Wake Dynamics in the Generalized Quasilinear Approximation*

Wind energy is an abundant renewable resource in a rapid growth period, reaching 117 GW of installed capacity in 2023: a 50% increase over the prior year. In the US, offshore wind, in particular, is experiencing dramatic growth. Because of the expense of offshore operation, wind turbines are clustered into farms. In order to maximize the efficiency of these farms, a detailed understanding of the structure of the combined wake dynamics as they interact with the marine atmospheric boundary layer is needed. We have begun a multi-year effort to use the techniques of direct statistical simulation and generalized quasilinear (GQL) approximation to understand the dynamics of offshore wind. As a first step, we report our findings on the classical Von Karman vortex street under the GQL approximation. GQL approximates the nonlinear effects by careful decimation of triadic interactions, ranging from the quasilinear approach in which fluctuations interact only with the mean all the way to a fully nonlinear direct numerical simulation. We find that very few nonlinear interactions are required to reproduce both wake structure and quantitative Strouhal-Reynolds relationships. We will conclude by suggesting generalizations of this work that are more directly applicable to offshore wind farms.