# Effects of Turbulence Modeling on the Simulation of Wind Flow over Typical Complex Terrains
## 1 Introduction  
As large-scale wind farms continue to be set up, few abundant wind resources are left in flat terrain, and many wind turbines are also being installed offshore, but the cost of offshore installations is twice as high as onshore installations due to the costs of expensive cables and bases [1], so wind farms over complex terrain are gaining more and more attention. Correctly predicting wind speed and turbulence levels over complex terrain is critical when choosing the proper wind turbine location, as high wind speeds and low turbulence levels are required for wind turbine operation to ensure high power generation and low fatigue loads. However, wind flow over complex terrain is always difficult to predict accurately because of the frequent changes in wind direction and the possibility of separation and high turbulence on the leeward side of hills [2]. Accurately estimating the wind flow at the wind turbine site is the primary task before designing a high-power production wind farm, which is also a great challenge. Wind turbines are located in the lower part of the atmospheric boundary layer, so studying the interactions between topography, wind turbines, and the atmospheric boundary layer is crucial for selecting suitable wind turbine locations and designing optimal wind farms with a high power generation efficiency and a long lifetime. Many researchers have conducted extensive research on atmospheric boundary layer characteristics and wind turbine wake over complex terrain. The main research methods include numerical simulations (including microscale, mesoscale, and meso-microscale coupled), experiments (including wind tunnel experiments [3] and field measurements [4]), and theoretical models (including wind flow models of complex terrain and models of the wake and terrain superposition). The experimental approach is only able to reflect a limited number of measurement locations, and the anemometer must be calibrated before the experiment, which is more difficult to satisfy in tests with complex terrain (previously calibrated anemometer sensors will fail due to variable wind direction and high turbulence intensity [1]); the theoretical analysis is based on many assumptions, and thus its accuracy remains limited when dealing with complex flows. In contrast, numerical methods can fully reflect the wind flow with much less time and at a more economic cost. The biggest problem faced by numerical methods is the solution of the turbulence, which usually includes the RANS (Reynolds-Averaged Navier-Stokes), LES (Large Eddy Simulation), DNS (direct numerical simulation), and DES (Detached Eddy Simulation). Among these methods, the most commonly used method to simulate wind flow over complex terrain is the RANS [5; 6]. The most commonly used RANS turbulence models for simulating wind flow over complex terrain are the standard \(k\)-\(\varepsilon\) model and the standard SST \(k\)-\(\omega\) model, which are both based on the assumption of isotropy. [PERSON] et al. [5], [PERSON] et al. [7], and [PERSON] et al. [8] showed that the results of the \(k\)-\(\varepsilon\) turbulence model and the SST \(k\)-\(\omega\) model on the windward side and the top of the mountain were consistent with experimental measurements. [PERSON] et al. [9] found that the SST \(k\)-\(\omega\) model was more effective than the standard \(k\)-\(\varepsilon\) turbulence model in terms of the prediction of the velocity in the separation zone and shear stress. To solve the problem of the difficult prediction of the wind flow on the leeward side due to high separation and turbulence, many researchers have also tried to modify the SST \(k\)-\(\omega\) model as well, such as modifying the turbulence model closure coefficients [10; 11], adding nonlinear source terms [12], or modifying the wall function [13]. The above modification methods improve the accuracy of wind flow simulation in complex terrain to some extent, but these methods are based on isotropic assumptions, which are inconsistent with the actual atmospheric boundary layer (ABL) [14].