Atmospheric stability can significantly influence the spreading of wind-turbine wakes. The previous studies often coupled atmospheric stability with the turbulence intensity and attributed the influence of atmospheric stability to the enhancement or suppression of turbulence due to the buoyancy effect. In this study, we decouple atmospheric stability with the ambient turbulence intensity, and the pure influence of atmospheric stability on the turbine wakes is investigated at a certain hub-height turbulence intensity via large-eddy simulation. We find that the spanwise turbulence transport plays a crucial role in wake recovery, and atmospheric stability influences this transport by redistributing the turbulence intensity between the three components and altering the spatial scales of the atmospheric motion. Under the convection condition, the spanwise turbulence intensity is greatly enhanced with enlarged flow scales. Hence, more Reynolds shear stress is generated under the shear effect between the ambient flow and the wake flow, which thus enhances spanwise turbulence transport, resulting in a faster recovery of turbine wakes. While for the stable condition, although the spanwise turbulence intensity is slightly enhanced, the flow scales are obviously reduced, resulting in a decrease in wake meandering, which leads to a decrease in turbulence transport in the wake region and a slower recovery of wind-turbine wakes.

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