Structure functions, scaling exponents and intermittency in the wake of a wind turbine array

Abstract

Hot-wire measurements obtained in a 3 × 3 wind turbine array boundary layer are utilized to analyze high order structure functions, intermittency effects as well as the probability density functions of velocity increments at different scales within the energy cascade. The intermittency exponent is found to be greater in the far-wake region in comparison with the near-wake. At hub height, the intermittency exponent is found to be null. Extended self-similarity scaling exponents of the second, fourth, and fifth order structure functions remain relatively constant as a function of height in the far-wake; whereas in the near-wake, these are highly affected by the passage of the rotor where tip vortices reside, thus showing a dependence on physical location. When comparing with proposed models, these generally overpredict the structure functions in the far-wake region. The probability density function distributions in the far-wake region display wider tails compared to the near-wake region, and the constant skewness hypothesis based on the local isotropy is disrupted in the wake.