The influence of free stream turbulence on the development of a wind turbine wake

The wake of an isolated model-scale wind turbine is analysed in a set of inflow conditions having free stream turbulence intensity between 3 % and 12 %, and integral time scales in the range of 0.1-10 times the convective time scale based on the turbine diameter. It is observed that the wake generated by the turbine evolves more rapidly, with the onset of the wake evolution being closer to the turbine, for high turbulence intensity and low integral time scale flows, in accordance with literature, while flows at higher integral time scales result in a slow wake evolution, akin to that generated by low-turbulence inflow conditions despite the highly turbulent ambient condition. The delayed onset of the wake evolution is connected to the stability of the shear layer enveloping the near-wake, which is favoured for low-turbulence or high-integral time scale flows, and to the stability of the helical vortex set surrounding the wake, as this favours interaction events and prevents momentum exchange at the wake boundary which hinder wake evolution. The rate at which the velocity in the wake recovers to undisturbed conditions is instead analytically shown to be a function of the Reynolds shear stress at the wake centreline, an observation that is confirmed by measurements. The rate of production of Reynolds shear stress in the wake is then connected to the power harvested by the turbine to explain the differences between flows at equivalent turbulence intensity and different integral time scales. The wake recovery rate, and by extension the behaviour of the turbine wake in high-integral time scale flows, is seen to be a linear function of the free stream turbulence intensity for flows with Kolmogorov-like turbulence spectrum, in accordance with literature. This relation is seen not to hold for flows with different free stream turbulence spectral distribution; however, this trend is recovered if the contributions of low frequency velocity components to the turbulence intensity are ignored or filtered out from the computation.