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Article

Study on the Wake Characteristics of the Loess Plateau Terrain Based on Wind Tunnel Experiment

by
Yulong Ma
1,
Shoutu Li
1,2,*,
Deshun Li
1,2,
Zhiteng Gao
3,
Xingduo Guo
1 and
Qingdong Ma
1
1
School of Energy and Power Engineering, Lanzhou University of Technology, Lanzhou 730050, China
2
Key Laboratory of Fluid Machinery and Systems, Lanzhou 730050, China
3
Institute of Energy Science, College of Engineering, Shantou University, Shantou 515063, China
*
Author to whom correspondence should be addressed.
Energies 2025, 18(4), 958; https://doi.org/10.3390/en18040958
Submission received: 7 January 2025 / Revised: 1 February 2025 / Accepted: 5 February 2025 / Published: 17 February 2025
(This article belongs to the Section A3: Wind, Wave and Tidal Energy)
Browse Figures
Figure 1
<p>New installed capacity in China in 2023: (<b>a</b>) new installed capacity in various regions of China from 2022 to 2023; (<b>b</b>) the proportion of new additions in various regions of China (NE for Northeast China; NC for North China; EC for East China; NW for Northwest China; SW for Southwest China; MS for Central South China).</p> "> Figure 2
<p>Landform and atmospheric boundary layer characteristics of the loess plateau: (<b>a</b>) wind farm in loess plateau; (<b>b</b>) boundary layer of the loess plateau.</p> "> Figure 3
<p>Experimental model: (<b>a</b>) Terrain Model of the Loess Plateau (TMLP); (<b>b</b>) Standard Three-dimensional Mountain Model (STMM).</p> "> Figure 4
<p>Experiment scheme and experiment environment: (<b>a</b>) experiment scheme; (<b>b</b>) dimensionless mean velocity profile; (<b>c</b>) turbulence intensity profile; (<b>d</b>) photograph of wind tunnel experiment.</p> "> Figure 5
<p>Mean velocity distribution of vertical cross-section at different spanwise positions: (<b>a</b>) TMLP; (<b>b</b>) STMM.</p> "> Figure 6
<p>Recovery of mean velocity per unit distance at different heights: (<b>a</b>) recovery of mean velocity at different positions of cross-section Y = 0 H; (<b>b</b>) recovery of mean velocity at different positions of cross-section Y = 1 H.</p> "> Figure 7
<p>Turbulence distribution of vertical cross-sections at different spanwise positions: (<b>a</b>) TMLP; (<b>b</b>) STMM.</p> "> Figure 8
<p>Time–frequency plot of fluctuating wind speed.</p> "> Figure 9
<p>The fluctuating velocity power density spectra of the incoming flow, TMLP wake, and STMM wake at three height positions: (<b>a</b>) at a height of 0.1 H; (<b>b</b>) at a height of 0.5 H; (<b>c</b>) at a height of 1 H.</p> ">
Versions Notes

Abstract

:
The northwest region of China’s loess plateau is an important area for wind power development. However, the unclear understanding of the evolution mechanism of the near-ground atmospheric boundary layer (ABL), which is influenced by its unique geomorphological features, has compromised the safety and stability of wind turbine operations. To address this challenge, wind tunnel experiments were conducted to investigate the mean and turbulent characteristics of wake flow generated by mountains in the loess plateau. The results indicate that the terrain significantly affects both the average velocity deficit and turbulence intensity distribution within the wake. Specifically, topographic features dominate turbulent energy transfer and modulate coherent structures in the inertial subrange. Additionally, the scale of these features enhances turbulence energy input at corresponding scales in the fluctuating wind speed spectrum, leading to a non-decaying energy interval within the inertial subregion.

1. Introduction

According to the Global Wind Report 2024 by the Global Wind Energy Council [1], global wind power development and investment continue to grow. In 2023, the worldwide installed wind capacity increased by 117 GW, with onshore wind contributing 106 GW, reaffirming its dominance. However, declining wind resources in flat terrains are driving the industry toward complex terrain development [2]. In China, significant attention is now focused on wind power in the Yungui Plateau and Tibetan Plateau (southwest China, SW) and the loess plateau (northwest China, NW). As shown in Figure 1a,b, these two regions accounted for 43.3% of China’s newly installed capacity in 2023, with the loess plateau alone representing approximately 27.5% [3]. Compared to the Yungui and Tibetan plateaus, the loess plateau exhibits more diverse topographic structures (Figure 2) and more complex flow field characteristics. These factors challenge both the exploitation of wind resources and the efficient, stable operation of turbines in this region. Therefore, investigating the terrain-specific flow dynamics of the loess plateau is of critical importance.
Numerous studies have investigated the atmospheric dynamics of the loess plateau [4,5,6]. For instance, Ma et al. [7] utilized the Weather Research and Forecasting (WRF) model to simulate the atmospheric boundary layer (ABL) observed over the loess plateau in May 2000, demonstrating its capability to capture key ABL characteristics. Liang et al. [8,9] analyzed boundary layer turbulence through field observations, proposing a method to isolate nonstationary motions from turbulence series and revealing terrain-induced anisotropy in turbulent structures. Yue et al. [10] validated that normalized turbulence intensity and horizontal turbulent kinetic energy (TKE) conform to Monin–Obukhov similarity theory (MOST) under stable stratification. Wei et al. [11] refined the intermittency intensity index using field data, enhancing turbulence intermittency assessment. Chen et al. [12,13] demonstrated that turbulence ergodicity depends on stability and scale, with large-scale structures in complex terrain more likely satisfying ergodic conditions. Zhang et al. [14] further explored terrain-specific turbulence features. Collectively, these studies highlight the complex and anisotropic nature of flow fields in this region. However, most focus on meteorological scales, making it challenging to resolve turbine-scale terrain impacts from such data. High-resolution spatial and temporal measurements are thus imperative for capturing microscale flow details.
Wind tunnel experiments have become a widely adopted method for investigating intricate flow field details due to their capability to acquire realistic, high-resolution data [15,16,17,18,19]. Numerous studies have employed diverse terrain models in such experiments. For instance, Cao and Tamura [20] examined the impact of surface roughness on turbulent boundary layer flow over a 2D steep hill, observing persistent flow separation. Their results indicate that both hill-surface and upstream roughness elements significantly affect the speed-up ratio. Miller and Davenport [21] investigated acceleration effects induced by twelve consecutive 2D mountains, while Zhang et al. [22] used particle image velocimetry (PIV) to quantify wakes behind 2D hills. They revealed that shear layers originating near the hill crest govern turbulence amplification and turbulent kinetic energy (TKE) production under both stable and neutral conditions. Wang et al. [23] further demonstrated that terrain truncation distorts velocity spectra—overestimating low-frequency and underestimating high-frequency energy—with spatially varying impacts on mean velocity and turbulence profiles.
The limitations of wind tunnel experiments based on two-dimensional (2D) hill models have driven researchers to adopt three-dimensional (3D) terrain representations. For example, Gong and Ibbetson [24] measured mean flow and turbulence over a 2D ridge and a circular hill, finding that linear theory accurately predicts upwind and hilltop mean flow but underperforms in turbulence prediction. Measurements over 3D hills revealed similar flow-turbulence characteristics to 2D ridges, albeit with attenuated perturbation amplitudes. Ishihara and Takahashi [25,26] investigated rough-surface 3D mountain models, demonstrating significant turbulence intensification in upper wake regions alongside surface wind speed reduction due to roughness. Shen et al. [27] studied streamwise and vertical flow fields on a typical three-dimensional hill, discovering that the most notable acceleration effect occurred at the crest of the hill in streamwise direction, with speed-up decreasing as height increased. Additionally, they found that wind speed-up along crosswind center line exceeded that along along-wind center line of hills. Lubitz and White [28] quantified wind direction effects on speed-up for 2D/3D hills, validating findings against field data. Yang et al. [29] combined wind tunnel tests with large eddy simulation (LES) to propose a terrain-specific turbulent kinetic energy (TKE) model for turbine wakes. Lange et al. [30] meticulously incorporated the edge details of the wind tunnel experimental model and discovered that precise terrain features have a significant impact on mean wind speed, wind shear, and turbulence. In fact, estimated annual energy production could decrease by at least 50% while turbulence levels may increase up to five times in worst-case scenarios with unfavorable wind directions. Uchida and Sugitani [31] conducted experiments on both two-dimensional mountain models and three-dimensional real terrain models in a wind tunnel. The results showed that even under identical wind directions, local speed-up can vary significantly for real terrain models. Demarco et al. [32] utilized the Hilbert–Huang transform method to obtain turbulent energy spectra for flow velocities at different heights. The observed convective turbulence energy spectra behavior was found to be consistent with those measured in an unstable ABL. Wind tunnel experiments based solely on idealized three-dimensional hill models are limited in their ability to guide reality; therefore, this paper employs an experimental model simulating actual terrains for conducting the tests.
In summary, research on flow field characteristics of the loess plateau has predominantly focused on meteorological-scale phenomena through field observations and mesoscale numerical simulations. However, such approaches often fail to resolve turbine-scale flow dynamics critical for wind energy applications. Wind tunnel experiments, recognized for their ability to generate high-resolution, physically realistic data, have emerged as a primary methodology. Despite their widespread use, few studies have applied wind tunnel techniques to investigate the loess plateau’s unique terrain-induced flow features. To address this gap, we propose an experimentally validated terrain-faithful model (inspired by idealized complex terrain frameworks [33]) to systematically analyze wake characteristics specific to the loess plateau. By integrating time-averaged velocity profiles, turbulence statistics, spectral properties, and wavelet coherence analysis, we elucidate the terrain’s impact on wake evolution. These findings aim to inform wind resource assessment and turbine siting strategies in mountainous regions of the loess plateau. The structure of this paper is organized as follows: Section 2 presents our experimental design plan; Section 3 provides specific measurement results along with discussions encompassing velocity profiles, mean velocity growth rates, turbulence distribution, fluctuating wind speed spectra, and wavelet analysis; finally, Section 4 concludes with a summary.

2. Experimental Setup

2.1. Wind Tunnel

The experiment was conducted in the low turbulence, open-circuit, and low-incoming-speed boundary layer wind tunnel at LUT in China [34]. The square closed test section is 2 × 2 m and the length is 17 m. The designed wind speed range of the wind tunnel is 0–20 m/s. The turbulence intensity of the wind tunnel was less than 1%, when the wind speed was 15 m/s, and the accuracy of the wind speed was less than ±5%.

2.2. Experiment Model

The research area of this paper focuses on the mountainous region in Tongwei, Gansu Province, China, which is characterized by a loess hilly mountain structure within the loess plateau. The elevation in this area ranges from 100 m to 220 m, with slopes varying between 15% and 60%. Due to limitations in the size of the experimental wind tunnel, this study adopts an average height of 160 m as the reference height and a slope angle of 60%. Based on geometric similarity principles, the mountain model is scaled down at a ratio of 400:1. Thus, as depicted in Figure 3a, the experimental model presented in this paper has a height (H) of 0.4 m and a bottom diameter (D) equal to 3 H. The proposed loess plateau mountain model draws inspiration from previous scholars’ models [24,27] and adopts cosine-shaped mountains. The geometric formula for constructing this model is as follows:
  z x , y = H c o s 2 π x 2 + y 2 1 2 2 L
To replicate the structure of the loess plateau, circular rings were incorporated onto the surface of the ideal mountain model. The size of each circular ring was designed based on the structural characteristics observed in real terrain. Given that step heights in actual terrain range from 2 to 6 m, which accounts for approximately 4% of the mountain’s height, adjustments were made due to the reduced height of our mountain model. Consequently, the step structures were increased to 8% of the mountain’s height, equivalent to approximately 0.03 m. To mitigate the effects resulting from this increase in step heights, a spacing distance between each ring was also set at 0.03 m. A total of six circular structures were established based on the mountain’s height. The experimental model of the loess plateau mountain is constructed entirely from polyethylene foam plastic. Figure 3b illustrates a standard three-dimensional mountain model with identical geometric parameters as those used for modeling the loess plateau mountains; its purpose is to facilitate comparison and analysis regarding how these mountains impact wake dynamics. For ease of reference throughout this paper, we will abbreviate “Terrain Model of the Loess Plateau” and “Standard Three-dimensional Mountain Model” as TMLP and STMM, respectively.

2.3. Experiment Scheme

The wind tunnel experiment setup is illustrated in Figure 4. In this experimental setup, the atmospheric boundary layer is generated using spires and floor roughness. Subsequently, both a mountain model representing the loess plateau and a standard three-dimensional mountain model are placed within the boundary layer, respectively. Finally, the wake characteristics are measured at various locations using a hot-wire anemometer. By comparing the wake with that of the standard three-dimensional mountain model, insights into flow characteristics and terrain-induced influences on the flow field of the loess plateau can be obtained.
The boundary layer environment studied in this paper is illustrated in Figure 4a. Drawing upon the research findings of Irwin [35], the neutral atmospheric boundary layer (the absence of temperature gradients and buoyancy-driven forces within the wind tunnel results in a Richardson number approaching neutral conditions (Ri ≈ 0), where the flow is primarily governed by mechanical turbulence, which aligns with the fundamental characteristics of a neutral boundary layer) is simulated through three wedge-shaped wooden spires, one wooden horizontal baffle plate, and three sets of wood roughness elements with varying sizes. The spires have a height of 1.7 m, a bottom width of 0.3 m, and are spaced at intervals of 0.5 m. Additionally, the horizontal baffle plate has a height of 0.15 m and a length of 1.95 m. The roughness elements consist of three sets of wooden cubes with dimensions of 0.2 × 0.1 × 0.1 m (arranged in 4 rows totaling 20), 0.15 × 0.075 × 0.075 m (arranged in 6 rows totaling 42), and finally, 0.05 × 0.05 × 0.05 m (arranged in 12 rows totaling 120), as illustrated in Figure 4a. The three sets of roughness elements are arranged in a staggered manner, with spanwise spacing of 0.4 m, 0.3 m, and 0.2 m, respectively, and streamwise spacing of 0.2 m, 0.15 m, and 0.05 m, respectively. In the wind tunnel coordinate system, the x-axis represents the streamwise direction, the y-axis represents the spanwise direction, and the z-axis represents the vertical direction.
According to the above experimental section arrangement, the wind shear in the experimental environment is expressed using an exponential rate:
U U h = Z Z h α
where Z is the height of the measuring point, Zh is the calibration height, U and Uh are the average velocity of each measuring point at the height of Z, Zh, which α is the profile index. According to the IEC-61400-1-2019 [36] standard for the wind shear index of the stable atmospheric boundary layer, the boundary layer index for simulation is α = 0.22, Zh = 0.4 m, and Uh = 8 m/s. The simulated real ABL thickness is about 400 m, scaled down to 1:400, and the thickness δ of the boundary layer in the wind tunnel is 1 m. Based on the above parameters, the dimensionless mean velocity profile and turbulence intensity profile of the neutral atmospheric boundary layer in wind tunnel experiments are obtained as shown in Figure 4b,c.
In order to eliminate the difference of magnitude between different data, the measurement data are transformed to the dimensionless form. and the wind speed is dimensionless according to the incoming wind speed Uh (8 m/s) at the calibration height:
  U * = U U h
where U* is the dimensionless horizontal velocity, and U is the measured wind speed.
The wake measurement scheme is illustrated in Figure 4a. There is a significant flow separation area near the wake behind the mountain, and the flow field in this area is complex, so wind turbines are not usually arranged in this area, therefore, the streamwise (x-direction) measurement range spans from 1 H to 10 H, encompassing a total of 10 measurement positions with a spacing of 1 H between each point. In the vertical (z-direction), measurements are taken from 0.125 H to 1.5 H, with 12 measurement positions set at intervals of 0.125 H. Similarly, in the spanwise (y-direction), measurements are conducted from 0 H to 1.5 H using 13 measurement positions spaced every 0.125 H. Consequently, a total of 1560 measurement points are established for wake analysis purposes. The speed at each point during experimentation is measured utilizing a Hanghua CTA-04 hot-wire anemometer model capable of sampling up to a maximum frequency of 100 KHz. The Y-shaped hot-wire probe features a resistance wire length measuring 2 mm and is securely affixed onto a three-dimensional measuring frame within the wind tunnel environment. The movement accuracy of the measuring frame is maintained at ±1 mm. The experiment employs a sampling frequency of 1000 Hz with a sampling time of 30 s, resulting in a data set comprising 30,000 data points per individual measurement position.
In wind tunnel experiments, the influence of Reynolds number on flow field characteristics cannot be neglected. In the present study, the Reynolds number is calculated based on the freestream velocity and the height H of the three-dimensional hill model, ranging approximately from 1.37 × 105 to 2.26 × 105. Although this Reynolds number range is notably lower than that typically encountered in actual atmospheric boundary layers, previous studies have demonstrated that flow characteristics gradually stabilize and become less sensitive to Reynolds number variations once it exceeds a critical value. The investigation by Chamorro et al. [37] revealed that mean velocity profiles become Reynolds number-independent at Re ≈ 4.8 × 104, while higher-order statistics such as Reynolds shear stress and turbulence intensity achieve independence at Re ≈ 9.3 × 104. The calculated Reynolds numbers in our experiments satisfy the minimum requirement for flow field stabilization in three-dimensional hill flow studies. Therefore, the experimental results can be considered statistically independent and reliable within the framework of this investigation.

3. Results and Discussion

3.1. Time-Averaged Characteristics of Wake Flow for TMLP

The velocity distribution of TMLP wakes’ vertical cross sections at various spanwise positions is illustrated in Figure 5a. From the Y = 0 H cross section (located directly behind the mountain), it can be observed that the minimum dimensionless velocity of TMLP is U* = 0.57, while that of STMM is U* = 0.63, exhibiting a difference of 10.5%.
When the streamwise distance of TMLP reaches 7 H, the lowest velocity returns to the incoming velocity at approximately the same height, with a measured value of 0.769. Consequently, the maximum streamwise distance of TMLP’s velocity deficit influence is around 7 H, while that of STMM’s velocity insufficiency is about 5 H. The maximum disparity between TMLP and STMM amounts to 0.149, representing a reduction of approximately 20.9% compared to STMM. This peak difference occurs at Y = 0 H cross section with a streamwise direction distance of 1 H and a height of 0.6 H. As the spanwise distance increases, the average speed of TMLP remains largely consistent with that of STMM within the range from Y = 0.75 H to Y = 1 H. The influence range of topographic structure on the mean velocity deficit of TMLP is therefore 2–3 times greater than that of STMM. Evidently, due to surface roughness effects (the geostrophic wind effect is not considered here) [38], TMLP exhibits lower mean velocities and a wider range of velocity deficit in its wake region, findings which align with An et al. [39] and Alinejad’s et al. [40] research results.
To investigate the velocity recovery of TMLP at different elevations, this paper introduces the mean velocity recovery per unit distance (with mountain height H as the reference distance) and the mean velocity recovery within a distance of 6 H from the mountain streamwise direction is calculated using an equation, as follows:
∆ u = U n + 1 H * − U n H *
The mean velocity recovery per unit distance at different heights at Y = 0 H is illustrated in Figure 6a. The ∆ u of TMLP decreases as the height and streamwise distance increase. Within the height range below 0.6 H, there is a relatively large velocity recovery of TMLP observed at almost all distances, with the maximum value occurring in an area with a height of 0.4 H and a streamwise distance of 1 H to 2 H, reaching a peak value of 0.119. In the height range from 0.6 H to 1 H, the velocity recovery does not simply decrease with increasing streamwise distance; instead, significant fluctuations are observed.
The results indicate that turbulence’s unstable structure in the wake significantly affects velocity recovery within this height range, yet TMLP still exhibits greater overall velocity recovery compared to STMM. Above a height of 1 H, TMLP consistently demonstrates smaller velocity recovery than STMM. The boundary line at 1 H marks a significant change in the magnitude relationship of velocity recovery on either side. This is primarily attributed to the topographic characteristics of TMLP, which decrease the mean velocity in the wake region and increase the turbulence intensity. Consequently, increased turbulence intensity promotes streamwise velocity recovery to some extent. Notably, at a height of 1.5 H, there is a remarkable increase in STMM’s velocity recovery due to the mountain’s substantial speed-up effect on the wake after the incoming flow traverses its windward surface. The speed-up height will vary depending on the slope and surface roughness of the mountain, which is known as the wind speed-up effect [17,20,21,24]. Additionally, it has been observed that the speed-up effect of TMLP occurs at a relatively low height of 1.375 H due to constant hindrance from the complex terrain structure when climbing through the windward surface. This not only hinders the acceleration effect but also reduces the height. Figure 6b illustrates the mean velocity recovery at different positions at Y = 1 H. It can be observed that there are minimal differences in velocity recovery between various positions of TMLP and STMM, with an average fluctuation around 0.015 as streamwise distance increases. This pattern is similar to variations seen in mean velocity at these positions. The research findings indicate that TMLP enhances wake velocity recovery below mountain height but also diminishes the speed-up effect.

3.2. Turbulence Characteristics for TMLP

3.2.1. Characteristics of Streamwise Turbulence Distribution

Figure 7a shows the turbulence intensity distribution of TMLP wakes’ vertical cross sections at various spanwise positions. It can be observed that as the streamwise distance increases, the turbulence of TMLP gradually diminishes. However, with increasing height, the turbulence initially rises and then declines. The stepped structure of TMLP exerts a more significant disturbance on the airflow, resulting in the turbulence intensity of TMLP being consistently higher than that of STMM at corresponding positions across all cross-sections. When the spanwise distance extends to Y = 1 H, the average turbulence intensity of TMLP is still 0.88% higher than that of STMM. At the Y = 0 H cross-section, the difference in turbulence intensity is very significant, with a maximum value of 0.313 for TMLP and 0.254 for STMM. The average turbulence intensity of TMLP is 2.41% higher than that of STMM. Within the range of Y = 0 H to Y = 0.5 H in the spanwise distance of TMLP, there is no significant change in the distribution range of turbulence intensity, and the high turbulence intensity region is still large. As the spanwise distance further increases, the distribution range of high turbulence intensity decreases significantly. In areas with heights below 1.1 H, TMLP always has higher turbulence intensity.
It is evident that the topographic structure of TMLP influences the turbulence distribution, and such differences in turbulence can significantly affect the operation of wind turbines. Therefore, further analysis of the turbulent structure within the wake field of TMLP is necessary.

3.2.2. The Time–Frequency Characteristics of Turbulent Structures

The turbulence exhibits local characteristics at both temporal and spatial scales, and the wavelet transform can effectively capture the time–frequency properties of temporal signals, enabling further analysis of the structural features of turbulence [41]. Therefore, in this study, we employ a continuous wavelet transform to investigate the time–frequency characteristics of TMLP fluctuating velocity. The Mexican hat wavelet function is chosen as it aptly represents the local attributes of signals in both time and frequency domains, making it suitable for analyzing fluctuation patterns. The sampling frequency utilized in this research is 1000 Hz, while the scaling factor (a) is determined as an equidistant sequence ranging from 0.5 to 70 with a tolerance level of 0.1. By considering the relationship between actual frequency (Fa) and scaling factor: Fa = Fc·fs/a, we determine that Fa ranges from 500 Hz to 3.57 Hz; here, Fc denotes the wavelet center frequency associated with the mother wave function which has been set at 0.25 Hz.
The results of the continuous wavelet analysis are presented in Figure 8, illustrating the analysis outcomes of TMLP and STMM at Y = 0 H, X = 1 H, and heights of 0.1 H, 0.5 H, and 1 H, respectively. It is evident that TMLP exhibits distinct quasi-periodic behavior at each height with a longer period as the frequency decreases. The red and blue bands represent interactions among coherent vortex structures; a positive slope indicates the merging of small-scale structures into larger ones while a negative slope signifies the breakup of relatively large structures [42]. From an energy transfer perspective, this cascade phenomenon and its reverse process appear to be more pronounced for frequencies below 100 Hz. At a height of 0.1 H, TMLP demonstrates higher energy amplitudes across all frequency bands compared to STMM; particularly around the frequency range of approximately 10 Hz where energy fluctuations are more intense—precisely when both flow types enter the inertia subrange—indicating greater turbulent kinetic energy for TMLP. When the frequency continues to increase, the intensity of TMLP’s energy remains higher than that of STMM. Consequently, TMLP exhibits a greater abundance of small-scale turbulent structures. At a height of 0.5 H, both types of mountains experience an increase in energy fluctuations, with the maximum energy value occurring at this position for both cases. Although TMLP’s maximum energy value appears in the low-frequency range, its occurrence lacks obvious regularity compared to the clearly periodic energy fluctuation near 10 Hz at 0.1 H. However, this fluctuation range is larger, confirming that the greatest impact of TMLP on wake turbulence is in the middle of the mountain. At a height of 1 H, while there is lower energy fluctuation compared to 0.5 H, it still surpasses that observed at 0.1 H. The two mountains continue to exhibit relatively evident periodicity in their energy fluctuations at this height, particularly within a frequency band around 10 Hz. The analysis above reveals the presence of a prominent and periodic turbulent structure with significant energy fluctuations around the frequency range of 10 Hz in the time–frequency plots of TMLP at various heights. Additionally, the frequency band between 10 and 150 Hz indicates a higher presence of small-scale turbulent structures within TMLP’s turbulence. Based on previous calculations regarding turbulence scale, it can be inferred that the turbulence scale corresponding to a frequency of 10 Hz aligns closely with TMLP’s characteristic scale. Consequently, this particular turbulence structure appears regularly with a period of approximately 0.5 s, signifying its status as a prominent coherent structure in TMLP’s wake. Furthermore, the turbulence scale associated with a frequency of 150 Hz corresponds to the stepped structure present on TMLP’s surface. In summary, energy fluctuations at different heights of TMLP are more intense than STMM, and there are more small-scale turbulent structures in the wake of TMLP, and the wake of TMLP contains an obvious coherent turbulent structure, which appears in a certain quasi-periodic regularity. The scale of the turbulent structure of TMLP is related to the scale of the mountain and its surface topographic features.

3.2.3. The Impact of Topographical Features on Turbulent Structures

In order to comprehend the turbulent structure of the wake of TMLP, it is imperative to analyze the fluctuating wind speed in the frequency domain for a comprehensive understanding of said turbulent structure. Figure 9a–c represent the power spectral density of fluctuating velocity at heights of 0.1 H, 0.5 H, and 1 H, respectively. From Figure 9, it becomes evident that there is a significant increase in energy contained within the fluctuating wind of TMLP as height increases, primarily due to the vertical velocity gradient resulting in heightened fluctuations in velocity and consequently amplifying the turbulent kinetic energy present within said fluctuating wind. The observed spectra at different heights exhibit classical power-law characteristics with an exponent value of -5/3, indicating that turbulence has reached full development.
The TMLP demonstrates slightly lower energy in the energy-containing range compared to the other two flows at heights of 0.1 H and 0.5 H, attributed to the attenuation of large-scale structures as the incoming flow interacts with the intricate surface of the TMLP. However, when the height is 1 H, the energy within TMLP’s energy-containing range becomes almost equivalent to that of the other two flows. The energy of the energy-containing range below the mountain height of TMLP is primarily influenced by terrain characteristics, thus leading to this conclusion. In terms of the inertial subrange, TMLP’s frequencies reaching this range at different heights are approximately 17.5 Hz, 11.6 Hz, and 7.6 Hz, respectively—indicating a negative correlation between height and frequency in reaching this subrange for TMLP’s wake. Simultaneously, this decrease in frequency signifies an increase in average spatial scale of turbulence within TMLP’s wake. On the other hand, STMM frequencies reaching the inertial subrange at different heights are about 9.6 Hz, 7.1 Hz, and 7.6 Hz, respectively. It is evident that the frequency of TMLP is significantly lower than that of STMM due to the topographic structure of TMLP, which diminishes the spatial scale of turbulence and consequently leads to an increase in frequency. Within the current frequency range, the spectra at different heights have not yet reached the dissipation range. However, it can be observed that the slope of TMLP’s high-frequency region has slightly decreased, and there is a significant decrease in energy dissipation rate at various heights, up to 40%. This phenomenon deviates from Kolmogorov’s second hypothesis regarding the −5/3 power law in inertial subrange. The reason behind this occurrence lies in the fact that when incoming flow passes through TMLP, it generates numerous small-scale structures. As large-scale wake structures transform into small-scale structures through turbulent cascade action and mix with terrain-generated small-scale structures, they enhance turbulent kinetic energy within this specific scale range. According to Taylor’s frozen hypothesis, the calculated energy enhancement scale is approximately 0.025 m, which closely aligns with the stepped structure scale of TMLP, thereby substantiating that the energy characteristics observed in the high-frequency range of TMLP are attributed to its terrain features. The high-frequency region of STMM exhibits a pronounced downward trend, indicating an earlier transition from the inertial subrange to the dissipation range. The reduced extent of the inertial subrange may be attributed to the rectifying effect exerted by the ideal mountain on turbulent flow. Additionally, TMLP demonstrates relatively stable energy platform regions in its spectra at altitudes of 0.1 H and 0.5 H, encompassing frequency ranges of 105–151 Hz and 197.8–262.5 Hz, respectively. These platform regions signify that energy within these frequency ranges does not decay but maintains a relatively stable trend over time. This phenomenon is absent in the other two types of flow, with the corresponding scale range for this platform region being approximately 0.015–0.04 m; coinciding with TMLP’s stepped structure scale once again, confirming its significant enhancement effect on turbulent structures of similar scales, and resulting in a frequency band where energy remains stable during turbulent transport processes. Guo et al. [43] also observed similar platform regions when analyzing wind turbine wake power spectra. In summary, TMLP reduces turbulent kinetic energy within its energy-containing range to some extent. However, the complex terrain features expand the frequency range of the inertial subrange and enhance energy in high-frequency regions during cascading transport processes. The spatial scale corresponding to this enhanced frequency region aligns with key structural features of terrain, suggesting that terrain characteristics have a substantial impact on turbulent energy [44].

4. Conclusions

Aiming at the influence mechanism of the loess plateau topography on wind turbines, the time-averaged and turbulent characteristics of the wake field of the loess plateau topography are studied through wind tunnel experiments. The following conclusions can be drawn:
The time-averaged flow analysis reveals a velocity deficit of approximately 25.8% in the wake of the Terrain Model of the Loess Plateau (TMLP). This deficit extends streamwise over a region spanning 6 H–8 H downstream of the mountain. Despite the significant wind speed reduction induced by TMLP, rapid mean velocity recovery is observed within a vertical range of 1 H and a streamwise distance of 1 H and 6 H. However, beyond 1 H, in height, TMLP exhibits negligible influence on velocity recovery due to its intricate stepped topography, which suppresses wind acceleration mechanisms near the summit.
For turbulence characteristics, the maximum turbulence intensity of TMLP reaches 0.313, with a larger range of high turbulence intensity observed. The peak turbulence intensity occurs at a height of 0.6 H and a streamwise distance of 1 H, specifically in the middle behind the mountain rather than in the near-ground area. Wavelet analysis results also indicate that the mountain’s impact on energy fluctuation is primarily concentrated in its central region. Furthermore, wavelet analysis reveals an initial increase followed by a decrease in both fluctuation and amplitude of energy as height increases. TMLP exhibits significant quasi-periodicity in energy fluctuations around a frequency of approximately 10 Hz, corresponding to a period of about 0.5 s. Additionally, TMLP demonstrates higher energy fluctuations at various positions with an average higher about 31.1%, indicating elevated turbulent kinetic energy levels compared to other locations studied. Moreover, distinct turbulent coherent structures are evident within TMLP’s turbulence field, exhibiting scales like those found within TMLP terrain features (approximately 0.4 m). Notably, numerous high-frequency small-scale structures ranging from approximately 0.015 to 0.04 m are generated by TMLP and resemble the scale of its ladder structure; these small-scale structures contribute to reducing energy dissipation within the high-frequency range (up to about 40%) present in TMLP’s turbulent power spectral density inertial subrange.
Although this experiment quantitatively investigated the influence of loess plateau topography on both time-averaged and turbulent characteristics in the wake flow, several limitations challenge the generalizability of the results. Firstly, inflow simplification: the steady-state shear boundary layer generated by spires and roughness elements in the wind tunnel differs from real atmospheric non-stationary turbulence, with incomplete turbulence structures and neglected thermal coupling, potentially biasing key parameter predictions (e.g., turbulence kinetic energy transport). Future studies should integrate multi-physics simulations with field observations to validate these parameters. Secondly, geometric simplification: while the terraced single-hill model reveals flow modulation mechanisms induced by abrupt topographic transitions, its isolated morphology fails to capture the spatial complexity of real mountainous terrains. Additionally, wind tunnel scaling effects distort terrain–boundary layer coupling and omit thermo-vegetation interactions. Multi-scale parameterization and coupled validation frameworks are required to enhance cross-scenario predictability. Thirdly, discrete hot-wire measurements: limited spatial resolution may omit fine-scale turbulence signals, leading to inaccuracies in critical metrics (e.g., turbulent kinetic energy dissipation rate) and energy spectrum analysis, while impairing the resolution of intermittency and coherent structure evolution. Subsequent experiments should increase spatial sampling density or incorporate Particle Image Velocimetry (PIV) for spatially continuous turbulence statistics.
In summary, the wind tunnel experiment results on the loess plateau terrain indicate that the presence of high turbulence characteristics in this area will expedite wake recovery of wind turbines, while the annual power generation of single wind turbines located in this region will decrease due to a reduction in mean wind speed. Therefore, further research is still required to investigate the impact of turbulent structural characteristics resulting from topographic features on wind turbine power.

Author Contributions

Conceptualization, Y.M. and S.L.; methodology, Y.M. and S.L.; software, Y.M.; validation, Y.M. and S.L.; formal analysis, Y.M. and Z.G.; investigation, Y.M., X.G. and Q.M.; writing—original draft preparation, Y.M.; writing—review and editing, Y.M.; Supervision, D.L. and S.L.; project administration, S.L.; funding acquisition, S.L. and Z.G. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by Young Doctor Support Project from Department of Education of Gansu Province, China (2024QB-034), China Postdoctoral Science Foundation (Nos. 2024M750568 and 2023M742229), the Key Research and Development Program of Gansu Province—Industrial Project under Grant (No. 25YFGA034) and National Natural Science Foundation of China (Nos. 12302301 and 52166014).

Data Availability Statement

The data presented in this study are available on request from the corresponding author.

Acknowledgments

The authors would like to express sincere appreciation to the editor and the anonymous reviewers for their valuable comments and suggestions for improving the presentation of the manuscript.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. New installed capacity in China in 2023: (a) new installed capacity in various regions of China from 2022 to 2023; (b) the proportion of new additions in various regions of China (NE for Northeast China; NC for North China; EC for East China; NW for Northwest China; SW for Southwest China; MS for Central South China).
Figure 1. New installed capacity in China in 2023: (a) new installed capacity in various regions of China from 2022 to 2023; (b) the proportion of new additions in various regions of China (NE for Northeast China; NC for North China; EC for East China; NW for Northwest China; SW for Southwest China; MS for Central South China).
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Figure 2. Landform and atmospheric boundary layer characteristics of the loess plateau: (a) wind farm in loess plateau; (b) boundary layer of the loess plateau.
Figure 2. Landform and atmospheric boundary layer characteristics of the loess plateau: (a) wind farm in loess plateau; (b) boundary layer of the loess plateau.
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Figure 3. Experimental model: (a) Terrain Model of the Loess Plateau (TMLP); (b) Standard Three-dimensional Mountain Model (STMM).
Figure 3. Experimental model: (a) Terrain Model of the Loess Plateau (TMLP); (b) Standard Three-dimensional Mountain Model (STMM).
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Figure 4. Experiment scheme and experiment environment: (a) experiment scheme; (b) dimensionless mean velocity profile; (c) turbulence intensity profile; (d) photograph of wind tunnel experiment.
Figure 4. Experiment scheme and experiment environment: (a) experiment scheme; (b) dimensionless mean velocity profile; (c) turbulence intensity profile; (d) photograph of wind tunnel experiment.
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Figure 5. Mean velocity distribution of vertical cross-section at different spanwise positions: (a) TMLP; (b) STMM.
Figure 5. Mean velocity distribution of vertical cross-section at different spanwise positions: (a) TMLP; (b) STMM.
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Figure 6. Recovery of mean velocity per unit distance at different heights: (a) recovery of mean velocity at different positions of cross-section Y = 0 H; (b) recovery of mean velocity at different positions of cross-section Y = 1 H.
Figure 6. Recovery of mean velocity per unit distance at different heights: (a) recovery of mean velocity at different positions of cross-section Y = 0 H; (b) recovery of mean velocity at different positions of cross-section Y = 1 H.
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Figure 7. Turbulence distribution of vertical cross-sections at different spanwise positions: (a) TMLP; (b) STMM.
Figure 7. Turbulence distribution of vertical cross-sections at different spanwise positions: (a) TMLP; (b) STMM.
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Figure 8. Time–frequency plot of fluctuating wind speed.
Figure 8. Time–frequency plot of fluctuating wind speed.
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Figure 9. The fluctuating velocity power density spectra of the incoming flow, TMLP wake, and STMM wake at three height positions: (a) at a height of 0.1 H; (b) at a height of 0.5 H; (c) at a height of 1 H.
Figure 9. The fluctuating velocity power density spectra of the incoming flow, TMLP wake, and STMM wake at three height positions: (a) at a height of 0.1 H; (b) at a height of 0.5 H; (c) at a height of 1 H.
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Ma, Y.; Li, S.; Li, D.; Gao, Z.; Guo, X.; Ma, Q. Study on the Wake Characteristics of the Loess Plateau Terrain Based on Wind Tunnel Experiment. Energies 2025, 18, 958. https://doi.org/10.3390/en18040958

AMA Style

Ma Y, Li S, Li D, Gao Z, Guo X, Ma Q. Study on the Wake Characteristics of the Loess Plateau Terrain Based on Wind Tunnel Experiment. Energies. 2025; 18(4):958. https://doi.org/10.3390/en18040958

Chicago/Turabian Style

Ma, Yulong, Shoutu Li, Deshun Li, Zhiteng Gao, Xingduo Guo, and Qingdong Ma. 2025. "Study on the Wake Characteristics of the Loess Plateau Terrain Based on Wind Tunnel Experiment" Energies 18, no. 4: 958. https://doi.org/10.3390/en18040958

APA Style

Ma, Y., Li, S., Li, D., Gao, Z., Guo, X., & Ma, Q. (2025). Study on the Wake Characteristics of the Loess Plateau Terrain Based on Wind Tunnel Experiment. Energies, 18(4), 958. https://doi.org/10.3390/en18040958

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