  The coupling between wind-waves and atmospheric surface layer turbulence sets
surface drag. This coupling is however usually represented through a roughness
length. Originally suggested on purely dimensional grounds, this roughness
length does not directly correspond to a measurable physical quantity of the
wind-and-wave system. Here, to go beyond this representation, we formalize
ideas underlying the Beaufort scale by quantifying the velocity of breaking
short waves that are the most coupled to near-surface wind. This velocity
increases with wind speed, reflecting the fact that stronger winds can be
visually identified by longer (and faster) breakers becoming predominant on the
sea surface. A phenomenological turbulence model further shows that this
velocity is associated with breaking waves that impede the most the formation
of turbulent eddies. Scales of such eddies are then constrained inside a
so-called roughness sub-layer. Unlike previous theoretical developments, the
proposed breaker velocity is a directly measurable quantity, which could be
used to characterize the coupling between wind and waves using remote sensing
techniques. This work provides a physical framework for new formulations of
air-sea momentum exchange in which the effects of surface currents and slicks
on surface drag can also be incorporated. Finally, it provides a long-sought
physical explanation for the Beaufort scale: a universal link between wave
breaking, wind speed and surface drag.
