An Analytical Approach to Modeling Wake Dynamics for Wind Turbine Arrays

Accurate prediction of wind turbine wake dynamics is critical for wind farm design, control, and optimization. While high-fidelity numerical simulations can represent wake behavior with considerable detail, their large computational requirements restrict their routine use in wind farm studies. In this work, we present a fast, physics-based analytical model for time-resolved wind turbine wake dynamics without requiring the numerical solution of governing differential equations or calibration of empirical parameters. The wake velocity deficit is formulated analytically in the meandering frame of reference using super-Gaussian and Gaussian distributions constrained by conservation of mass and momentum, providing a physically consistent description of the near- and far-wake regions. Wake meandering is modeled as the response of the wake to large-scale turbulent eddies in the incoming atmospheric boundary layer. Interactions among multiple turbine wakes are accounted for using a momentum-conserving superposition approach. Validation against Large Eddy Simulation shows that the proposed framework captures the key features of the wake while maintaining a substantially reduced computational cost. The proposed framework offers an efficient and physically grounded tool for dynamic wake modeling with potential applications in wind farm design and control.