Application of a Combined Synthetic-Perturbation Method for Turbulent Inflow in Time-Varying Urban LES

Abstract

This study investigates inflow turbulence strategies for large-eddy simulations (LES) of urban boundary layers under time-varying atmospheric conditions. A combined approach integrating a digital-filter-based synthetic turbulence generator (STG) with the cell perturbation method (CPM) is proposed to reduce turbulence adjustment distance and improve vertical mixing. Using the PALM model, 24 h simulations were conducted over a real urban domain in Seoul, capturing diurnal transitions in stability and wind direction. Six experiments were compared: two reference runs with extended upstream fetch, and four analysis runs without fetch, applying different inflow strategies (NOT, STG, CPM, and CPM + STG). Results indicate that CPM + STG mitigates abrupt structural transitions and sustains turbulence kinetic energy (TKE) more consistently than STG alone, while requiring lower computational cost than extended-fetch configurations. Under unstable daytime conditions, CPM + STG enhanced vertical mixing and preserved local boundary-layer height closer to background values, whereas nighttime performance was dominated by building-induced shear regardless of inflow strategy. These findings suggest that the combined CPM + STG approach achieves a balance between physical realism and computational efficiency, demonstrating its potential as a robust inflow strategy for time-varying urban LES within limited domain sizes.

1. Introduction

Urban environments face multiple challenges—including air pollution, heat stress, and disaster response—all of which are strongly influenced by turbulent flow structures. Turbulence governs pollutant dispersion, heat transport, and the movement of hazardous gases, making its accurate numerical representation essential for urban simulations. Prior studies have demonstrated the role of turbulence in shaping urban-scale operations and mesoscale flow behavior (e.g., [1,2]). Large-Eddy Simulation (LES) has emerged as a powerful tool for resolving urban turbulence, but it faces technical hurdles such as constructing realistic urban geometries [3] and representing complex physical processes [4,5]. Among these, the specification of inflow boundary conditions—critical for defining interactions with the ambient atmosphere—remains a major source of modeling uncertainty. This study focuses on addressing that issue.

The atmospheric boundary layer (ABL) in urban areas is highly non-stationary and inhomogeneous due to complex surface features—such as building canopies and street canyons—and diurnal changes in stability and wind direction. Inflow conditions from mesoscale models or observations often fail to capture turbulence spectra and correlation structures because of limited spatiotemporal resolution. Consequently, turbulence must be generated within the domain, making LES predictions highly sensitive to interactions between time-varying inflow and near-surface turbulence [6]. Furthermore, canopy-generated turbulence requires several kilometers of development to fully evolve (so-called “fetch”) and mix into the upper boundary layer [7,8], and achieving building-scale resolution under varying conditions demands significant computational resources.

To reduce computational cost, many urban LES studies have used periodic boundaries or fixed inflow directions [9,10,11]. Yet, periodic boundaries reintroduce outflow into the inflow, causing inconsistencies and contamination [7,12]. Their reliance on equilibrium initial conditions also makes them unsuitable for evolving environments. Because realistic urban flows involve vertical wind veering and time-dependent shifts in wind direction, a single inflow condition is structurally infeasible [7,10,11]. Capturing such non-stationarity requires non-periodic boundaries and methods that actively prescribe turbulent inflow characteristics [13,14,15,16,17].

Several turbulent inflow generation methods (TIGMs) have been developed to mitigate these challenges. Among them, the Digital Filter-based Synthetic Turbulent Generator (DF-STG) [18,19,20] and the Cell Perturbation Method (CPM) [21,22,23] are widely applied in atmospheric and urban LES (e.g., [2,24,25]). DF-STG imposes synthetic turbulence at the inflow boundary based on prescribed statistics and length scales, while CPM triggers turbulence transition by introducing volumetric potential temperature perturbations near the inlet.

DF-STG generates synthetic turbulence by filtering random fields to match prescribed scales, which can compromise physical consistency. Such limitations are common among synthetic approaches; even with initial spectra or Reynolds stresses, nonphysical structures decay near the inflow and require a fetch to reorganize [13]. CPM similarly initiates turbulence through volumetric perturbations without pre-existing flow, also requiring a fetch to reach fully developed turbulence. Owing to these contrasting mechanisms, DF-STG exhibits relatively slow adjustment, whereas CPM responds more rapidly; however, once quasi-equilibrium is attained, both methods tend to converge toward comparable statistical properties under quasi-stationary and homogeneous conditions [23,26].

To reduce fetch constraints, DF-STG has been extended by incorporating scalar components into the Reynolds stress tensor, with temperature used as the scalar [27,28]. However, improvements depend on well-defined correlations between Reynolds stresses and scalar quantities; without them, scalar augmentation offers little benefit [29]. CPM has also been modified by adding momentum perturbations to temperature perturbations, creating the Force CPM [30]. While momentum perturbations increased initial energy, temperature-only perturbations were more effective in reducing fetch, and combining wind and temperature perturbations provided no significant improvement.

Building on these insights, this study proposes a combined approach that merges the spectral and correlation-prescribing capability of DF-STG with the low-cost, non-divergent turbulence-inducing mechanism of CPM. The goal is to exploit their complementary strengths to overcome limitations in reducing fetch and maintaining physical coherence in synthetic turbulence fields. Here, thermal perturbations are applied not to mimic heat transport but to reorganize nonphysical structures inherent to synthetic flows. In addition, the initial turbulence field is designed to reflect physical attributes such as length and time scales, rather than relying on random energy-containing distributions. This framework aims to improve the realism and stability of inflow turbulence under temporally varying urban boundary-layer conditions.

The reliability of current turbulent inflow strategies under conditions where urban morphology interacts with temporal variability remains insufficiently examined [8,18,24,31]. Urban LES is further limited by computational costs, restricting domain size and making inflow turbulence characteristics, homogenization rates, structure reformation, and stability under temporal variability critical for simulation sensitivity [32,33,34]. Previous notions of fetch largely assume flat, homogeneous conditions; however, the inhomogeneous and non-stationary urban boundary layer requires diagnostic frameworks that capture complex interactions, including scale coupling adequacy, phase lag, and synchronization with the upper boundary layer.

This study examines and compares several turbulent inflow generation methods in a realistic urban domain under continuous diurnal forcing (24 h), using PALM (Parallelized Large-eddy Simulation Model) [35,36,37]. PALM provides a framework designed for urban applications, including modules for urban ABL analysis, high-resolution urban representation [36], and boundary condition inputs with temporal variability [38]. DF-STG [7,18] is natively embedded, and CPM has been modularized [39], enabling both methods and their combined approach to be tested within a unified code base. This setup ensures that differences observed arise from methodological effects rather than implementation inconsistencies

Moving beyond conventional flat and quasi-stationary evaluations, this study systematically compares multiple inflow strategies within an urban ABL under continuous temporal variability. The framework emphasizes interactions among inflow turbulence, canopy-induced turbulence, and diurnal transitions, assessing physical consistency and structural robustness. Based on this analysis, we examine the applicability of the combined approach and benchmark it against existing methods to guide boundary condition strategies in urban LES. The paper is organized as follows: Section 2 describes the study area, data sources, and experimental design; Section 3 analyzes diurnal variability and computational cost; Section 4 presents the main conclusions.

2. Methodology

2.1. Study Area and Analysis Period

The study domain encompasses the Gwanghwamun district in central Seoul, Republic of Korea (Figure 1). The core analysis area spans 2 km × 2 km centered on Sejong-daero, representing a typical high-density urban environment with a heterogeneous mix of high-rise buildings, commercial and office complexes, and residential structures. Surrounding regions exhibit similar building densities, coupled with intricate road networks and irregular building layouts that generate characteristic urban canopy turbulence. This complex morphology provides an ideal setting for examining interactions between inflow turbulence and canopy-induced turbulence and has been the focus of numerous previous studies and observational campaigns (e.g., [4,40]).

Figure 1. Satellite view of the study area. (a) Broader Seoul metropolitan region with the yellow box indicating the intermediate domain surrounding the target area. (b) Close-up of the intermediate domain showing detailed urban morphology, including high-rise clusters, mixed land use, and dense street networks. The red box marks the core analysis domain (2 km × 2 km) centered on the Gwanghwamun district.

The analysis period corresponds to 5–6 August 2019, coinciding with the BBMEX (Building Block 3-dimensional urban Meteorological Experiment) campaign [30]. The campaign investigated thermal environments and turbulence characteristics in densely built urban areas during heatwave conditions. Meteorological conditions from this period were used to configure the LES.

2.2. Data and LES Configuration

PALM (version 6.0) is a LES model that explicitly resolves large scale turbulence and has been widely adopted for microscale urban flow analysis through the PALM-4U system, which incorporates modules for representing complex urban physical processes. Among its built-in components, PALM includes options for turbulent inflow generation, such as the Recycling-Rescaling method [41,42] and DF-STG. Recently, CPM has also been integrated into PALM [39], enabling DF-STG, CPM and their combined approach to be implemented within a unified code base.

For urban LES applications, PALM provides interfaces for high-resolution urban representation (so-called “static”) and for specifying initial and boundary conditions (so-called “dynamic_driver”) [38]. Previous studies have demonstrated that prescribing directional surface temperatures for roads and building walls enhances the realism of simulated urban thermal environments [4,5]. Accordingly, we developed an interface (“static_driver”) that combines surface information (“surf_static”) with directional surface temperature data. Figure 2 presents the input datasets and interface structure employed for urban LES in PALM.

Figure 2. Schematic overview of input data and processing steps for PALM LES modeling [4,38].

To construct a detailed urban environment, high-resolution GIS (Geographic Information System) datasets of terrain, buildings, and land cover were collected from national standard sources. Terrain data were obtained from the National Geographic Information Institute (NGII) using the 1:25,000 digital topographic map v2.0 contour layer. Building data were based on the building layer from the Ministry of the Interior and Safety’s (MOIS) Korean Road Name Address database, with building height information updated using the open spatial information platform. The average building height in the study area is 34 m, with the tallest building reaching 158 m. Land cover data were obtained from the Ministry of Environment’s (ME) detailed land cover map. Figure 3 shows the processed GIS datasets prepared for PALM model input. Meteorological forcing was provided by ERA5 reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF) (Figure 4). Wind, potential temperature, and specific humidity from ERA5 grid points covering the study domain were vertically interpolated to define initial and boundary conditions. Surface forcing was prescribed using directional surface temperature observations for roads and building walls in the study area (Figure 5). Missing values for certain orientations (north, south, and west walls) were corrected using ratios derived from Lee and Lee [5]. These detailed urban representations and boundary conditions ensured the fidelity of microscale atmospheric simulations within the urban domain.

Figure 3. Urban configuration of the target domain constructed from GIS datasets. The map integrates multiple layers, including building grids and types, vegetation classes, topography, soil and pavement types, and water bodies, providing a detailed representation of the urban surface for LES modeling.

Figure 4. Time–Height cross sections of meteorological forcing derived from ERA5 reanalysis for the simulation period (5–6 August 2019). Panels show (a) wind speed, (b) wind direction, (c) potential temperature, (d) specific humidity.

Figure 5. Time series of surface temperature for different urban surfaces during 5–6 August 2019 (LST). Solid lines represent in situ measurements at the target site, while dashed lines indicate estimated wall temperatures based on ratios from Lee and Lee [5]. Surfaces include building walls (east, north, south, west), road, and roof.

2.3. Experimental Design

Four analysis experiments were designed based on the turbulent inflow strategy: (1) no prescribed inflow turbulence (NOT), (2) application of the DF-STG (STG), (3) application of the CPM (CPM), and (4) simultaneous application of CPM and STG (CPM + STG). Previous evaluations of inflow turbulence strategies have typically relied on LES with periodic boundary conditions within a fixed domain (e.g., [20,23,29,43]). However, periodic boundaries cannot be applied in simulations incorporating temporal variability, necessitating an alternative reference. To quantify the influence of inflow turbulence, we examined the interaction between inflow prescription and fetch length. A reference domain was established by extending the computational domain upstream of the analysis region, and LES results from this extended domain served as the baseline.

Lee et al. [8] demonstrated that under neutral conditions, turbulence generated by complex urban morphology remains confined near the surface and does not fully develop vertically within 3 km, underscoring the need for a substantial fetch. Similarly, Park et al. [10] and Gronemeier et al. [9] applied the recycling-rescaling method in urban LES and introduced upstream buffer zones to minimize boundary effects, recommending fetch lengths of approximately 1 km under convective conditions and 2 km under neutral conditions due to building-induced blocking. Nevertheless, no absolute criterion has been established for urban LES with inflow turbulence. Moreover, previous studies assumed fixed wind directions, whereas the present work accounts for diurnal wind shifts, requiring more cautious fetch configuration. Accordingly, we adopted 1 km as the minimum convective fetch and introduced two additional reference experiments for relative comparison: NOT4k (no inflow turbulence with 4 km domain) and STG4k (STG applied with 4 km domain). STG4k represents the most optimized turbulence configuration among the current experimental setups, while NOT4k serves as a reference for minimal inflow turbulence.

Figure 6 depicts the domain configuration for the reference and analysis regions, and Table 1 summarizes the primary model settings. The horizontal grid spacing was set to 5 m to resolve both daytime convective and nighttime stable conditions. Vertical grid spacing began at 4 m near the surface and increased by a factor of 1.08 above 336 m, up to a maximum of 20 m. The domain comprised 160 vertical levels, with a top height of 1681 m. The simulation covered 24 h, from 15 LST on 5 August to 15 LST on 6 August 2019, and outputs were stored at 10 min intervals.

Figure 6. Computational domains for the real urban-area simulation. Panel (a) shows the reference area, (b) shows the analysis area where detailed LES experiments were conducted. The background image shows a satellite photograph, and red areas indicate road networks. Grid lines are overlaid on the domain boundaries at 10-grid intervals in both horizontal and vertical directions.

Table 1. Model configuration and input parameters for the urban-area simulations.

Parameter	Value
Domain name	Reference area	Analysis area
Horizontal grid	800 × 800 (dx = dy = 5 m)	400 × 400 (dx = dy = 5 m)
Vertical layer	160 (4 m stretching with 1.08 above 336 m) (top height 1681 m)
Integrated time	86,400 s (5–6 August 2019 (+24 h))
Surface forcing	Observed surface temperatures
Lateral B/Cs	ERA5 + NOT4k/STG4k	ERA5 + NOT/STG/CPM/CPM + STG
Pressure solver	Multigrid
Roughness	0.1 m
z0h_factor	0.01

STG requires specification of turbulence time and length scales and the Reynolds stress tensor. These quantities, which are difficult to observe directly, are estimated in PALM using empirical similarity relationships involving friction velocity ($u_{\ast }$), ABL height ($z_i$), and Obukhov length [18]. For continuous simulations, STG parameters must be periodically updated to capture temporal variability in inflow conditions. In this study, the turbulence analysis interval was set to 30 min, and STG parameters were updated at the same frequency (“dt_stg_adjust”).

CPM determines the amplitude of potential temperature perturbations amplitude (${\tilde{\theta }}_{pm}$) was similarly determined dynamically based on parameters computed within the model domain to account for temporal variability. Estimation of the perturbation interval requires near-surface wind speed information. Muñoz-Esparza et al. [23] recommended using the first grid cell of a mesoscale model and restricting the perturbation cell height to 2/3 of the ABL height. Alternatively, Lee et al. [8] simplified the mean profile in urban LES and applied building morphology-based similarity relationships to determine the perturbation interval, proposing a perturbation cell height of 0.95 $z_i$. Following Lee et al. [8], we set reference height for near-surface wind speed to the mean building height (z = 35.0 m) and the perturbation cell height to 0.95 $z_i$.

2.4. Comparative Framework

To examine the influence of inflow turbulence on turbulence development within the urban LES domain, inter-case comparisons were performed. The analysis focused on turbulence structures in horizontal and vertical cross sections and the evolution of the Turbulent Kinetic Energy (TKE) with fetch. In real-case urban LES, wind direction varies with height, resulting in multiple inflow boundaries and diurnal shifts in inflow/outflow faces. For analysis, the streamwise direction was determined at each time step based on the 30 min domain-averaged wind direction at 2.3 of the ABL height—a level commonly adopted to minimize surface influence while representing upper-layer flow (e.g., [8,18,23]). The spanwise width was set to 500 m, forming a 1 km analysis section.

Vertical mixing was assessed using two metrics: the background ABL height ($z_i^{back}$) representing large-scale stratification, and the local ABL height ($z_i^{loc}$) indicating the depth of turbulence mixing within the LES domain. Their relative difference provides insight into the extent of vertical mixing. $z_i^{back}$ was derived from ERA5 boundary conditions using the Bulk Richardson number method with critical threshold of $R{i}_b$ = 0.25, which provides consistent estimates across diurnal cycles [44]. The calculation of $R{i}_b$ and $z_i^{back}$ follows:

$${Ri}_B\left(z\right) = {\displaystyle \frac{g}{{\theta }_s}}{\displaystyle \frac{\left(\theta \left(z\right)-{\theta }_s\right)}{U{\left(z\right)}^2}}z,$$

(1)

$$z_i^{back}=\left\{z | R{i}_B\left(z\right)\ge 0.25\right\}$$

(2)

where $g$ is gravitational acceleration, ${\theta }_s$ is virtual potential temperatures near the surface and at $z$, respectively, and $U_z$ is the horizontally averaged wind speed at $z$. $z_i^{loc}$ was defined as the e-folding height where TKE decreases to approximately 37% of its maximum value, capturing local turbulence mixing. The calculation of $z_i^{loc}$ follows:

$$z_i^{loc}=\left\{z | TKE\left(z\right)\le TK{E}_{max}\times e^{-1}\right\},$$

(3)

This framework accounts for terrain-induced turbulence variability while enabling consistent comparison of inflow strategies.

3. Results

3.1. Daytime Case Analysis

This section examines how complex urban terrain and different inflow turbulence strategies influence flow and structural development within the boundary layer under unstable atmospheric conditions. The analysis focuses on 12 LST on 6 August 2019, a period characterized by strong surface heating and prevailing easterly winds. The inflow boundaries were positioned along the eastern (x = 2000 m) and northern (y = 2000 m) edges of the domain.

Figure 7 illustrates the spatial distribution of vertical velocity for each inflow strategy across different altitudes. At 50 m, noticeable differences among strategies were limited to a few hundred meters from the inflow boundary. The reference experiments (NOT4k, STG4k), along with STG and CPM + STG, exhibited more structured flow features in this region, while NOT and CPM showed less organized patterns. These differences were confined near the inflow boundary, and flow structures ended to converge across all experiments within the domain. This suggests that the impact of inflow turbulence may decrease beyond the boundary, as surface elements begin to induce turbulence independently of inflow conditions.

Figure 7. Horizontal cross sections of vertical velocity for the daytime case at 12LST on 6 August 2019. Panels compare six inflow configurations: NOT4k, STG4k, NOT, STG, CPM, and CPM + STG. Rows correspond to different heights: (a–f) 50 m, (g–l) 300 m, (m–r) 600 m, (s–x) 900 m. Thick dashed lines indicate the mean inflow direction, and thin dashed lines outline the analysis strip centered on this direction, extending 500 m on each side (1km total width).

Above 300 m, differences among inflow turbulence strategies became more evident. The reference experiments exhibited thick turbulence bands and roll structures aligned with the prevailing wind across much of the domain above 300 m. In contrast, NOT4k showed limited convective structures beyond 600 m near the inflow boundary, suggesting that turbulence generated within the urban canopy may not have propagated effectively aloft. STG4k exhibited convective structures up to 600 m, with plume-like formations emerging at 900 m. For NOT, vertical structures were weak near the inflow and developed gradually under surface forcing, with fetch increasing with height and becoming minimal at 900 m. STG exhibited striated synthetic patterns near the inflow that transitioned into convective structures, extending over approximately 1 km at 900 m before evolving into localized convective rolls similar to STG4k, which may have facilitated mixing into the upper layer. CPM produced small-scale disturbances near the inflow through volumetric perturbations but showed similar downstream behavior to NOT, with relatively modest convective development. These characteristics persisted at higher altitudes. This outcome contrasts with Lee et al. [8], which investigated neutral conditions over urban terrain. In that study, ${\tilde{\theta }}_{pm}$ was derived from the Eckert number ($E_c$) and applied uniformly at 0.198 K across all altitudes. By comparison, the present study estimated ${\tilde{\theta }}_{pm}$ under convective conditions using the potential temperature variance similarity approach [21,45]. Although stronger perturbations were imposed (3.300 K near the surface; 0.352 K at 900 m), CPM alone showed limited turbulence development, suggesting potential constraints under convective regimes. Nevertheless, CPM appeared to moderate the abrupt development of convective rolls near the inflow, contributing to a smother flow field. CPM + STG produced patterns broadly similar to STG but exhibited more gradual transitions between synthetic and reformed structures, suggesting that volumetric perturbations may support a more natural evolution of synthetic turbulence and allow convective features to persist over a wider region compared to STG alone.

Figure 8 compares vertical distribution of vertical velocity, horizontal wind speed, TKE, and potential temperature along a streamwise cross section. TKE was estimated by averaging buffer zones oriented perpendicular to the prevailing easterly wind, with a width of 1 km (dashed area in Figure 7) at varying inflow distances to reduce local effects. Within $z_i^{loc}$, turbulence appeared to be active in convective motions, horizontal structures, and TKE distribution, reflecting the growth characteristics of the internal boundary layer. At this time, $z_i^{back}$ was 1382 m, whereas $z_i^{loc}$ remained lower across all experiments, with notable differences depending on inflow distance and strategy. Among the reference experiments, NOT4k increased from about 400 m near the inflow to 900 m at the outflow, while STG4k grew from roughly 900 m to 1000 m, suggesting a narrower growth range compared to NOT4k. Similar trends appeared for NOT and STG: NOT exhibited gradual growth but reached only about 700 m at the outflow, the lowest among all experiments, whereas STG maintained about 900 m, comparable to the inflow height of the reference runs. Near the inflow, STG produced $z_i^{loc}$ approaching $z_i^{back}$ but declined sharply beyond 400 m, suggesting that a 1 km fetch may be insufficient for fully mixing turbulence generated from the surface, although it allows partial adjustment to imposed inflow turbulence. Even with this fetch, the STG method may not achieve full boundary-layer growth driven by large-scale motions, potentially resulting in reduced vertical mixing. CPM showed similar trends to NOT. Vertical distribution of potential temperature and vertical velocity suggested that volumetric perturbations influenced the depth near the inflow but did not appear to generate substantial TKE. CPM yielded $z_i^{loc}$ slightly higher than NOT, implying that local disturbances induced by volumetric forcing interacted with surface turbulence and may have contributed to modest mixing. CPM + STG resembled STG overall but exhibited a more gradual decline in $z_i^{loc}$ beyond 400 m, which led to the highest $z_i^{loc}$ observed at the outflow. This outcome suggests that CPM + STG may have preserved initial turbulence statistics over a longer distance, which could have facilitated the transmission of large-scale motions into the interior. This process appears to have supported stronger interactions between the internal boundary layer and the upper flow, potentially enhancing vertical mixing.

Figure 8. Vertical cross sections of key flow variables for the daytime case at 12LST on 6 August 2019. Each row presents a different variable: (a–f) vertical velocity, (g–l) horizontal wind speed, (m–r) turbulent kinetic energy, and (s–x) potential temperature. Columns compare six inflow configurations: NOT4k, STG4k, NOT, STG, CPM, and CPM + STG. Gray dashed lines indicate the background atmospheric boundary-layer (ABL) height, while black dashed lines show the local ABL height within the analysis domain.

Figure 9 presents a quantitative comparison of TKE development with respect to inflow distance across different altitudes. At 50 m, local variability appeared similar across all strategies, suggesting that this layer appears to be influenced by surface roughness elements regardless of the inflow condition. However, the magnitude of TKE varied among strategies. The reference experiments maintained a certain level of TKE from the inflow due to fetch-induced development, with STG4k consistently exhibiting higher TKE than NOT4k throughout the 3 km domain, suggesting that the influence of inflow turbulence may persist over long distances. NOT and CPM, which lacked inflow turbulence containing initial TKE, showed gradual TKE growth within the first 400 m but remained lower than other strategies. STG and CPM + STG generally exhibited higher TKE, with STG showing a relatively stronger tendency. CPM + STG maintained intermediate levels-higher than NOT4k but lower than STG and STG4k. In both STG-based and NOT-based configurations, adding volumetric perturbations through CPM was associated with lower TKE compared to the corresponding strategies without CPM. This suggests that volumetric perturbations may not directly evolve into large turbulent structures but may contribute to small-scale disturbances that support vertical mixing and local boundary-layer growth. At 300 m, the influence of surface forcing appeared to diminish, reducing local variability, although relative differences among strategies remained similar to those at 50 m. At 600 m, the reference experiments, NOT, and CPM exhibited comparable TKE variability, whereas STG and CPM + STG exhibited relatively higher TKE within approximately 1.5 km downstream of the inflow, with showed reduced variability. This behavior may reflect the residual impact of synthetic turbulence imposed at the inflow boundary, which weakened in the analysis experiments but weakened in reference experiments due to the 1 km fetch. This tendency continued at 900 m, where CPM + STG exhibited higher TKE than STG but remained between STG4k and NOT4k, without showing excessive growth. Moreover, CPM + STG showed the smallest spatial variability in TKE across the inflow distance, suggesting that this approach may have preserved more consistent turbulence statistics throughout the domain. Taken together, the results show that the combined inflow strategy (CPM + STG) exhibits distinct structural characteristics compared to other approaches. Specifically, CPM + STG maintained appropriate levels of TKE across all altitudes without excessive amplification, while preserving the initial turbulence statistics with minimal spatial variability. These features contributed to the sustained presence of large-scale motions and consistent vertical development throughout the domain, distinguishing CPM + STG from other inflow strategies in terms of turbulence continuity and structural coherence.

Figure 9. Streamwise evolution of turbulent kinetic energy along the analysis strip for the daytime case at 12LST on 6 August 2019. Panels correspond to different heights: (a) 50 m, (b) 300 m, (c) 600 m, (d) 900 m.

To examine the relationship between the persistence of inflow turbulence statistics in CPM + STG and the transition of nonphysical structural patterns associated with synthetic turbulence, Figure 10 compares the frequency distribution of vertical velocity within 1 km of the inflow for the daytime unstable condition, stratified by altitude. Across all altitudes, the distribution appeared centered near 0 m s⁻¹ and was generally symmetric. However, depending on altitude and strategy, higher frequencies near 0 m s⁻¹ were observed, suggesting regions with minimal vertical motion and potentially reduced turbulence intensity. Reference experiments exhibited relatively broad velocity distributions up to higher altitudes, whereas NOT4k showed a sharp increase in frequency near 0 m s⁻¹ beginning at 500 m, suggesting reduced turbulence near the inflow. In contrast, STG4k maintained broader distributions to higher levels, with frequencies near 0 m s⁻¹ exceeding 10% only above 900 m, suggesting more persistent turbulent motions compared to NOT4k. At 50 m, most strategies displayed relatively uniform distributions due to surface influence, but NOT and CPM showed limited turbulence absence near the inflow, with this tendency increasing with height. CPM exhibited a wider distribution and more moderate frequency characteristics than NOT, which may reflect the influence of volumetric perturbations. Strategies with synthetic turbulence (STG, CPM + STG) showed concentrated frequencies within specific velocity ranges, which may be associated with structural patterns imposed at the inflow. This tendency appeared to intensify with height, as surface influence weakened and inflow conditions become more dominant. Notably, CPM + STG exhibited lower peak frequencies near 0 m s⁻¹ and a smoother, broader distribution than STG, suggesting that volumetric perturbations may have supported a more gradual transition of synthetic turbulence and contributed to structurally coherent evolution. At 1100 m, frequencies near 0 m s⁻¹ exceeded 15% for STG4k and STG, whereas CPM + STG remained below 10%, suggesting that CPM + STG may have sustained broader turbulent motions and preserved coherent structures to higher altitudes.

Figure 10. Frequency distributions of vertical velocity within the first 1 km of the analysis strip for the daytime case at 12LST on 6 August 2019. Panels correspond to different heights: (a) 50 m, (b) 100 m, (c) 200 m, (d) 300 m, (e) 400 m, (f) 500 m, (g) 600 m, (h) 700 m, (i) 800 m, (j) 900 m, (k) 1000 m, and (l) 1100 m.

3.2. Nighttime Case Analysis

This section analyzes the nighttime case under stable atmospheric conditions. The analysis focuses on 05 LST on 6 August 2019, representing a stable period during the simulation. At this time, easterly winds prevailed, and the inflow boundaries were positioned along the eastern (x = 2000 m) and southern (y = 0 m) edges of the domain.

Figure 11 illustrates the spatial distribution of vertical velocity for each inflow strategy across different altitudes. Under stable conditions, buoyancy suppressed turbulence, while building-generated shear stress appeared to induce localized turbulent structures near the surface. Unlike the daytime case, where differences among strategies became more pronounced with height, nighttime conditions showed relatively small differences across strategies at all altitudes, with variations primarily between reference and analysis experiments. Reference experiments showed turbulent motions near the inflow due to fetch-induced development, whereas analysis experiments did not reveal distinct turbulent structures regardless of the inflow strategy. Additionally, reference experiments revealed turbulent flows above 200 m near the southern edge of the domain, likely originating from Nam-san (mountain) located upstream, suggesting that terrain-induced turbulence can propagate several kilometers even under stable conditions. This also suggests that, compared to daytime, the influence of upstream terrain and building-induced structures may become more pronounced at night, when buoyancy-driven turbulence is suppressed. In contrast, analysis experiments exhibited strong localized updrafts near the inflow, which may be attributed to laminar flow rapidly rising under building-induced shear. These updrafts extended up to 300 m with compensating downdrafts observed downstream during the adjustment process.

Figure 11. Horizontal cross sections of vertical velocity for the daytime case at 05LST on 6 August 2019. Panels compare six inflow configurations: NOT4k, STG4k, NOT, STG, CPM, and CPM + STG. Rows correspond to different heights: (a–f) 50 m, (g–l) 100 m, (m–r) 200 m, (s–x) 300 m. Thick dashed lines indicate the mean inflow direction, and thin dashed lines outline the analysis strip centered on this direction, extending 500 m on each side (1km total width).

Figure 12 compares vertical distributions of vertical velocity, horizontal wind speed, TKE, and potential temperature along a streamwise cross section. $z_i^{back}$ was only 47 m, whereas $z_i^{loc}$ reached approximately 200 m across all strategies. This discrepancy reflects the inability of $z_i^{back}$ to capture localized mixing driven by mechanical turbulence in urban terrain. Current inflow strategies did not account for these morphological effects, which could have led to turbulence prescriptions at very low altitudes and minimal differences among strategies. Reference experiments exhibited weaker updrafts, downdrafts, and lower TKE compared to analysis experiments, likely due to large-scale motion adjustment through fetch. Near the inflow, horizontal wind speeds were weaker in reference experiments, which may reflect turbulence development and large-scale adjustment, whereas analysis experiments introduced stronger winds. These stronger inflows interacted with high-rise buildings, which may have contributed to intense shear and elevated TKE in building wakes, observed across the domain.

Figure 12. Vertical cross sections of key flow variables for the nighttime case at 05LST on 6 August 2019. Each row presents a different variable: (a–f) vertical velocity, (g–l) horizontal wind speed, (m–r) turbulent kinetic energy, and (s–x) potential temperature. Columns compare six inflow configurations: NOT4k, STG4k, NOT, STG, CPM, and CPM + STG. Gray dashed lines indicate the background atmospheric boundary-layer (ABL) height, while black dashed lines show the local ABL height within the analysis domain.

Figure 13 provides a quantitative comparison of TKE evolution with inflow distance across different altitudes. Analysis experiments exhibited higher TKE and greater spatial variability than reference experiments, consistent with differences in large-scale motion adjustment. Within 500 m of the inflow, strategies with synthetic turbulence (STG, CPM + STG) produced higher TKE than strategies without prescribed inflow turbulence (NOT, CPM). Beyond 500 m, however, these differences diminished, indicating that the influence of inflow turbulence strategies under stable conditions was highly localized and limited to the immediate vicinity of the inflow boundary.

Figure 13. Streamwise evolution of turbulent kinetic energy along the analysis strip for the nighttime case at 05LST on 6 August 2019. Panels correspond to different heights: (a) 50 m, (b) 100 m, (c) 200 m, (d) 300 m.

This result experimentally supports existing understanding that, in urban canopy layers, flow is rapidly adjusted, and turbulence diffusion is suppressed due to the stable atmospheric structure. Although current inflow turbulence strategies are primarily designed to reproduce large-scale forcing and do not explicitly reflect urban morphological characteristics, the rapid adjustment of flow within the urban canopy suggests that this limitation does not critically affect overall simulation performance. Moreover, the development of turbulence across the domain appears to be more strongly governed by the modulation of large-scale forcing, indicating that the impact of inflow turbulence strategies may be relatively limited under such conditions. Nonetheless, the observed long-range propagation of turbulence generated by upstream terrain features, including elevated landforms and tall buildings, suggests that external morphological influences can affect urban flow structures well beyond the inflow region. This observation implies that future inflow condition designs may benefit from considering such terrain information, as a means to enhance the physical consistency of boundary conditions in urban LES modeling.

3.3. Time-Varying Comparison

This section extends the daytime and nighttime analyses to examine temporal variability throughout the diurnal cycle. Figure 14 and Figure 15 present the evolution of TKE with inflow distance at 50 m and 900 m altitudes throughout the simulation. These results capture the diurnal variation of TKE and highlight that differences among strategies were more pronounced during daytime conditions, as stable nighttime conditions exhibited limited sensitivity to inflow turbulence strategies beyond the immediate inflow region.

Figure 14. Spatiotemporal evolution of turbulent kinetic energy at 50 m for the time-varying case on 5–6 August 2019. (a) NOT4k, (b) STG4k, (c) NOT, (d) STG, (e) CPM, (f) CPM + STG.

Figure 15. Spatiotemporal evolution of turbulent kinetic energy at 900 m for the time-varying case on 5–6 August 2019. (a) NOT4k, (b) STG4k, (c) NOT, (d) STG, (e) CPM, (f) CPM + STG.

At 50 m, TKE exhibited highly complex local variability but generally increased beyond 1 km from the inflow, reflecting turbulence development near clusters of high-rise buildings in the central domain. Despite the dominance of surface-generated turbulence at this altitude, differences among inflow strategies persisted throughout the diurnal cycle. Strategies prescribing inflow turbulence (STG4k, STG, CPM + STG) led to elevated TKE levels not only within 500 m of the inflow but also across the entire domain. TKE was higher during the daytime period on 6 August (11–15 LST) compared to 5 August (15–18 LST), likely due to the combined effects of synoptic wind conditions and the temporal evolution of turbulence growth and decay.

At 900 m, where surface influence was minimal, the impact of inflow turbulence strategies became more evident. Strategies without prescribed inflow turbulence (NOT4k, NOT, CPM) severely underpredicted TKE beyond approximately 1 km from the inflow during all daytime periods, with the most pronounced discrepancies on 6 August. STG4k exhibited substantial differences between the inflow and outflow, as turbulence generated by surface elements propagated upward after synthetic turbulence dissipated through fetch, indicating that fetch alone does not fully overcome limitations in vertical mixing. STG maintained elevated TKE near the inflow, whereas CPM + STG produced the most spatially uniform distribution across a wide range of times, maintaining consistent turbulence statistics in the upper levels throughout most daytime periods.

Figure 16 evaluates vertical mixing performance through the ratio of $z_i^{loc}$ to $z_i^{back}$ as a function of inflow distance. Each ABL height is shown in Figure A1. During nighttime, $z_i^{loc}$ consistently exceeded $z_i^{back}$ across all strategies. However, these lower $z_i^{back}$ were rapidly adjusted by the urban canopy, limiting the influence of inflow turbulence strategies under stable conditions. As a result, the discrepancy between $z_i^{back}$ and $z_i^{loc}$ does not substantially affect the overall simulation outcome. In contrast, under daytime conditions, large-scale boundary layer dynamics were adequately captured by the imposed meteorological forcing, and the evolution of local mixing served as a meaningful indicator of how well small-scale turbulence adapted to these resolved large-scale motions. Accordingly, for daytime periods, ratios within ±25% of unity (green–yellow range) were interpreted as indicative of internal mixing comparable to large-scale motions, serving as a relative rather than absolute benchmark. On 5 August, adequate internal mixing was achieved beyond 1 km even without explicit inflow turbulence, whereas synthetic turbulence exhibited limited vertical growth due to insufficient initial TKE. CPM + STG induced reasonable mixing near the inflow through volumetric perturbations. On 6 August, strategies without prescribed turbulence failed to achieve adequate mixing, and STG4k showed restricted growth despite the inclusion of fetch. STG and CPM + STG supplied initial TKE near the inflow but gradually declined downstream. Notably, STG exhibited sharp reductions in $z_i^{loc}$ near the inflow at 12 LST, a feature absent at other times, while CPM + STG maintained $z_i^{loc}$ more consistently across multiple periods, indicating more stable performance.

Figure 16. Spatiotemporal evolution of the ratio of local atmospheric boundary-layer (ABL) height to the background ABL height for the time-varying case on 5–6 August 2019. (a) NOT4k, (b) STG4k, (c) NOT, (d) STG, (e) CPM, (f) CPM + STG.

These analysis results show that daytime convective boundary layers are reasonably captured at the background scale by ERA5, while limited LES domains struggle to fully reproduce their depth. In contrast, nocturnal stable boundary layers are better represented in LES due to localized mechanical turbulence induced by urban canopy effects. Based on these findings, Figure 14, Figure 15 and Figure 16 clarify how inflow turbulence strategies influence the diurnal evolution of local and background ABL heights and TKE.

During daytime, reproducing the background-scale boundary layer is essential because it provides the large-scale environment in which local turbulence develops and adjusts. Strategies that fail to approach this background scale tend to underestimate vertical mixing. Approaches that prescribe explicit inflow turbulence, such as STG and CPM + STG, maintained higher TKE compared to NOT or CPM. Among them, the combined CPM + STG method showed the most consistent improvement, preserving initial turbulence statistics and yielding local ABL heights closer to the background reference than individual strategies or simple fetch adjustments.

At night, the shallow stable boundary layer reduces sensitivity to inflow turbulence, and current approaches rely on mesoscale forcing supplemented with synthetic perturbations. This reliance makes it difficult to fully capture localized mechanical mixing, often leading to discrepancies in nocturnal turbulence representation. Future improvements should therefore consider not only incorporating morphological characteristics of urban surfaces and terrain but also accelerating the adjustment of mesoscale forcing into microscale turbulence. Such integration would enhance the effectiveness of inflow turbulence strategies under stable conditions and improve the representation of nocturnal boundary-layer dynamics.

3.4. Computational Cost

This section compares the computational cost associated with different inflow turbulence strategies and the inclusion of fetch. Figure 17 summarizes the cost components for each experiment, with percentages above the bars indicating relative increases compared to the NOT strategy. All simulations were performed on the KMA supercomputer (Duru). Reference experiments (NOT4k, STG4k) utilized 800 CPU cores, whereas analysis experiments (NOT, STG, CPM, CPM + STG) employed 400 CPU cores.

Figure 17. Comparison of computational cost among six inflow configurations: NOT4k, STG4k, NOT, STG, CPM, CPM + STG. Percentage value above selected bars denotes the relative increase in total cost compared to the NOT case.

Reference experiments showed the highest computational cost because of the inclusion of upstream fetch. STG4k exhibited greater cost increases than NOT4k, reflecting the additional operations required for synthetic turbulence generation. These results indicate that substantial cost increases occurred even with twice the computational resources, and the disparity would be greater under equal allocation. Among analysis experiments, NOT recorded the lowest cost due to its simple boundary condition without inflow turbulence prescription. STG increased costs by approximately 49% relative to NOT, because of synthetic turbulence computations. CPM, by contrast, showed a similar cost to NOT, not only because volumetric perturbations are computationally less demanding but also because its implementation was optimized to minimize unnecessary inter-core communication. Interestingly, CPM + STG required slightly less cost than STG despite combining both approaches. While it is not clear whether this reduction reflects improved numerical stability from physical enhancements or simply differences in computational environment, the result nonetheless indicates that adding CPM did not substantially increase the computational burden of STG.

Overall, these findings underscore the direct impact of inflow turbulence strategies on computational efficiency. Including fetch in reference experiments substantially increased cost, yet such investment does not necessarily translate into improved LES outcomes. Without appropriate turbulence prescriptions, allocating computational resources to fetch not only raises costs but also undermines the reliability of the results. For practical urban LES applications, selecting strategies that balance computational resources, and physical accuracy is essential. CPM + STG offers improved vertical mixing performance at lower cost compared to STG4k, making it a promising option for urban LES where both computational efficiency and physical realism are critical.

4. Summary and Conclusions

This study conducted LES-based numerical experiments to reproduce diurnal variability in the urban boundary layer and compare the performance of various inflow turbulence strategies. As a central focus of this study, we proposed a combined approach of synthetic turbulence generation (STG) with volumetric perturbations (CPM) within the PALM model. Experiments included reference runs with upstream fetch (NOT4k, STG4k) and analysis runs without fetch but with different inflow strategies (NOT, STG, CPM, CPM + STG).

Under unstable daytime conditions, inflow strategies significantly influenced boundary-layer growth and upper-level mixing. STG sustained high TKE near the inflow but decayed rapidly with short fetch, whereas CPM induced localized mixing but was insufficient alone. CPM + STG provided smoother structural transitions and more consistent vertical mixing across multiple periods. In contrast, stable nighttime conditions showed limited sensitivity to inflow strategies, with mechanical turbulence from urban morphology dominating. This suggests that incorporate morphological effects into inflow prescriptions may offer potential benefits for improving nighttime LES performance.

Time-varying analysis revealed that inflow turbulence strategies contributed to TKE maintenance and vertical mixing, particularly in the upper boundary layer. CPM + STG consistently preserved local mixing heights closer to background inversion heights across diverse periods, meeting the ±25% benchmark for internal mixing more frequently than other strategies. STG exhibited sharp reductions in local mixing heights at specific times, whereas CPM + STG maintained more stable performance.

From a computational perspective, reference experiments with fetch incurred the highest cost, with STG4k significantly exceeding NOT4k due to synthetic turbulence operations. Among analysis runs, STG increased costs by ~49% relative to NOT, while CPM remained similar to NOT. CPM + STG required slightly less cost than STG despite combining both methods, indicating that volumetric perturbations do not substantially amplify computational burden. CPM + STG thus offers improved vertical mixing at lower cost compared to STG4k, making it a promising option when balancing efficiency and physical realism.

Overall, this study demonstrates through LES experiments that the combined Synthetic-Perturbation method enables a practical balance between physical realism and computational efficiency in urban boundary-layer simulations. These results suggest practical implications for urban meteorology and environmental modeling. Improved representation of turbulence and vertical mixing may benefit applications such as urban weather forecasting, air quality simulations, and assessments of thermal comfort and pollutant dispersion in complex cityscapes. By balancing computational efficiency with physical realism, the combined Synthetic-Perturbation method presents a promising direction for developing more reliable and scalable LES frameworks that could inform both scientific research and, potentially, operational applications in urban environments. Future studies may extend this approach to diverse urban morphologies and climatic conditions, further evaluating its robustness and broadening its applicability.