Wave-Induced Stress and the Drag of Air Flow over Sea Waves

Abstract

In this paper we are concerned with the effect of wind-generated, long gravity waves on the air flow. We study this example of resonant wave-mean flow interaction using the quasilinear theory of wind-wave generation. This theory is an extension of the Miles' shear flow instability in that the effect of the gravity waves on the mean wind profile is taken into account as well. The direct effect of air turbulence on the mean wind profile is modeled by a mixing length model. We present results of the numerical calculation of the steady state wind profile for given wave spectra. Results are found to be sensitive for the parameterization of the high-frequency tail of the wave spectrum. Following a proposal by Snyder on the fetch or wave age dependence of the Phillips constant, a strong dependence of the drag of air flow over sea waves on the wave age is found. For young wind sea (small wave age) a strong coupling between wind and waves is found, whereas there is hardly no coupling for old wind sea. This sensitive dependence of the aerodynamic drag over sea waves on the wave age explains the scatter in plots of the experimental observed drag as a function of the wind speed at 10 meters. Consequences for the coupling of weather and wave models and for remote sensing (e.g., the scatterometer) are briefly discussed.