Large-eddy simulation of gusty wind turbulence over travelling wave

Wind gustiness in the marine atmospheric boundary layer significantly affects the dynamics of air-sea interaction and the harvest of offshore wind energy. To understand the hydrodynamic impact of the wind gust event, we perform large-eddy simulation of wind turbulence over a travelling wave to investigate the response of the turbulent flow subject to impulsive wind speed increase and decrease. Analyses of the turbulent kinetic energy budget show that the streamwise velocity variance changes instantaneously with the mean shear while other components remain constant. We show that, because of the memory effect in turbulence evolution, the ratio of the Reynolds normal stress to the Reynolds shear stress cannot be assumed to be constant. On the other hand, the wave-coherent motions have a nearly real time response to the wind gust events and their evolution patterns exhibit a strong dependency on the wave age. For intermediate and large wave ages, the unsteady wave-coherent vertical velocity is consistent with a viscous curvilinear model developed by Cao et al. (J. Fluid Mech., vol. 901, 2020, A27) and Cao & Shen (J. Fluid Mech., vol. 919, 2021, A38). We also observe the hysteresis effect in the time evolution of the form drag and the viscous drag. Our discoveries thus provide evidence for the necessity of improved nonequilibrium turbulence and wind input modelling to account for the wind gustiness effect in future studies.