that develop with very steep streamwise gradients in the wave profile, or 'breaking', supporting dissipation and mixing in the thin surface layer.…”

On the physical mechanism of front–back asymmetry of non-breaking gravity–capillary waves

“…However, despite the considerable progress in accumulation of data, the physical mechanisms of asymmetry have not been identified yet. Possible mechanisms include wave breaking and strong wind forcing (Fedorov & Melville 2009). Laboratory experiments by Leykin et al (1995) and Zavadsky & Shemer (2017) were conducted for the range of wind speeds where wave breaking is likely to be essential.…”

“…At present, such an ambitious undertaking is far beyond the art of the possible. There are works which tackle some aspects of the listed elements, for example, viscous decay due to molecular viscosity (Fedorov & Melville 1998), generation of vorticity at the free surface (Hung & Tsai 2009), exact three-dimensional simulation of the Navier–Stokes equations in the absence of wind and turbulence (Hung & Tsai 2009), interaction of waves with a turbulent surface layer (Fedorov & Melville 2009) and the generation of spay (Troitskaya et al. 2018).…”