Large-eddy simulation (LES) resolves large-scale turbulence directly and parametrizes small-scale turbulence. Resolving micro-scale turbulence, e.g., in wind turbine wakes, requires both a sufficiently small grid spacing and a domain large enough to develop turbulent flow. Refining a grid locally via a nesting interface effectively decreases the required computational time compared to the global grid refinement. However, interpolating the flow between nested grid boundaries introduces another source of uncertainty. Previous studies reviewed nesting effects for a buoyancy-driven flow and observed a secondary circulation in the two-way nested area. Using a nesting interface with a shear-driven flow in LES, therefore, requires additional verification. We use PALM model system 21.10 to simulate a boundary layer in a cascading self-nested domain under neutral, convective, and stable conditions and verify the results based on the wind speed measurements taken at the FINO1 platform in the North Sea.

We show that the feedback between parent and child domains in a two-way nested simulation of a non-neutral boundary layer alters the circulation in the nested area, despite spectral characteristics following the reference measurements. Unlike the pure buoyancy-driven flow, a non-neutral shear-driven flow slows down in a two-way nested area and accelerates after exiting the child domain. We also briefly review the nesting effect on the velocity profiles and turbulence anisotropy.

Large-eddy simulation (LES) allows performing a detailed process study for areas and situations where we lack appropriate field measurements. For this reason, LES is widely used for high-fidelity simulations of wind flows in wind energy applications. When considering the turbulent flow, the grid resolution should be sufficiently high to resolve the relevant turbulence scales

We use the Fortran-based LES code PALM 21.10

The reference measurements contain wind speed directional components

Aggregated statistics of 1 h sonic anemometer time series.

The sonic anemometers were installed at the meteorological mast at 40, 60, and 80 m. The measurements were processed by

The wind speed

The roughness length

We perform a free-flow large-eddy simulation (LES) using the Fortran code PALM developed at Leibniz Universität Hannover

By default, PALM solves prognostic equations for the velocity components

A nested simulation in PALM consists of at least one child domain inside a parent domain. Each child domain can simultaneously be a parent domain for another child domain, thus forming a cascading self-nested structure. The top-level parent domain is further referred to as the root domain to make a distinction from inner parent domains. Overall, PALM supports simulation of one root domain and up to 63 child domains.

The nesting algorithm is constructed in a way to optimize computational time for multiple child domains

After the interpolation, the prognostic equations are solved for a child domain. In the case of cascading nesting, the procedure is repeated until the solution is found for all nested domains at the current step. In a one-way nesting case, the simulation proceeds to the pressure-correction step, so the solution in parent domains remains unaffected by the solution in child domains. In a two-way nesting case, PALM uses an anterpolation scheme – a term suggested by

One of the ways PALM can simulate a turbulent flow is a precursor scheme, which does not require complex dynamic input data and effectively reduces the domain size required for turbulence development

The size of the precursor domain is usually smaller than for the main run, and the

The grid characteristics of the root and innermost child domain in the PALM simulation were selected to closely match the SOWFA simulation in

Grid parameters for NBL and CBL nested domains (Fig.

Grid parameters for SBL nested domains (Fig.

Nested domains schematic.

We perform one-way and two-way nested simulations. To evaluate the nesting effect, we also simulate domains without nested grids using the same precursor flow. Due to high computational time and memory requirements, we only simulate non-nested domains for the grid spacing of

Input parameters of the precursor runs.

The precursor profiles undergo development during a simulation and thus may deviate from the initial profiles. The precursor's input parameters are then selected so that the resulting steady-state profiles of mean wind speed and turbulence intensity follow the values estimated from the measurements, particularly the wind speed at the reference height.
The Coriolis force is switched off; hence the required wind speed and turbulence intensity profiles in the precursor run are enforced by a combination of the parameters: the initial mean wind

During the precursor simulation, the initial profiles are altered due to the influence of pressure forcing and heat fluxes. The resulting precursor profiles are provided in Table

Steady state of the precursor runs – turbulent inflow for the main run.

We run main simulations for 3 h with a dynamic time step selected by the model. The simulation is then continued for another hour with the fixed time step of

We evaluate the model performance based on turbulence characteristics: power spectrum, coherence, co-coherence, and phase. The coherence represents a correlation between time series

The co-coherence represents the real part of the coherence

The phase

Since the measurement time series are available only for three levels, 40, 60, and 80 m, the spectra are calculated and compared at

We also review flow characteristics relevant to the turbine performance analysis: power law coefficient and turbulence anisotropy.

The power law is commonly applied to assess wind resources at the hub height from near-surface wind speed measurements.

The anisotropic turbulence naturally develops in a simulation with an anisotropic grid resolution

All LESs are run at 1024 cores for each case with a time step of

CPU time in seconds used per second of simulated time. All simulations run at 1024 cores with a time step of

Both NBL and CBL simulations have the same domain structure and grid spacing (Table

Two-way nested simulations require additional

It should be noted that, unless obtaining high-frequency time series is the main goal of a simulation, the time step can be gradually increased for non-nested runs in order to speed up the computation. The computational time will, nevertheless, increase in a similar proportion with the global grid refinement. The time step in nested runs is still limited by the lowest grid spacing in child domains. For example, the dynamic step in the regarded configuration does not exceed 0.075 s to satisfy Courant–Friedrichs–Lewy condition.

Depending on the simulation conditions, LES produces different results in the nested area. If the true neutral case is defined in PALM explicitly via setting a corresponding flag, the one-way and the two-way nested simulations behave similarly with respect to grid spacing and feedback between domains (Fig.

NBL, flow at the reference height of 119 m for different wind speed components:

Since the child domains anterpolate their solution back to the parent domain, the area of reduced flow speed spreads to the root domain. While the effect is less prominent for the instantaneous fields, it becomes apparent in the 10 min averaged flow (Fig.

SBL, flow at the reference height of 119 m for different wind speed components:

The 10 min average profiles, SBL two-way nested case.

LES resolves scales larger than the grid spacing directly but approximates smaller scales. In a well-resolved flow, the unresolved (subgrid) scales should not exceed the resolved ones. This relation holds for all simulations performed, implying that the grid spacing of

Comparison of resolved and subgrid-scale momentum fluxes for different stability simulations and nesting modes.

Comparison of near-surface resolved and subgrid-scale momentum fluxes for different stability simulations and nesting modes.

The subgrid-scale fluxes consistently remain near zero for all levels except near-surface cells, where the turbulence intensity is expected to be high due to the surface influence (Fig.

Since the flow is driven by the pressure gradient instead of the Coriolis force, the flow is aligned with the

Spectra for the horizontal velocity

Spectra for the vertical velocity

In one-way nested simulations, the parent domain does not receive feedback from the child domain. Consequently, the spectral characteristics of non-nested domains with the grid spacing of

The two-way nesting mode ensures feedback between the nested domains. Therefore, the root and child domain spectra lie closer to each other and to the one-way spectra of the most refined child domain (

Despite the NBL case being simulated as a true neutral condition, it showed good agreement with the measurements on par with the CBL case. The result suggests that it is possible to omit a weak heat flux in neutral cases to save computational time and avoid secondary circulation in the two-way nesting mode.

The SBL simulations largely overestimate the energy contained in low-frequency eddies. The inertial subrange of the corresponding measurement time series also starts at higher frequencies, unlike in the NBL and CBL cases. The LES does not fully resolve high frequencies despite gradually reduced grid spacing. Hence the overall agreement for the SBL case is worse than for NBL and CBL. When comparing available measurement profiles for the specific period of SBL time series, we did not observe anomalies or irregularities, such as reported by

In order to match the SBL spectra shape, we performed a short SBL simulation with lower forcing, which led to a decreased turbulence intensity but stronger mean profile shear. The results are provided in Appendix.

The coherence, co-coherence, and phase are plotted against the reduced frequency:

where

The coherence and co-coherence calculated for NBL and CBL coarse domains (

Coherence for the horizontal velocity

Co-coherence for the horizontal velocity

The phase plots are in line with the coherence. The time series are in phase for

Phase plot for the horizontal velocity

In general, the power law coefficient follows the known trend, also observed in the measurement profile fits (Table

Estimated power law coefficient.

The estimated power law coefficient

The anisotropy estimation captures only general trends seen in the measurements with the nesting modes being radically different between each other (Fig.

Comparison of anisotropy across the regarded stability and nesting cases. The color map is centered at the value

We performed nested LES of three stability cases for the horizontal mean wind speed of 12–13 m s

We confirmed that the nesting mode does not affect the true neutral simulation, unlike when the temperature equation is solved along with other prognostic equations for CBL and SBL conditions. In the case of CBL or SBL, the flow inside the child domain differed for the one-way and two-way nesting. The two-way nested simulation produced a secondary circulation resulting in a decreased velocity and increased turbulence intensity in the child domains. Due to a strong horizontal shear, the irregularities in lateral and vertical velocity profiles were spread non-uniformly; e.g., the downward flow was stronger at the exit of the nested domain. The horizontal flow accelerated after leaving the nested area so that the mass conservation law was not violated eventually. Unlike the existing research on buoyancy-driven flows, the two-way nesting effects in a shear-driven flow emerged in the first hour of the LES and did not dissipate as the simulation proceeded for 3 more hours.

In theory, the two-way nesting is a good option to refine the grid in the area of interest of a non-homogeneous flow, e.g., wind turbine wakes, as the feedback between parent and child domain allows accounting for the irregularities after the flow exits the nested area. However, the fast development of a secondary circulation in the shear-driven flow limits the two-way nesting application strictly to the true neutral condition. The one-way nested simulation did not add anomalies to the flow; each child domain only refined the grid spacing and resolved small turbulence scales. We, therefore, recommend using the one-way nesting mode for the wind turbine wake simulation. In the case when the two-way nesting mode is preferable, only a true neutral setup does not produce secondary circulation.

We performed a test simulation of an SBL precursor for the same wind speed but weaker pressure gradient (

Precursor run profiles with original and reduced pressure forcing.

Main run spectra with original and reduced pressure forcing.

The PALM model system is freely available at

MK performed the LES simulations and analysis in accordance with the plan developed by MPB; JR and FGN provided valuable discussions explaining the discrepancies with the measurement data.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors would like to thank DEWI (Deutsches Windenergie Institut) for providing the FINO1 high-resolution sonic anemometer data and Astrid Nybø from the University of Bergen for the additional information and guidance.

The large-eddy simulations for this study have been performed by using the high-performance-computer facilities of the Norwegian e-infrastructure Uninett Sigma2 (project number NS9696K).

This paper was edited by Sylwester Arabas and reviewed by two anonymous referees.