**4.3. A wind farm in a stable boundary layer**

Of special interest for wind-energy applications is the study of the stable boundary layer, which typically develops during the night in mid-latitudes, and also during the day in cold regions (e.g., polar regions). Under these conditions, the surface is colder than the surrounding air, the flow stratifies and turbulence is generated by shear and destroyed by dissipation and negative buoyancy. Near the top of the boundary layer, the wind can become super-geostrophic and form the so-called low-level jet. Moreover, the Coriolis effect associated with planetary rotation leads to a change of wind direction with height. This creates an additional lateral shear, which is considerable for large-sized wind turbines. As a result, compared with daytime boundary layers, stable boundary layers provide not only larger energy potential, but also larger structural fatigue loads associated with strong vertical and lateral shear.

In order to reduce uncertainties when studying the effects of a wind farm on a SBL, it is important to start with a SBL case, without wind turbines, that has been well established and tested with LES. Such case was launched for an LES inter-comparison study as part of the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS) initiative [11]. It represents a typical quasi-equilibrium moderately SBL, similar to those commonly observed over polar regions and equilibrium nighttime conditions over land in mid-latitudes. The GABLS case is used here as a baseline case (no-turbine case).

18 Computational and Numerical Simulations

results from simulations using the ALM.

distance of x/D=20.

and lateral shear.

**4.3. A wind farm in a stable boundary layer**

**Figure 14.** Kinematic shear stress at different downwind distances. ◦: results from wind-tunnel measurements; solid line:

Figure 14 compares the measured and simulated total shear stress (summation of the resolved part and the SGS part) at selected locations. Again results obtained using the ALM are in good agreement with the wind-tunnel measurements. It is clear that the turbine introduces stresses that are locally much larger in magnitude than the stresses in the incoming flow. In the near-wake region, a region above the turbine hub bears large negative stress and a lower region bears large positive stress. As the wake grows with downwind distance, the relative change becomes smaller. Also, similar to the other turbulence statistics, the change in kinematic stress with respect to the incoming flow is not negligible until the far-wake at a

Of special interest for wind-energy applications is the study of the stable boundary layer, which typically develops during the night in mid-latitudes, and also during the day in cold regions (e.g., polar regions). Under these conditions, the surface is colder than the surrounding air, the flow stratifies and turbulence is generated by shear and destroyed by dissipation and negative buoyancy. Near the top of the boundary layer, the wind can become super-geostrophic and form the so-called low-level jet. Moreover, the Coriolis effect associated with planetary rotation leads to a change of wind direction with height. This creates an additional lateral shear, which is considerable for large-sized wind turbines. As a result, compared with daytime boundary layers, stable boundary layers provide not only larger energy potential, but also larger structural fatigue loads associated with strong vertical

In order to reduce uncertainties when studying the effects of a wind farm on a SBL, it is important to start with a SBL case, without wind turbines, that has been well established and tested with LES. Such case was launched for an LES inter-comparison study as part of the To study the effect of a wind farm on the GABLS case [59], a V112-3.0MW wind turbine is "immersed" (using the ALM) in the GABLS domain such that the wind-turbine center is located at *xc* = 80 m, *yc* = 280 m, and *zc* = 119 m (hub height). This wind turbine has a rotor diameter of *D* = 112 m, and rotates at 8 RPM, corresponding to a tip speed ratio of approximately 7 for an optimal performance at a free-stream wind speed of approximately 6 m/s. Three blades consist of Risø-P airfoil. Like in the original GABLS case, the vertical height of the computational domain is *Lz* = 400 m. The domain size in the y-direction is fixed to be *Ly* = 5*D* = 560 m, and two x-direction dimensions corresponding two typical wind-turbine spacings that are studied: (i) *Lx* = 8*D* = 896 m (the corresponding LES is abbreviated as the 8D case); (ii) *Lx* = 5*D* = 560 m (the corresponding LES is abbreviated as the 5D case). Periodic boundary conditions are applied horizontally to simulate an infinitely large wind farm. It should be noted that the baseline case (without turbines) attains a quasi-steady state in 8 - 9h [10, 11]. Therefore, in order to examine the wind-turbine effects relative to the baseline case, the wind turbine is only introduced in the last hour of simulation.

Figure 15 shows the time evolutions of the boundary height, the surface momentum flux and the surface buoyancy flux. Data are saved each 15 seconds. When wind turbines are installed, there exists a significant increase of the boundary-layer height. Specifically, over the last 15 min, the 8D case yields a SBL height of approximately 225 m (increased ≈ 28%), and the 5D case yields a SBL height of approximately 250 m (increased ≈ 43%). The current simulation results support the tendency that smaller wind-turbine spacing yields larger boundary-layer increases. Further, the magnitudes of the surface momentum flux and the surface buoyancy flux decrease with time. Specifically, over the last 15 min, the 8D case yields a momentum-flux magnitude of approximately 0.05 m2/s2 (reduced ≈ 30%), corresponding to a friction velocity of 0.23 m/s; the 5D case yields a momentum-flux magnitude of approximately 0.043 m2/s2 (reduced ≈ 40%), corresponding to a friction velocity of 0.21 m/s. The 8D case yields a buoyancy-flux magnitude of approximately −3.8 × <sup>10</sup>−<sup>4</sup> <sup>m</sup>2/s3 (reduced ≈ 15%), corresponding to a heat flux of −13.5 W/m2; the 5D case yields a buoyancy-flux magnitude of approximately −3.2 × <sup>10</sup>−<sup>4</sup> <sup>m</sup>2/s3 (reduced ≈ 28%), corresponding to a heat flux of −11.4 W/m2. It is interesting to note that it takes some time before wind turbines are able to affect surface fluxes. This delay in the change of the fluxes is likely associated to the time it takes for the multiple wakes to expand horizontally and affect the entire surface area. Overall, the reduced surface heat flux phenomenon obtained from the current research is consistent with the results from low-resolution wind-farm simulations performed by [7]. The reduced surface momentum and heat flux magnitudes indicate a reduction in the level of turbulent mixing and transport near the surface. Regarding the overall thermal-energy budget, this reduced heat flux is consistent with the increase of air temperature in the boundary layer as shown later in figure 17(b).

Figure 16(a) shows the formation (initial stages) of blade-induced three-dimensional helicoidal tip vortices, detected using |*ω*|-definition (0.3 times of the maximum vorticity, 35) in the 5D case. Due to the strong shear and non-uniformity of the incoming boundary-layer flow, helicoidal vortices are stretched as they travel faster at the top tip level compared with

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the bottom tip level. Figure 16(b) shows the kinetic energy power spectrum sampled over the last 15 min at 0.5D downwind of the wind-turbine top tip height. Consistent with experimental results [e.g., 19], a clear peak, coinciding with three times the frequency of rotor rotation, appears in the near-wake region. The power spectra also show the buoyancy frequency as well as the inertial subrange. As expected, the power spectrum drops at a scale

Large-eddy simulation of turbulent flows with applications to atmospheric boundary layer research

**Figure 17.** Vertical distribution of mean (a) x-direction velocity U and y-direction velocity V, and (b) potential temperature. Gray

Figure 17(a) shows the mean profiles of wind speeds, and figure 17(b) shows the mean potential temperatures. In agreement with other studies [e.g., 27], when wind turbines are installed, there is a significant increase of the boundary height. The baseline case clearly shows a super-geostrophic nocturnal jet peaking near the top of the boundary layer. However, the extraction of energy by the turbines, leads to a distortion of the velocity field (compared with the baseline case) and an elimination of the low-level jet in the wind farm simulations. Also, as expected, the closer the distance between the wind turbines, the larger extraction of kinetic energy from the mean flow. Further, compared to the potential temperature profile from the baseline case, blade motions enhance the vertical mixing and transfer more thermal energy from higher levels to lower levels. This leads to an increase of temperature below the top tip level and a decrease between the tip-height and the SBL height. Interestingly, the two wind-turbine simulations deliver almost identical potential temperature profiles, which indicates that wind-turbine effects on scalars are relatively

A typical design lifetime of modern wind turbines is 20 years. However, many have been dismantled after only a few years of service owing to unsuccessful designs and siting arrangements. The primary cause of failure is that, in a wind farm, the effects of accumulated wakes can lead to increased fatigue loads on wind turbines. Here, study focuses on the turbulent velocity fluctuation, which is directly relevant to the fatigue load. Figure 18 shows vertical profiles of the turbulent kinetic energy for selected downwind locations (*x*/*D* = 1, 2, 3, and 4). The baseline case results are consistent with other GABLS cases [10]. In the current scenario, turbulence in the wake is notably persistent because each turbine generates turbulence which compensates for the tendency of decay. When wind

dash dotted lines show Monin-Obukhov similarity curves. Figure is modified from Lu and Porté-Agel [59].

corresponding to the resolution of the LES.

(a) (b)

weaker than their effects on momentum.

**Figure 15.** Evolutions of (a) stable boundary-layer height; (b) surface momentum flux; and (b) surface buoyancy flux. Solid lines: results obtained from the baseline case; dashed lines: results obtained from the 8D case; dash dotted lines: results obtained from the 5D case. Figure is modified from Lu and Porté-Agel [59].

**Figure 16.** (a) Iso-surface of vorticity showing the three-dimensional structures of a instantaneous field of the 5D case at t=30s; (b) Power spectrum sampled at the location (*xc* + 0.5*D*, *yc* , *zc* + 0.5*D*) over the last 15min of the 5D case. Figure is modified from Lu and Porté-Agel [59].

the bottom tip level. Figure 16(b) shows the kinetic energy power spectrum sampled over the last 15 min at 0.5D downwind of the wind-turbine top tip height. Consistent with experimental results [e.g., 19], a clear peak, coinciding with three times the frequency of rotor rotation, appears in the near-wake region. The power spectra also show the buoyancy frequency as well as the inertial subrange. As expected, the power spectrum drops at a scale corresponding to the resolution of the LES.

20 Computational and Numerical Simulations

(a)

(b) (c)

from the 5D case. Figure is modified from Lu and Porté-Agel [59].

(a) (b)

from Lu and Porté-Agel [59].

×

**Figure 15.** Evolutions of (a) stable boundary-layer height; (b) surface momentum flux; and (b) surface buoyancy flux. Solid lines: results obtained from the baseline case; dashed lines: results obtained from the 8D case; dash dotted lines: results obtained

**Figure 16.** (a) Iso-surface of vorticity showing the three-dimensional structures of a instantaneous field of the 5D case at t=30s; (b) Power spectrum sampled at the location (*xc* + 0.5*D*, *yc* , *zc* + 0.5*D*) over the last 15min of the 5D case. Figure is modified

**Figure 17.** Vertical distribution of mean (a) x-direction velocity U and y-direction velocity V, and (b) potential temperature. Gray dash dotted lines show Monin-Obukhov similarity curves. Figure is modified from Lu and Porté-Agel [59].

Figure 17(a) shows the mean profiles of wind speeds, and figure 17(b) shows the mean potential temperatures. In agreement with other studies [e.g., 27], when wind turbines are installed, there is a significant increase of the boundary height. The baseline case clearly shows a super-geostrophic nocturnal jet peaking near the top of the boundary layer. However, the extraction of energy by the turbines, leads to a distortion of the velocity field (compared with the baseline case) and an elimination of the low-level jet in the wind farm simulations. Also, as expected, the closer the distance between the wind turbines, the larger extraction of kinetic energy from the mean flow. Further, compared to the potential temperature profile from the baseline case, blade motions enhance the vertical mixing and transfer more thermal energy from higher levels to lower levels. This leads to an increase of temperature below the top tip level and a decrease between the tip-height and the SBL height. Interestingly, the two wind-turbine simulations deliver almost identical potential temperature profiles, which indicates that wind-turbine effects on scalars are relatively weaker than their effects on momentum.

A typical design lifetime of modern wind turbines is 20 years. However, many have been dismantled after only a few years of service owing to unsuccessful designs and siting arrangements. The primary cause of failure is that, in a wind farm, the effects of accumulated wakes can lead to increased fatigue loads on wind turbines. Here, study focuses on the turbulent velocity fluctuation, which is directly relevant to the fatigue load. Figure 18 shows vertical profiles of the turbulent kinetic energy for selected downwind locations (*x*/*D* = 1, 2, 3, and 4). The baseline case results are consistent with other GABLS cases [10]. In the current scenario, turbulence in the wake is notably persistent because each turbine generates turbulence which compensates for the tendency of decay. When wind

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previous GABLS LES studies [10, 11]. Also in agreement with other studies [19], our results show that when wind turbines are immersed in a non-uniform boundary-layer flow that already bears momentum exchanges (negative flux), the magnitude of the negative flux is largest at the top-tip level due to an enhanced vertical mixing of momentum induced by the turbine wakes at that height. This strong mixing and entrainment of relatively warm air (with higher potential virtual temperature) from the free atmosphere, induced by the wind-turbine wakes, leads also to a strong enhancement of the negative heat flux at the top-tip level. It is also important to note that, consistent with the results as shown in figure 15, figures 19(a) and 19(b) also show that the magnitude of the surface momentum and heat fluxes undergo substantial reductions with respect to the no-turbine base case. This reduction is larger than 30% for the surface momentum flux, and larger than 15% for the surface heat flux. Overall, the results presented here indicate that large wind-farms have the potential to impact local

Large-eddy simulation of turbulent flows with applications to atmospheric boundary layer research

This chapter gives an overview of our recent research efforts aimed at improving parameterizations and making LES a more reliable technique to planetary boundary layer research. Large-eddy simulation has shown its capabilities in simulations of high-Reynolds-number flows that, at present, could not be solved by DNS. It has been proved to be very useful in understanding the turbulent exchange in atmosphere and ultimately in parameterization improvement in traditional meteorological models; and also it assists theoreticians and weather/climate modelers with reliable information about the averaged vertical structure of the ABL, as well as with better estimations of key ABL parameters. The outlook for using LES in planetary boundary layer modeling is very good. The number of

The need for accurate simulation has provided much of the impetus for the development of numerical methods in turbulence research. The proposed new nonlinear formulation has been examined in LESs of several types of turbulent flows. The new SGS closure presents a significant improvement with respect to simple eddy-viscosity/diffusivity-type models, also delivers more accurate representation of the energy cascade in the inertial sub-range.

Possible future model modifications of the new SGS closure include the development of dynamic and scale-dependent dynamic procedures to optimize the values of the model coefficients using information of the resolved scales. Moreover, one could develop and assess more advanced modifications (e.g., one-equation models), which could offer alternatives to

Further, the next stage of wind-energy application will encompass more realistic physics and a variety of atmospheric conditions. These include the consideration of other inflow and surface boundary conditions, wind-farm configurations, and the effects of topography, air moisture, and the like. Future studies will use the LES framework to further study the effects of wind-farm size, atmospheric stability (neutral, convective and stable), topography, and wind-farm configuration. Also, there is a need for reliable coupling of LES with weather

models to account for the effects of large-scale atmospheric forcing.

meteorology.

**5. Prospects for the future**

high-quality LES studies is rapidly increasing.

relax some of the model assumptions.

**Figure 18.** Vertical distribution of turbulent kinetic energy (measured over the last 15 min) obtained from the baseline case (solid), the 8D case (dashed) and the 5D case (dash dotted) through the axis of the turbine at different downwind locations. Figure is modified from Lu and Porté-Agel [59].

**Figure 19.** Vertical distributions of (a) x-direction momentum flux and (b) buoyancy flux. Figure is modified from Lu and Porté-Agel [59].

turbines are placed in the boundary layer, turbulence is reduced below the turbine bottom and significantly enhanced in the wake region; this observation agrees with single turbine experimental results [19]. As revealed in other researches on wind-turbine wakes in shear flows including experiments [19, 92] and simulations [90], the large values of turbulence intensity are found at both the top-tip and bottom-tip levels, and the turbulence intensity above the hub-height is generally larger than that below the hub-height. It is argued that this is due to the enhancement in mean shear at the top-tip level.

Besides extracting kinetic energy and generating turbulence, wind-turbine blade motions also mix fluid parcels. The investigation of fluxes is of interest because local meteorology is considerably affected by the overall exchanges of momentum, heat, moisture, etc. Figure 19 shows the vertical distributions of mean total (resolved part plus SGS part) vertical flux of axial momentum and heat. The results obtained from the baseline case are consistent with previous GABLS LES studies [10, 11]. Also in agreement with other studies [19], our results show that when wind turbines are immersed in a non-uniform boundary-layer flow that already bears momentum exchanges (negative flux), the magnitude of the negative flux is largest at the top-tip level due to an enhanced vertical mixing of momentum induced by the turbine wakes at that height. This strong mixing and entrainment of relatively warm air (with higher potential virtual temperature) from the free atmosphere, induced by the wind-turbine wakes, leads also to a strong enhancement of the negative heat flux at the top-tip level. It is also important to note that, consistent with the results as shown in figure 15, figures 19(a) and 19(b) also show that the magnitude of the surface momentum and heat fluxes undergo substantial reductions with respect to the no-turbine base case. This reduction is larger than 30% for the surface momentum flux, and larger than 15% for the surface heat flux. Overall, the results presented here indicate that large wind-farms have the potential to impact local meteorology.
