The study of a turbulent air flow over capillary-gravity water surface waves by direct numerical simulation

The present study is concerned with direct numerical simulation (DNS) of turbulent air flow over a waved water surface. Three-dimensional, turbulent Couette flow is considered in DNS as a model of a constant-flux layer in the marine atmospheric surface layer. Two-dimensional stationary waves at the water surface are prescribed and assumed to be unaffected by the air-flow. We consider capillary-gravity water surface waves and are interested in the influence of "parasitic" capillary ripples riding on the carrier, energy-containing waves, on the properties of the air-flow. The surface waves are prescribed and considered to be stationary, the capillaries being in phase with the carrier wave. The surface elevations spectra are also prescribed and mimicking stationary capillaries riding on Stokes waves observed in a 2D numerical simulation of water-surface capillary-gravity waves by Hung & Tsai (2009). The bulk air velocity and the carrier water surface waves lengths are considered in our DNS in the range of 3 to 5 m/s and 3 to 7 cm, respectively. Under these conditions, the capillaries are found to be submerged within the viscous sublayer of the atmospheric boundary layer. Our DNS results show that although the flow fields are characterized by instantaneous separations of the boundary layer, the ensemble (wave-phase) averaged flow fields are non-separating and well predicted by a quasilinear theoretical model. We find also that capillaries mitigate the development of coherent (horse-shoe) vortex structures as compared to the no-ripples flow-case. We further use DNS results and quasilinear model formulation to parameterize the water surface roughness height in terms of critical layer thickness and the amplitude of a dominant, energy-containing harmonic of the water surface elevation spectrum.