A synthetic inflow turbulence generator was implemented
in the idealised Weather Research and Forecasting large eddy simulation
(WRF-LES v3.6.1) model under neutral atmospheric conditions. This method is
based on an exponential correlation function and generates a series of
two-dimensional slices of data which are correlated both in space and in
time. These data satisfy a spectrum with a near “

Atmospheric boundary layer flow involves a wide range of scales of eddies,
from quasi-two-dimensional structures at the mesoscales to three-dimensional
turbulence (normally with higher Reynolds number, i.e.

Dhamankar et al. (2018) reviewed three broad classes of methods to generate the turbulent inflow conditions for LES models, mainly for engineering applications. The first class is the library-based method, which relies on an external turbulence library to provide inflow turbulence. The turbulence library can be based on either (a) the precursor or concurrent simulation (e.g. Munters et al., 2016) on the same geometry to a main LES simulation; or (b) a pre-existing database (e.g. Schluter et al., 2004; Keating et al., 2004) from experiments or computations (on a different geometry to a main LES simulation). Although this method is usually limited to specialised applications, it can provide good-quality inflow turbulence. The second class is the recycling–rescaling-based method (e.g. Lund et al., 1998; Morgan et al., 2011), in which the velocity field is recycled from some suitably selected downstream plane back to the inflow boundary plane. Although this method may be effective in producing well-established turbulence, there are some limitations, e.g. the requirements of an equilibrium region near the inlet and a relatively large domain. The turbulence profile determined by the geometry of the precursor simulation can be added on the top of any given mean profile, which could be modified and varied in time for more realistic applications. The third class is the synthetic turbulence generator, which includes a variety of methods such as the Fourier transform-based method (e.g. Kraichnan, 1970; Lee et al., 1992), proper orthogonal-decomposition-based method (e.g. Berkooz et al., 1993; Kerschen et al., 2005), digital-filter-based method (e.g. Klein et al., 2003; Xie and Castro, 2008; Kim et al., 2013), diffusion-based method (e.g. Kempf et al., 2005), vortex method (e.g. Benhamadouche et al., 2006) and synthetic eddy method (e.g. Jarrin et al., 2006). The synthetic turbulence generator has the potential to be used for a wide range of flows. Due to the imperfection of the synthetic turbulence, which is not directly derived from generic flow equations, these methods normally require some inputs and a certain adjustment distance for turbulence to become well-established. For more information about the above synthetic turbulence generation methods, we recommend Tabor and Baba-Ahmadi (2010), Wu (2017), and Bercin et al. (2018).

Several other methods have been developed to generate inflow turbulence for atmospheric boundary layer flow in nested WRF-LES models. Mirocha et al. (2014) introduced simple sinusoidal perturbations to the potential temperature and horizontal momentum equations near the inflow boundaries. This method can speed up the development of turbulence and generally has a satisfactory performance in the nested WRF-LES domains, providing promising results. Muñoz-Esparza et al. (2014) extended the perturbation method of Mirocha et al. (2014) and proposed four methods, i.e. the point perturbation method, cell perturbation method, spectral inertial subrange method, and spectral production range perturbations, to generate perturbations of potential temperature for a buffer region near the nested inflow planes. The cell perturbation method was found to have the best performance regarding the adjustment distance for the turbulence to be fully developed. It has the advantages of negligible computational cost, minimal parameter tuning, not requiring a priori turbulent information, and efficiency to accelerate the development of turbulence. Muñoz-Esparza et al. (2015) further generalised the cell perturbation method of Muñoz-Esparza et al. (2014) under a variety of large-scale forcing conditions for the neutral atmospheric boundary layer. The perturbation Eckert number (describing the interaction between the large-scale forcing and the buoyancy contribution due to the perturbation of potential temperature) was identified as the key parameter that governs the transition to turbulent flow for nested domains. They found an optimal Eckert number to establish a developed turbulent state under neutral atmospheric conditions. These methods impose temperature perturbations at specific length scales and timescales related to the highest resolved wave number in the LES. It was demonstrated in Muñoz-Esparza et al. (2015) that a distance of about 15 boundary layer depths is required to allow the flow to be fully turbulent when the temperature perturbation method is adopted in the one-way nesting WRF model. It is to be noted that the temperature perturbation method was introduced for mesoscale to microscale coupling approach where smooth mesoscale flow (no resolved turbulence) forces microscale flow by using the one-way nesting approach in WRF. Muñoz-Esparza et al. (2014) stated “the perturbation method is to provide a mechanism that accelerates the transition towards turbulence, rather than to impose a developed turbulent field at the inflow planes as the synthetic turbulence generation methods pursue”, and “the use of temperature perturbations presents an alternative to the classical velocity perturbations commonly used by most of the techniques.” The optimisation and generalisation of these methods would require intensive testing. Muñoz-Esparza and Kosovic (2018) extended the cell perturbation method of the inflow turbulence generation to non-neutral atmospheric boundary layers. Instead of adopting temperature perturbations in the original cell perturbation method, Mazzaro et al. (2019) further explored the random force perturbation method (FCPM) in the multiscale nested domains.

Due to its accuracy, efficiency, and, in particular, the capability for high Reynolds number flows, the synthetic inflow turbulence generator (Xie and Castro, 2008) has been implemented and tested on codes developed for engineering applications, such as Star-CD (Xie and Castro, 2009) and OpenFOAM (Kim and Xie, 2016), and the micro-scale meteorology code PALM (PALM, 2017; Maronga et al., 2020). This study focuses on an implementation of this synthetic inflow turbulence generator (Xie and Castro, 2008) in the idealised WRF-LES (v3.6.1) model under neutral atmospheric conditions. In this paper, Sect. 2 describes the methodology of the WRF-LES model and the technique of the synthetic inflow turbulence generator, Sect. 3 presents the results of the WRF-LES model with the use of the synthetic inflow turbulence generator, and Sect. 4 states the conclusions and future work.

The atmospheric boundary layer is simulated by the compressible
non-hydrostatic WRF-LES model, which computes large energy-containing eddies
at the resolved scale directly and parameterises the effect of small
unresolved eddies on the resolved field using sub-grid-scale (SGS) turbulence
schemes (Moeng et al., 2007). The Favre-filtered equations are as follows
(Nottrott et al., 2014; Muñoz-Esparza et al., 2015):

For the closure of Eq. (2),

The synthetic inflow turbulence generator in Xie and Castro (2008)
adopted the digital filter-based method and is used in this study. For
simplicity, a one-dimensional problem (the streamwise velocity,

Finally, the velocity field is obtained by using the simplified
transformation proposed by Lund et al. (1998),

Integral length scales prescribed at the inlet used in the inflow BASE case (LS1.0).

In this study, we firstly configured a WRF-LES model with periodic boundary
conditions in both the streamwise and spanwise directions to obtain prior mean
profiles of first and second moments of turbulence, such as the vertical
profiles of mean velocity and Reynolds stress components, which are required
as inputs by the synthetic inflow turbulence generator. Additional essential
quantities as inputs of the inflow generator are three integral length scales
in the

For the cases with the synthetic turbulence at the inlet and periodic
conditions in the spanwise direction, the constant pressure gradient force
is not necessary anymore. Instead, a pressure-drop between the inlet and
outlet is implicitly derived from the prescribed mean momentum profiles as
part of the synthetic inflow and the outflow boundary conditions in the
solver. The periodic case is used for the validation of the results from the
inflow case. The WRF-LES is solved at a time step of 0.2 s. A spin-up period
of 6 h is adopted for all inflow cases to allow turbulence inside the domain
to reach quasi-equilibrium. The further 1 h outputs with 5 s interval
(approximately the advection timescale of the smallest resolved eddies,
which is equivalently twice the grid resolution of 20 m) were used for the
analysis. We take advantage of the homogeneous turbulence in the spanwise
direction (Ghannam et al., 2015) and calculate all resolved-scale
turbulent quantities by averaging in the spanwise direction (the

In the synthetic inflow turbulence generator, a uniform mesh is used with
resolutions of

Horizontal slice of instantaneous streamwise velocity component,

Figure 2 illustrates the horizontal slices of the instantaneous streamwise
velocity component at

Spatial variation of

Figure 3 shows the development of the

Horizontal profiles (spatially and temporally averaged) of

Figure 4 illustrates the

Spatially and temporally averaged vertical profiles of

Figure 5 shows the

Spectra of streamwise velocity component for a series of downwind
locations at the height of

Figure 6 illustrates the spectra of the streamwise velocity component at a
series of downwind locations (

The spectrum for the periodic case is calculated using the same method as
that used for the inflow case, with an additional average over the
streamwise direction

Development of local friction velocity (averaged over spanwise
direction and time) with various integral length scales.

It is not trivial to obtain “accurate” integral length scales of the inlet
turbulence generator. Indeed these data are always incomplete. Therefore, it
is necessary to conduct sensitivity tests of the integral length scales.
Figure 7 shows the influence of integral length scale on the development of
local friction velocity. Various integral length scale ratios (ranging from
0.6 to 1.4) to those (

Horizontal profiles (spatially and temporally averaged) of

Figure 8 shows the effects of integral length scale on the horizontal
profiles of the normalised mean streamwise velocity, normal and shear
turbulent stresses, and TKE at

Vertical profiles (spatially and temporally averaged) of

Figure 9 shows effects of integral length scale on vertical profiles of the
mean velocity, normal and shear turbulent stresses, and TKE at a typical
streamwise location (

Spectra of streamwise velocity component for a series of downwind
locations at

Figure 10 shows the effect of the integral length scale on the spectra of
the streamwise velocity component at

A synthetic inflow turbulence generator (Xie and Castro, 2008) was implemented in an idealised WRF-LES (v3.6.1) model under neutral atmospheric conditions. A WRF-LES model with periodic boundary conditions was firstly configured to provide a priori turbulence statistical data for the synthetic inflow turbulence generator. Previous studies (e.g. Xie and Castro, 2008) suggest that it is important to have an approximation of the integral length scales, which are the key inputs of the inflow turbulence generator. The results from the inflow cases were then compared with those from the periodic case. Sensitivity tests were conducted for the response of the local friction velocity, the mean flow, the Reynolds stresses, and the turbulence spectra for the flow cases for varying integral length scales.

The inflow case with the baseline integral length scales generates similar
turbulence structures to those for the periodic case after an adjustment
distance of

Horizontal and vertical profiles of mean velocity and second-moment
statistics further confirm that a short adjustment distance is required for
the development of synthetic turbulence. The mean velocity profiles at all
tested locations were in very good agreement with the reference data, while
the turbulence second-moment statistics profiles were in reasonable
agreement with the reference data about

In summary, the synthetic inflow turbulence generator is implemented
successfully into the idealised WRF-LES model. The generated synthetic turbulence is correlated both in space and in time in the exponential
form. The spectrum of these data shows an inertial subrange of

The standard version of WRF v3.6.1 tar file is available at

The study was conceived by XC and ZTX. JZ implemented the synthetic inflow turbulence generator code (from ZTX) to the WRF-LES model (v3.6.1) and ran model simulations. All authors contributed to writing the paper.

The authors declare that they have no conflict of interest.

This work used the ARCHER
UK National Supercomputing Service (

This research has been supported by the UK Natural Environment Research Council (NERC) (grant no. NE/N003195/1).

This paper was edited by James R. Maddison and reviewed by three anonymous referees.