Turbulent field beneath monochromatic waves subjected to varying wind conditions

Abstract

Wind-wave interaction affects momentum, energy, and chemicals transfer at the air–water interface. In this study, we report on the turbulent flow field beneath laboratory monochromatic waves subjected to different wind speeds and direction (following or opposing). The flow field is decomposed into three main components: a mean, a swell-induced, and a fluctuating term, the latter including the effects of wind-induced ripples and turbulence. After a brief survey on the mean and wave-induced fields, we focus our attention on the fluctuating-turbulence field. Our results show that the turbulent stresses increase with increasing water friction, and that the condition of wind opposing the swell results in enhanced momentum transfer at deeper water levels. The distribution of fluctuating kinetic energy (TKE) along the swell phase indicates a maximum at the trough, which was addressed to the kinematics of the free surface by previous researchers. Furthermore, we investigate all the terms in the 2D energy equations that contribute to the TKE production by assuming that waves propagate with a rigid translation. A close look to the TKE budget suggests positive production of TKE on the leeside before the trough for all wind conditions, with destruction of TKE windwards for wind following the swell, possibly due to a sheltering effect. For opposing wind, however, positive production is almost ubiquitous along the swell phase, and this would justify larger mean TKE production for that particular condition. These findings are discussed to address possible causes; the phase-dependent behavior of TKE budgets are attributed to the combined action of swell-induced acceleration, wind shear on the crest, the stochastic phase offsets of the wind waves, and microscale breaking. A quadrant analysis highlights the main direction of momentum transfer and helps the individuation of the bursts, i.e., of strong events that support high momentum transfer. As expected, the net momentum transfer due to the fluctuating components is from air to water, with conditional averages (i.e., the quadrant map of the fluctuating velocities) confirming that finding. Finally, the analysis of the fluctuating principal stresses tensor reports that anisotropy increases for increasing water friction, although the system tends to isotropic conditions immediately below the air–water interface. For wind following the swell, the principal axes approaches the free surface with an angle $-\pi /4$, which is typical when a shear current is dominant near the surface. Important implications of these findings include the availability of further data to improve wave forecasting and prediction of swell and wind conditions.