A number of studies have shown an apparent reduction of the water-side friction velocity and enhancement of the water-side roughness length in the oceanic boundary layer, as estimated from profiles of the mean current induced by the wind in the presence of surface waves. This has been attributed primarily to wave breaking. I this talk I will present a simple analytical model for the current induced by the wind and modified by non-breaking surface wind-waves in the oceanic surface layer, based on a first-order turbulence closure and including the effect of a vortex force representing the Stokes drift of the waves. The shear stress is partitioned between a component due to shear in the current and a wave-induced component, which decays over a depth proportional to the wavelength. The current profile becomes flatter for strong wave forcing (quantified by the turbulent Langmuir number) owing to a smaller fraction of the total shear stress being supported by the current shear, causing a reduction of the friction velocity and increase of the roughness length diagnosed from the current relative to their true values. A version of the model where the shear stress decays to zero with depth is able to adequately predict the surface current speed from lab experiments.
Figure: Wind-induced current from lab experiments (symbols) against model results (lines), plotted in wall coordinates (normalized speed against normalized depth). Different lines (red to violet) correspond to increasing wind-speed/wave influence