Intercomparison of Synthetic Inflow Turbulence Generation Methods for Large-Eddy Simulation Models in Thermally Driven Convective Boundary Layer Simulations

概要

SOLA, 2023, Vol. 19, 165−172, doi:10.2151/sola.2023-022

165

Intercomparison of Synthetic Inflow Turbulence Generation Methods
for Large-Eddy Simulation Models
in Thermally Driven Convective Boundary Layer Simulations
Takuto Sato and Hiroyuki Kusaka
Center for Computational Sciences, University of Tsukuba, Tsukuba, Japan
(Manuscript received 11 April 2023, accepted 1 June 2023)
Abstract  In this study, synthetic inflow turbulence generation methods developed in computational fluid dynamics
(CFD) and meteorological fields were applied to thermally driven convective boundary layer (CBL) simulations. Methods developed in the CFD field include the Reynolds stress Cholesky decomposition and digital filter-based method (DF
method), and the cell perturbation method (CPM) is a method developed in the meteorological field. Intercomparison
results show that both methods can reproduce turbulence in thermally driven CBLs when a proper driver region is ensured. The turbulence reproduced using the DF method in a thermally driven CBL has a shorter driver region than that
reproduced using CPM. However, CPM can be applied to a simulation without limiting the inflow boundary, although it
requires a longer driver region than the DF method. Therefore, it was confirmed that both methods have unique merits
that can be useful for downscaling from meteorological mesoscale models to microscale large-eddy simulation models.
Citation: Sato, T., and H. Kusaka, 2023: Intercomparison of synthetic inflow turbulence generation methods for largeeddy simulation models in thermally driven convective boundary layer simulations. SOLA, 19, 165−172, doi:10.2151/
sola.2023-022.

1. Introduction
Dynamical downscaling from meteorological mesoscale models (RANS models) to microscale models (large-eddy
simulation (LES) models) is an effective approach for improving the accuracy of simulations of the thermal environment and pollutant dispersion in urban areas (Xie 2011; Nakayama et al. 2012). Downscaling from RANS to LES
models requires the grid-scale turbulence of the LES models to be added to the mean flow fields obtained from the
RANS model simulation. Various methods have been proposed to achieve this, mainly in the field of computational
fluid dynamics (CFD) (Keating et al. 2004; Tabor and Baba-Armadi 2010; Wu 2017; Vesaturo et al. 2018; Plischka et al.
2022). Among these, synthetic inflow turbulence generation methods can potentially generate turbulence at a lower
computational cost compared to conducting additional simulations for turbulence generation.
One synthetic turbulence generation method developed in the CFD field is that based on the Reynolds stress Cholesky decomposition and digital filters (Xie and Castro 2008, hereafter DF method), which generates inflow turbulence
based on the Reynolds stress and integral length scale of turbulence. This method was first proposed for generating
inflow turbulence of wind speed, but was later extended to generate inflow turbulence with both wind speed and scalars
(Okaze et al. 2017a). Okaze et al. (2017b) considered the scalar temperature and performed a simulation in a stratified
wind tunnel, and the results obtained were in good agreement with the observations. Thus, the extended DF method
proposed by Okaze et al. (2017a, b) can potentially be applied to downscaling experiments.
The cell perturbation method (CPM) is a method developed in the meteorological field (Muñoz-Esparza et al. 2014).
This method does not generate turbulence at the inflow boundary; instead, it adds a potential temperature perturbation
to the area near the inflow boundary to trigger turbulence. Because this method does not restrict the inflow boundary,
it is suitable for meteorological simulations in which the inflow boundary conditions change spatiotemporally. This
method has also been applied to meteorological simulations of a real city (Lee et al. 2019) to confirm its effectiveness.
Muñoz-Esparza et al. (2015) compared the reproducibility of turbulence between the standard DF method and
CPM from simulations that assumed a neutral atmosphere. They showed that the standard DF and CPM could generate
sufficient turbulence when the appropriate driver regions were set, and that the DF method reproduced the turbulence
spectrum near the inflow boundary better than the CPM, while the CPM showed faster turbulence growth.
Compared to cases under a neutral atmosphere, cases in thermally driven convective boundary layers (CBLs) are
characterized by more pronounced turbulence generation owing to the occurrence of thermals. Therefore, the differences in the characteristics of turbulence generation methods remain unclear when assuming non-neutral atmospheric
conditions. In particular, the difference between the extended DF method and CPM in terms of the reproducibility of
Corresponding author: Hiroyuki Kusaka, Center for Computational Sciences, University of Tsukuba, Tennodai, Tsukuba, Ibaraki 305-8577,
Japan. E-mail: kusaka@ccs.tsukuba.ac.jp.
©The Author(s) 2023. This is an open access article published by the Meteorological Society of Japan
under a Creative Commons Attribution 4.0 International (CC BY 4.0) license (http://creativecommons.org/license/by/4.0).

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Sato and Kusaka, Intercomparison of Synthetic Inflow Turbulence Methods for CBL Simulations

turbulence in thermally driven CBLs is unclear.
In this study, we aimed to compare the reproducibility of turbulence in thermally driven CBLs between CPM and
the extended DF method. For this purpose, numerical simulations of idealized thermally driven CBLs were conducted
using both methods. The results of this study contribute to the development of new options for inflow turbulence generation methods for downscaling from mesoscale meteorological models to microscale LES models.

2. Method
The LES model used in this study was City-LES (Ikeda et al. 2015), a meteorological LES model developed at the
Center for Computational Sciences, University of Tsukuba, that can explicitly resolve buildings based on three-dimensional non-hydrostatic Boussinesq approximation equations. This model is suitable for this study because it considers
atmospheric stratification. The sub-grid scale model used in this study was the TKE 1-equation model (Deardorff 1980).
A fifth-order upwind scheme was used as the discretization scheme for advection terms (Skamarock et al. 2008).
Three numerical experiments were conducted: (1) an experiment in which periodic boundary conditions were
imposed on the lateral boundaries (PER), (2) an experiment in which inflow turbulence was generated based on the
extended DF method, and (3) an experiment in which the potential temperature perturbation was generated based on
CPM. The result of the PER was used as a reference, and the results of the experiments using the extended DF method
and CPM were compared in terms of the reproducibility of turbulence, similar to that of PER.
The common settings for the three experiments were as follows. The horizontal and vertical resolutions were set to
40 m. The number of grid points in the flow direction (x), spanwise direction (y), and vertical direction (z) were set as (nx,
ny, nz) = (412, 256, 62). Time integration was performed for two hours, and the last 10 minutes were used for analysis.
The time-average for the vertical profiles and spectrum estimation were performed using the results of this 10 min. The
initial wind speed was 5 m/s above 200 m and logarithmically decelerated at lower altitudes. The potential temperature
gradient Γ was set to Γ = 0.004 K/m for all vertical layers. An idealized city with the roughness parameter z0 = 1.0 m
was used as the bottom boundary condition of momentum. Momentum fluxes were calculated using the bulk method.
For the bottom boundary condition of heat, a sensible heat flux of 100 W/m2 was provided for the entire region. The top
boundary condition of the momentum was the free-slip condition with a damping layer 1,500 m above the surface. The
top boundary condition of the potential temperature was fixed at the initial potential temperature.
The extended DF method generates inflow turbulence based on filtered random numbers to satisfy spatiotemporal
correlations (Okaze et al. 2017a). To achieve this, the extended DF method requires the Reynolds stress and an integral
length scale. In this study, the Reynolds stress and integral length scale were obtained from the PER results. The integral length scale was estimated, as described by Nakanishi and Niino (2009), using the turbulent kinetic energy q2/2
and altitude z as follows:
∞

L = 0.23



∫ 0 qzdz
. (1)
∞
∫ 0 qdz

The timescale was obtained from Taylor’s frozen turbulence hypothesis using L and the initial wind speed, as described above.
CPM does not add turbulence to the inflow boundary; instead, it adds a mosaic-like perturbation of potential temperature to the area near the inflow boundary to trigger turbulence. The magnitude of the perturbation was determined
based on the Eckert number

U g2
c pθ pert

= 0.2 . Given a value Ug = 5 m/s, we obtain θ pert = 0.12. The cell size was set to

(x × y × z) = (8 × 8 × 1) grid points, as described by Lee et al. (2019). The update frequency was tp , which satisfied
t pU w
dc

=1. Uw and dc indicate the wind speed at the bottom grid (approximately 2.6 m/s from the periodic boundary re-

sults of 50–60 min) and cell diagonal length, respectively. The cells were assigned a height of 2/3 of the CBL altitude,
as estimated from the sensible heat fluxes. The perturbation was generated based on a uniform random number, and
(x × y) = (3 × 32) cells were placed in front of the inflow boundary. Mazzaro et al. (2019) recently proposed an extended CPM method (force CPM). This method adds force perturbation instead of potential temperature to trigger turbulence in the domain. Mazzaro et al. (2019) found that the force CPM and original CPM have similar performances.
Therefore, the authors recommended using the original CPM, and therefore, we used the original CPM in this study.

3. Results
Figure 1 shows the vertical profiles of streamwise wind speed and potential temperature. In the streamwise wind
speed profiles (upper panels of Fig. 1), the shapes of the vertical profiles near the inflow boundary were close to the
inflow wind profile, whereas those downwind were close to the PER wind profile. This indicates that both the CPM and

SOLA, 2023, Vol. 19, 165−172, doi:10.2151/sola.2023-022
1000

Height [m]

900

1000
900

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DF

900

800

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800

700

700

700

600

600

600

500

500

400

400

300

300

200

200

100

100

500
400
300
200
100
0

1000
900

Height [m]

CPM

1000m
2000m
4000m
8000m
12000m
16000m
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

CPM

0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

0

u [m/s]

1000
900

1000

DF

900

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500

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0

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0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

θ' [K]

0

167

PER

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

PER

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0

Fig. 1. Vertical profiles of time- and spanwise-mean quantities. Upper panels: streamwise wind speed, bottom panels: potential
temperature anomaly (θ ¢ = θ - Θ, Θ is the reference potential temperature) profiles.

DF can fix the inflow profiles. It can also be observed that the shape of the profiles became uniform at 4 km downwind
in the lower layers of the CBL and at 4–8 km in the upper layers of the CBL in the CPM and DF. In the potential temperature profiles (bottom panels of Fig. 1), thermally driven CBLs were formed in both the CPM and DF, which were
comparable to those of the PER (the height of the thermally driven CBLs was approximately 650 m). The potential
temperature increase was similar in all three cases. However, differences were observed in the near-ground profiles. In
particular, the potential temperature near the surface of the CPM was higher than that of the DF and PER. This is because of the underestimation of mixing, particularly at z < 100 m. This lack of turbulence occurred because mosaic-like
perturbations still existed and did not trigger sufficient turbulence.
Figure 2 shows the horizontal cross-sections of the streamwise wind speed in the lower (z = 180 m; z/zi = 0.33; zi
is the estimated CBL height, zi = 546.6 m) and upper (z = 580 m, z/zi = 1.06) layers of the CBL. Wind speeds in the
CPM and DF were higher than those in the PER. This is because the wind speed was fixed at the inflow boundaries.
However, the downwind flow fields of the CPM and DF were similar to those of the PER, and the wind speeds were not
significantly different from those of the PER. The results of the CPM at z = 580 m show that no turbulence was added
at this altitude. By contrast, in the DF results at z = 580 m, a turbulent component was added; however, it did not fit the
turbulence generated in the thermally driven CBL.
Figure 3 shows the horizontal cross sections of the vertical wind speed in the same altitudes to the Fig. 2. The CPM
results at z = 180 m showed mosaic-like perturbations near the inflow boundary. These perturbations disappeared, and
a linear upwelling associated with the thermals was observed approximately 3 km downwind. Approximately 4 km
downwind, the wind-speed distribution resembled that of PER. No turbulence was observed approximately 3 km from
the inflow boundary in the CPM results at z = 580 m. This was not surprising as no potential temperature perturbation
was added at this altitude. However, thermals were observed approximately 3–4 km downwind from the inflow boundary. The flow field was similar to that of the PER approximately 6 km downwind from the inflow boundary. The results
of the extended DF method at z = 180 m showed that turbulence components with a large spatial scale were injected

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Sato and Kusaka, Intercomparison of Synthetic Inflow Turbulence Methods for CBL Simulations

CPM z = 180m

CPM z = 580m

m/s

DF z = 180m

DF z = 580m

PER z = 180m

PER z = 580m

6.0
5.6
5.2
4.8
4.4
4.0
3.6
3.2
2.8
2.4
2.0

1 km
Fig. 2. Horizontal distribution of streamwise wind speed. Left column: z = 180 m, right column: z = 580 m.

2.0
1.6
1.2
0.8
0.4
0.0
−0.4
−0.8
−1.2
−1.6
−2.0

Fig. 3. Horizontal distribution of vertical wind speed. Left column: z = 180 m, right column: z = 580 m.

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CPM z = 180m

CPM z = 580m

K

3.0

DF z = 180m

DF z = 580m

2.8
2.6
2.4
2.2
2.0

PER z = 180m

PER z = 580m

1.8

1 km
Fig. 4. Horizontal distribution of potential temperature perturbation. Left column: z = 180 m, right column: z = 580 m.

from the inflow boundary. However, these turbulence components did not represent the spatial structure of the thermals
as they were based on random numbers. The spatial structure of the thermals was observed 2–3 km downwind of the
inflow boundary. The extended DF method result at z = 580 m showed that the inflow turbulence was injected from
the inflow boundary, even at this height. The upwelling associated with the thermals appeared to be generated further
upwind compared to that with CPM. This may be because the turbulent component generated by the extended DF
method triggers turbulence at this altitude.
Figure 4 shows the horizontal cross-sections of the potential temperature at the same altitude as shown in Figs. 2
and 3. In all three methods, the distribution characteristics were similar to those of the vertical wind speed. However,
the DF and CPM results differ from those of the PER. In the results for z = 180 m of the DF, a region of large potential
temperature perturbation was observed approximately 2–3 km downwind. It was considered that the turbulence generated at the inflow boundary transitioned to that in the thermally driven CBLs in this region. This transition region
was also observed in the CPM. The driver region should include this transition region to generate reasonable turbulent
components using the DF and CPM.
Figure 5 shows the power spectral density of the vertical wind at z = 180 m and z = 580 m. The results 4, 8, 12,
and 16 km downwind from the inflow boundary are shown because these positions are characterized by significant
turbulence (Fig. 2). Based on the CPM results, it can be concluded that the overall spectra were well reproduced at the
two altitudes. However, CPM overestimated the spectra for wavenumbers of 1 × 10−3 < n < 3 × 10−3 4 km downwind.
This wavelength was approximately 500 m, which is similar to the CBL height, suggesting that the thermals were
overestimated at 3–4 km downwind. However, the results of the extended DF method showed no noticeable differences
compared with those of PER. This result suggests that the extended DF method can generate a plausible turbulence with
a shorter driver region than the CPM.
Figure 6 shows the histograms of the vertical wind at two altitudes (z = 180 m and z = 580 m). The data are the
same as those used to estimate the spectrum. The CPM results show that the shape of the histogram differs from that
of PER 4 km downwind of the inflow boundary. CPM shows a peak at w = −0.75 m/s, a low frequency of −0.5 < w <
0.5 m/s, and a slightly higher frequency at w > 1 m/s at z = 180 m. At z = 580 m, the CPM overestimated the peak at
w = 0 m/s compared to the PER. The reason for these differences in the shape of the histogram is the overestimation of
the thermals at z = 180 m and the absence of perturbations at z = 580 m. The extended DF method showed histograms

Sato and Kusaka, Intercomparison of Synthetic Inflow Turbulence Methods for CBL Simulations

Power [m2/s2]

10

0

10

1

10

2

10

3

10

4

CPM z = 180m

10
0

10

1

10

2

10

3

10

4

10

3

10

2

10

10

1

10

2

10

3

10

4

1

DF z = 180m

10

4

10

3

10
10

10

2

Wavenumber n

10

1

CPM z = 580m

0

10

Power [m2/s2]

Power [m2/s2]

10

4

4000m
8000m
12000m
16000m

Power [m2/s2]

170

0

10

1

10

2

10

3

10

4

4

10

3

10

2

10

1

10

2

10

1

DF z = 580m

10

4

10

3

Wavenumber n

Fig. 5. Power spectral density of vertical wind. Left column: the result at z = 180 m, right column: the result at z = 580 m. The
colored lines show the positions downwind from the inflow boundary as shown in the figures. The black dashed line indicates the
result of PER averaged in all four positions.

similar to those of PER for lower and upper altitudes. This indicates that the extended DF reproduces the thermals more
effectively than CPM, particularly near the inflow boundary.
In summary, at z = 180 m, the CPM can generate sufficient turbulence by setting a driver region of length 4–5 km,
whereas the extended DF method requires a driver region of length 4 km. The difference in the length of the driver
region was small because both methods actively generated turbulent components at this height. However, at z = 580 m,
CPM generated sufficient turbulence when a driver region of length 6–8 km was set, whereas the extended DF method
requires a 4 km-long driver region. CPM did not generate turbulent components at this altitude. Therefore, a driver
region longer than that used in the extended DF method is required.

4. Conclusion and remarks
In this study, we applied the inflow turbulence generation methods developed in the meteorological and CFD fields
(i.e., CPM and the extended DF method, respectively) to thermally driven CBLs and compared the reproducibility of
the turbulence. It was confirmed that both methods can reproduce turbulence in thermally driven CBLs well when a
proper driver region was ensured. CPM requires driver regions of lengths 4–5 km and 6–8 km in the lower and upper
layers of the thermally driven CBL, respectively. In contrast, the extended DF method requires a driver region that is 4
km in length in all layers of the thermally driven CBL. These results indicate that the extended DF method reproduces
turbulence better than the CPM, especially near the inflow boundary. Despite these differences in accuracy, the CPM
and extended DF methods are effective in downscaling mesoscale meteorological models to microscale LES models. In
particular, CPM is effective in coping with spatiotemporally variable inflow boundary conditions, while the extended
DF method is effective in terms of its ability to generate a plausible turbulence upwind.
This study has some limitations. First, buildings were not explicitly resolved, as the difference between the inflow
turbulence methods may become unclear when buildings are resolved because they generate significant turbulence.
Second, inflow turbulence methods other than the DF method should be discussed. For instance, a method for recycling
turbulent components was proposed in the CFD field. The extension of these methods to thermally driven CBLs should
be considered in future studies.

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0.30

CPM z = 180m

0.25
0.20

4000m
8000m
12000m
16000m

0.15
0.10
0.05

Relative Frequency

Relative Frequency

SOLA, 2023, Vol. 19, 165−172, doi:10.2151/sola.2023-022

−3

−1

0

1

2

0.20
0.15
0.10
0.05

−3

DF z = 180m

0.20
0.15
0.10
0.05
0.00

0.30

−2

−1

0

1

2

3

1

2

3

1

2

3

DF z = 580m

0.25
0.20
0.15
0.10
0.05
0.00

−3

−2

−1

0

1

2

3

PER z = 180m

−3

Relative Frequency

Relative Frequency

0.25

3

Relative Frequency

Relative Frequency

−2

0.25

0.30

CPM z = 580m

0.00

0.00
0.30

0.30

0.25
0.20
0.15
0.10
0.05
0.00

0.30

−2

−1

0

PER z = 580m

0.25
0.20
0.15
0.10
0.05
0.00

−3

−2

−1

0

w [m/s]

1

2

3

−3

−2

−1

0

w [m/s]

Fig. 6. Histograms of vertical wind speed. The colored lines show the positions downwind from the inflow boundary as shown in
the figures.

Acknowledgements
This study was supported by JSPS KAKENHI (grant number JP21K03656). This study used the computational
resources of Oakforest-PACS, Cygnus, and Wisteria/BDEC01 provided by the Multidisciplinary Cooperative Research
Program at the Center for Computational Sciences, University of Tsukuba. We are grateful to Assoc. Prof. Tsubasa
Okaze at the Tokyo Institute of Technology for his advice on implementation.
Edited by: T. Takemi

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