  Analytical wake models need formulations to mimic the impact of wind turbines
on turbulence level in the wake region. Several correlations can be found in
the literature for this purpose, one of which is the formula proposed in A.
Crespo, J. Hernandez, Turbulence characteristics in wind-turbine wakes, Journal
of Wind Engineering and Industrial Aerodynamics 61 (1) (1996) 71 - 85, which
relates the added turbulence to the induction factor of the turbine, ambient
turbulence intensity, and normalized distance from the rotor through an
equation with one coefficient and three exponents for the effective parameters.
Misuse of this formula with an incorrect exponent for the ambient turbulence
intensity is propagating in the literature. In this note, we implement the
original and the incorrect formulation of turbine-induced added turbulence in a
Gaussian wake model to quantify its impact by studying the Horns Rev 1 wind
farm. The results reveal that the turbulence intensity and the normalized power
of the waked turbines predicted by the wake model with the correct and the
incorrect implementation of turbine-induced added turbulence correlation have a
difference equal to 1.94% and 3.53%, respectively, for an ambient turbulence
intensity of 7.7%. For an ambient turbulence intensity of 4%, these
discrepancies grow to 2.7% and 4.95%.

Fluid Dynamics