Solution of the Fokker–Planck equation in a wind turbine array boundary layer

• Solutions to the Fokker–Planck equation for a complex flow.
• Comparison of solutions to experimental data obtained via hot-wire.
• Description of the evolution of the probability density function of velocity increments.
• Characterization of the near- and far-wake for a wind turbine array boundary layer.

Hot-wire velocity signals from a model wind turbine array boundary layer flow wind tunnel experiment are analyzed. In confirming Markovian properties, a description of the evolution of the probability density function of velocity increments via the Fokker–Planck equation is attained. Solution of the Fokker–Planck equation is possible due to the direct computation of the drift and diffusion coefficients from the experimental measurement data which were acquired within the turbine canopy. A good agreement is observed in the probability density functions between the experimental data and numerical solutions resulting from the Fokker–Planck equation, especially in the far-wake region. The results serve as a tool for improved estimation of wind velocity within the array and provide evidence that the evolution of such a complex and turbulent flow is also governed by a Fokker–Planck equation at certain scales.