Modeling the effects of swell and vertical wave motions in wall-modeled Large Eddy Simulation of offshore wind farms

Wind-driven waves provide feedback to the airflow by extracting energy and momentum from the wind. In addition, long-wavelength swell waves can be generated by remote storm events and impart energy and momentum to the wind. In Large Eddy Simulation, wave effects have been modeled through a single roughness length, or, more recently, through a form drag model that accounts for the wind-wave relative velocity and surface gradients. These models are implemented as strictly as drag and as surface parameterizations that do not include vertical motions of the wave surface. In this work, a recent wave drag model from Aiyer et al. (2023) is extended to model nonlocal waves, such as swell, through an empirical parameterization. The vertical wave motions are modeled using a transpiration-based wall model to incorporate surface kinematics in an equilibrium wall modeling framework. The effect of vertical wave motions on the phase-averaged wave fluctuation velocities and stresses is probed using LES. The model is applied to study flow past an offshore wind turbine, and the effects of the wave kinematics (transpiration effect) and the wave dynamics (wave drag) on the wind turbine wake are quantified.