**1. Introduction**

As wind energy grows as a main energy resource for the whole world, further research is still needed to reduce the cost of wind energy to keep it economically competitive [1]. Turbine wakes affect both the power production and operation and maintenance costs of wind energy. Wind tunnel experiments at meter-scale or even smaller wind turbines [2–8] and field measurements of subscale wind turbines (e.g., the SWiFT facility [9–12]) play a vital rule in understanding the dynamics of turbine wakes and provide valuable datasets for validating computational models. However, the sizes of these meter-scale turbines and subscale turbines are often much smaller than a full-scale wind turbine, which calls into question how well these small-scale wind turbines can represent full-scale wind turbines [13].

When designing a meter-scale or a subscale wind turbine, geometric, kinematic and dynamic similarities should be maintained to ensure their equivalence to a full-scale wind turbine. For a meterscale wind turbine, which can be about 1000 times smaller than a full-scale wind turbine, it is even

challenging to ensure only geometric similarity (e.g., the rotor diameter and chord length) and the kinematic similarity (e.g., the tip speed ratio *λ* = Ω*R*/*U*, where Ω is the rotor rotating speed, *R* is the rotor radius and *U* is the incoming wind speed). As such, researchers often build a meter-scale wind turbine in a way that the power coefficient and thrust coefficient are similar to that of a full-scale wind turbine [6]. For the scale effects on turbine wakes, Howard and Guala [14] compared the velocity deficits of a meter-scale turbine with that of the University of Minnesota 2.5 MW EOLOS turbine and observed significant differences at *x*/*D* = 1.5 and *x*/*D* = 2.5 turbine downwind locations but relatively small differences at *x*/*D* = 3 turbine downwind location, where *D* is the rotor diameter. Heisel, Hong and Guala [15] further compared the wake meandering from the meter-scale turbine and the EOLOS turbine and observed similar meandering frequencies related to the bluff body shear layer instability.

For a subscale wind turbine, which may be 3 or 4 times smaller than a full-scale wind turbine, the geometric similarity and the kinematic similarity can be ensured relatively easier compared to meter-scale wind turbines. However, because of the difference in Reynolds number, the dynamic similarity, namely the distributions of lift and drag coefficients along the blade for wind turbines, still cannot be guaranteed easily while keeping the geometric and kinematic similarities. Kelley et al. [16] proposed to loosely maintain the dynamic similarity by keeping the same dimensionless bound circulation along the blade by relaxing the constraints on the geometric similarity. Although the aerodynamics of a subscale wind turbine can be made closer to a full-scale wind turbine, an important difference is that the subscale wind turbine is located closer to the ground where the mean shear stress and the turbulence intensity change significantly with distance from the ground. However, how this difference affects the representation of a subscale wind turbine wake to that of a full-scale wind turbine is not clear yet. To address this issue, in this work we simulate a subscale wind turbine and a full-scale wind turbine, which are geometrically and kinematically equivalent, and are dynamically equivalent by applying the same lift and drag coefficients in turbine parameterizations, and under the same turbulent boundary layer inflow.

It is noted that this work is different from the studies in the literature on investigating the effects of inflow turbulence on turbine wakes. In the literature, the turbine wakes under different turbulent inflows, which are due to different ground roughness lengths, were investigated in [2,17] using wind tunnel experiments and large-eddy simulation, respectively. The effects of different inflow turbulence on turbine wakes, which is caused by different thermal stratifications, were studied using wind tunnel experiments and large-eddy simulation in [18,19], respectively. In [20], turbine wakes under different inflow turbulence caused by an upwind hill of different heights were simulated using large-eddy simulation. In [21], the coherent tip vortices of a utility-scale wind turbine were investigated for inflows of different turbulence intensities. In [22], the wake meandering of a utility-scale wind turbine was investigated for inflows of different turbulence intensities. All these studies were focused on the wake of one-size wind turbine. To the best of our knowledge, no studies have been carried out on comparing wakes from turbines of different sizes, which is critical as we use the knowledge from a subscale wind turbine to a full-scale wind turbine.

The rest of the paper is organized as follows: in Section 2 we briefly describe large-eddy simulation with actuator surface models for turbine blades and nacelle; we then compare the results from the two turbines of different sizes in Section 4; at last we draw conclusions from this work in Section 5.
