Breaking of wind waves and the sea surface wind stress

Abstract

In the conventional treatment of the coefficient of sea surface wind stress by plotting it against 10-m wind speed, there are inevitable discrepancies among results of various investigators. The reason is considered to lie primarily in the fact that the state of the sea surface or of waves is disregarded, which may have great influence on the sea surface wind stress. Former concepts concerning the conditions which control the sea surface wind stress are discussed, and it is shown that a more universal expression may be obtained by plotting the coefficient against a kind of roughness Reynolds number:Re 2 *=u*H/ν, whereu* is the friction velocity of air, ν the kinematic viscosity of air, andH the characteristic wave height.H is used here to treat some data in wind-wave tunnels, as a tentative variable, one step towards a more rigorous approach to the problem. This variableRe 2 *, orRe 4 *=u *w /L/v w =2πgu *w /v w n 1, where the subscript ω represents values for water,L andn 1 the characteristic wave length and frequency, respectively, is also the condition describing the air entrainment or the breaking of wind waves. In this case, these Reynolds numbers are interpreted as the quantity describing the intensity of turbulence of the water surface itself. It is shown, using data from our wind-wave tunnel experiments, that the breaking commences asRe 2 * reaches 1×103, or asRe 4 * reaches 3×103. Simultaneously, the stress-coefficient begins to increase sharply at this value ofRe 2 *. This phenomenon is understood as an increased momentum transfer from the air to the water through “boundary penetration of turbulence” caused by the breaking of wind waves. Further, it is suggested that there is a possibility that this excess momentum transfer does not increase wave momentum, but reinforces drift current.