Low Turbulence Intensity Research Articles

Automatic Compressive Sensing of Shack–Hartmann Sensors Based on the Vision Transformer

Shack–Hartmann wavefront sensors (SHWFSs) are crucial for detecting distortions in adaptive optics systems, but the accuracy of wavefront reconstruction is often hampered by low guide star brightness or strong atmospheric turbulence. This study introduces a new method of using the Vision Transformer model to process image information from SHWFSs. Compared with previous traditional methods, this model can assign a weight value to each subaperture by considering the position and image information of each subaperture of this sensor, and it can process to obtain wavefront reconstruction results. Comparative evaluations using simulated SHWFS light intensity images and corresponding deformable mirror command vectors demonstrate the robustness and accuracy of the Vision Transformer under various guide star magnitudes and atmospheric conditions, compared to convolutional neural networks (CNNs), represented in this study by Residual Neural Network (ResNet), which are widely used by other scholars. Notably, normalization preprocessing significantly improves the CNN performance (improving Strehl ratio by up to 0.2 under low turbulence) while having a varied impact on the Vision Transformer, improving its performance under a low turbulence intensity and high brightness (Strehl ratio up to 0.8) but deteriorating under a high turbulence intensity and low brightness (Strehl ratio reduced to about 0.05). Overall, the Vision Transformer consistently outperforms CNN models across all tested conditions, enhancing the Strehl ratio by an average of 0.2 more than CNNs.

OpenFlume: An accessible and reproducible benchtop flume for research and education

Open-channel flumes are an important tool in fluid mechanics research and education. However, the few commercially available small-scale flumes are generally expensive and lack complete characterization. In this work, we present an open-source, low-cost, modular benchtop laboratory flume that is designed to be accessible and reproducible. The flume is assembled from widely available materials and hardware, and fabricated exclusively using tools and machinery commonly found in workshop spaces. The recirculating water flow through the system is driven by a controllable electric coolant pump designed for automobiles. Our design has a flow cross-section of 5 × 5 cm, adjustable flow velocity, and a modest overall footprint. All design files and build instructions are shared in a digital repository ensuring openness and reproducibility. The flow in the test section is characterized using particle image velocimetry (PIV) and is shown to be of high uniformity with low turbulence intensity. Furthermore, direct measurements of the drag force on a submerged sphere are reported for a range of control parameters, and exhibit good agreement with established empirical values.

Design and characterization of the university of Toronto hybrid anechoic wind tunnel

A detailed overview of the hybrid anechoic wind tunnel at UTIAS is presented, highlighting its design and performance features. The findings demonstrated that the tunnel achieves a uniform flow with very low turbulence intensity, matching the performance of similar open-loop wind tunnel facilities. The anechoic chamber effectively reduces noise with a cutoff frequency of around 160 Hz, providing a suitable environment for a broad spectrum of aeroacoustic measurements. The versatility of the wind tunnel was illustrated through its application in various aerodynamic and aeroacoustic studies, showcasing examples such as the NACA 0012 airfoil, the multi-element 30P30N configuration, and finite-span airfoil investigations. Moreover, the facility's Overall Sound Pressure Level (OASPL) is on par with other prominent global aeroacoustic wind tunnels, indicating its competitive performance and utility in the field.

Simulation study on flow field regulation of flotation column with stirring device

ABSTRACT Flow field regulation plays an important role in the optimization of column flotation units with agitation function. This paper aims to discuss the regulating effect of baffle design on the flow field in stirred column flotation units by numerical simulation. A series of geometric models of changing baffle structure and layout were established, and detailed flow field simulation analysis was carried out by using COMSOL software. The results show that the internal flow field of the traditional standard cylindrical tank will cause the solid particles to adhere to the wall movement and the bubbles to the middle area, resulting in the uneven distribution of particles and bubbles, and the internal flow field is not conducive to the mineralization process and the stability of the foam layer. This limitation can be significantly improved by introducing baffles. The results show different baffle shapes and layouts are as follows: wide and narrow on top, narrow on the bottom and wide on top, and only arranged at the bottom of the column body, can increase the average turbulent kinetic energy in the collision zone by 22%, 46% and 43%, and the average turbulent dissipation rate by 18%, 43% and 36%, respectively, while maintaining the turbulence intensity in the transport zone. Among them, the baffle plate with wide top and narrow bottom has the best effect. Arranging baffles with a length shorter than 2/3 of the height of the cylinder at the upper part inside the cylinder can also enhance the turbulence intensity in the collision zone, but at the same time, it also increases the turbulence intensity in the transport zone. Moreover, as the length of the baffle decreases, the enhancement effect becomes stronger. Since this method significantly affects the transport zone, it is more suitable for columnar mixing devices. The study also reveals that by adjusting the proportion of wide and narrow baffles, the center of the turbulent region can be laterally shifted to the short baffles, and the flow field distribution can be adjusted. Meanwhile, with the increase in the number of long baffles, the intensity of the flow field in the device will gradually decrease. By moving the center of the turbulent region to the side inlet, the particle dispersion can be accelerated, but in general, the particles will accumulate toward the region with lower turbulence intensity. These findings have important guiding significance for the design and optimization of the flow field of the stirred column flotation unit, which is helpful in improving the agitation uniformity and flotation efficiency.

Simultaneous measurement of the distributed longitudinal strain and velocity field for a cantilevered cylinder exposed to turbulent cross flow

The structural response of a cantilevered cylinder under free-stream conditions both with low and high turbulence intensity generated by turbulence-generating grids is analysed with concurrent measurements of the velocity field and the distributed strain. The thin-walled cylinder, with a diameter (D) of 50 mm, is mounted in a water flume as a cantilevered beam supported at one end, with 95% of its body submerged and exposed to cross flow yielding a Reynolds number of Re = 25000. We employ a novel combination of simultaneous particle image velocimetry and distributed strain measurements using Rayleigh backscattering fibre optic sensors. These sensors are embedded onto the surface of the cylinder to measure the experienced strain (ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}) of the structure along its spanwise direction, covering both the windward and leeward faces of the cylinder. The sensors fine spatial resolution allows us to discern the influence of the flow on the structural response of the cylinder in two distinct regions of the structure: upstream and downstream of the mean separation location. This differentiation allows us to isolate the local effects introduced by the free-stream conditions on the loading events over the body from the global force generated by the vortex shedding and other coherent motions present within the flow. Distinguishing between these direct and indirect effects helps determine which is more relevant for fatigue-life cycle analysis. The cross power spectral density between the fluctuating velocity field and the strain reveals that the load is dominated by the vortex shedding, and this relationship is intensified with the introduction of free-stream turbulence. It also helps to discern the different dynamics imposed by the two free-stream turbulence conditions.

Open-jet facility for bio-inspired micro-air-vehicle flight experiment at low speed and high turbulence intensity

Bio-inspired micro-air-vehicles (MAVs) usually operate in the atmospheric boundary layer at a low Reynolds number and complex wind conditions including large-scale turbulence, strong shear, and gusts. We develop an open jet facility (OJF) to meet the requirements of MAV flight experiments at very low speed and high turbulence intensity. Powered by a stage-driven fan, the OJF is capable of generating wind speeds covering 0.1 – 16.8 m/s, with a velocity ratio of 100:1. The contraction section of the OJF is designed using an adjoint-driven optimization method, resulting in a contraction ratio of 3:1 and a length-to-diameter ratio of 0.75. A modularized design of the jet nozzle can produce laminar or high-turbulence wind conditions. Flow field calibration results demonstrate that the OJF is capable of producing a high-quality baseline flow with steady airspeed as low as 0.1 m/s, uniform region around 80% of the cross-sectional test area, and turbulence intensity around 0.5%. Equipped with an optimized active grid (AG), the OJF can reproduce controllable, fully-developed turbulent wind conditions with the turbulence intensity up to 24%, energy spectrum satisfying the five-thirds power law, and the uniform region close to 70% of the cross-sectional area of the test section. The turbulence intensity, integral length scale, Kolmogorov length scale, and mean energy dissipation rate of the generated flow can be adjusted by varying the area of the triangular through-hole in the wings of the AG.

Effect of turbulence intensity on bubble-particle detachment mechanism in a confined vortex

Bubble-particle detachment induced by turbulence is the primary factor for the low recovery of coarse particles, which has attracted much attention in recent years. The prevailing centrifugal detachment theory has achieved broad consensus. However, due to the complexity of bubble-particle aggregate motion in the turbulent field, the influence of turbulence intensity on bubble-particle detachment mechanism remains unclear. In this study, a controlled rotating vortex was generated using a custom-made fluid channel to systematically investigate the effect of turbulence intensity on bubble-particle centrifugal detachment. Firstly, detachment behaviours of bubble-particle aggregates were captured using high-speed cameras, followed by flow field visualization of bubble-particle detachment processes using Computational Fluid Dynamics (CFD). Experimental results reveal three typical detachment modes of bubble-particle aggregates in the confined vortex: fluid shear, bubble oscillation, and particle centrifugal motion, with particle centrifugal detachment becoming dominant with increasing turbulence intensity. This shift is attributed to changes in turbulence intensity directly affecting the trajectories of bubble/aggregates and indirectly influencing the detachment mode of bubble-particle. Compared to low turbulence intensity, bubble-particle aggregates exhibit smaller rotational radii under high turbulence intensity, reducing the probability of fluid shear and bubble oscillation detachment by mitigating the influence of high-speed shear zones at the top of the cavity. Conversely, particles located at the edge of aggregates are more susceptible to acceleration by sidewall flow fields, favouring detachment through particle centrifugal motion. Moreover, unlike traditional centrifugal detachment theories, particles do not merely undergo independent circumferential motion on the bubble surface but participate as a whole with bubbles in centrifugal motion governed by vortices. These findings are expected to provide fundamental insights into the bubble-particle detachment mechanism in turbulent fields.

Effect of inlet flow turbulence on hydro–acoustic coupling and flame–vortex interactions in a premixed dump combustor

The present work examines the effect of inlet flow turbulence on the flame–vortex modulations, hydro–acoustic coupling and recirculation zone dynamics at the onset of instability. The flow turbulence intensity varied using a custom-designed turbulence generator with different slot-width blockage plates placed upstream to the nominal flame-stabilization zone. The high-speed recordings of the CH*/OH* chemiluminescence and particle image velocimetry are used to deduce the relation between the flame–acoustic, flame–vortex and hydrodynamic–acoustic features during the unsteady combustion. The bifurcation analysis map revealed the effect of high inlet flow turbulence on postponing the onset of instability to higher inlet flow parameters. The initial observations showed potential changes in the acoustic behaviour and dynamical state of premixed turbulent combustion with an increase in inlet flow turbulence. The spatial Rayleigh index map illustrates a significant change in the acoustic driving region at high inlet flow turbulence based on the flame stabilization, heat release zone and flame–acoustic modulation in the shear layer and recirculation zone. The velocity spectral analysis and dynamic mode decomposition (DMD) spectrum suggested a correlation between the acoustic modulation and hydrodynamic instabilities, resulting in higher heat release rate oscillations. The high inlet flow turbulence modulates the vertical flapping motion of the flame front and flame roll-up in the recirculation region as evident by DMD spectrum and spatial modes. The flame–vortex dynamics during the dynamic transition events showed that the high inlet flow turbulence influenced the vortex shedding along the shear layer and recirculation zone dynamics. At low turbulence intensity, the vortex, in turn, supports the bulk flame movement through the induced velocity, which interacts with the free stream to create regions of low velocity. In contrast, the vortex in the shear layer and flame resides along the shear layer at higher turbulence. The paper concludes that at higher inlet flow turbulence, the recirculating flame reduces the hydro–acoustically modulated flow velocity fluctuations, which significantly affect the upstream flame propagation propensity.

Onsite measurements of pedestrian-level wind and preliminary assessment of effects of turbulence characteristics on human body convective heat transfer

Wind is an important factor affecting outdoor thermal comfort in urban environment, but its turbulence characteristics at the pedestrian level and effects on convective heat transfer (hc) from a human body remain poorly understood. Previous studies were only conducted in wind tunnels with low turbulence intensity, small turbulence integral length scale, and fixed prevailing wind direction. To address this knowledge gap, this field study was conceived to monitor the pedestrian level wind in actual outdoor settings and to measure the hc of a thermal manikin at the same time. The results show that both longitudinal and lateral turbulence intensity significantly enhance whole body hc. It remains to be examined whether the small-scale wind direction variation can be included in the lateral turbulence intensity or vice versa. The integral length scale found at the two sites were larger than a typical manikin dimension, and the whole body hc peaked when these two scales were comparable. As the first major field study to quantify convection heat loss of a thermal manikin exposed to real-life urban boundary layer wind, it is demonstrated crucial to consider realistic turbulence characteristics in the field when evaluating hc over a human body for urban microclimate design.

Development and Verification of an Improved Wake-Added Turbulence Model in FAST.Farm

We introduce a generalized wake-added turbulence (WAT) model in the multiphysics, multiturbine simulation tool FAST.Farm. The WAT model introduces additional small-scale turbulence that represents the breakdown of vortical structures and shear layers in the wake. The article describes the development, implementation, calibration, and verification of the model. The novelties of the model include support for wake asymmetry, buildup of WAT across the wind farm, and secondary effects of wake-induced turbulence (e.g., wake meandering) driven by smaller-scale turbulence structures that arise from wake breakdown. Large-eddy simulations were run to support the calibration of the WAT parameters and verification of the model. Previous studies hypothesized that the lack of WAT modeling was the source of underprediction of fatigue loads, in particular for cases at low turbulence intensities and/or stable atmospheric boundary layers. This study confirms that the newly implemented WAT model enhances the loads predictions in these cases.

Nacelle modeling considerations for wind turbines using large-eddy simulations

Two setups are used to investigate differences between modeling a wind turbine nacelle by means of an actuator-line model (ALM) and a wall-model (WM) using large-eddy simulations. One advantage of the ALM is that it requires a lower mesh refinement, making it less computationally costly. In the first setup, the nacelle is in standalone configuration and the ALM results show a much lower turbulence intensity and a significantly slower wake recovery when compared to the WM cases. In the second setup, the nacelle is in a rotor-nacelle assembly configuration and many variations of the ALM are tested in order to match the results from the experiment addressed in the OC6 task phase III. Contrary to previous findings that the nacelle might affect the turbine loads, this study shows that the improved match with the experiment stems from the increased mesh refinement in the nacelle region rather than the actual presence of the nacelle. Nevertheless, the wake profiles in the near-wake show a very good agreement between the ALM and WM, regardless of the refinement in the nacelle region. These cases also show a higher wake deficit than not using any nacelle at all.

Assessing the effect of turbine size on the coherent structures in the wake using DMD

The aim of this study is to evaluate and quantify the effect of the incoming flow on the coherent structures characterizing the wake of two NREL reference wind turbines with different dimensions: the NREL 5-MW and the NREL 15-MW. The Dynamic Mode Decomposition (DMD) approach has been used to detect dynamically-relevant flow structures. We employ the Sparsity-Promoting version of the DMD (SPDMD) algorithm for ranking the most relevant modes, in order to extract a limited subset of relevant flow features that optimally approximate the original data sequence. The dataset on which the SPDMD is based consists of ordered snapshots obtained by Large Eddy Simulations (LES), where the Actuator Line Method (ALM) simulates the rotor and the Immersed Boundary Method (IBM) models the tower and nacelle. To ensure a realistic comparison, the two turbines are subjected to two turbulent inflows with the same mean Atmospheric Boundary Layer (ABL) obtained through a precursor simulation. The results reveal significant differences in the dependence of the absolute value of the DMD amplitudes on the angular frequency for the two turbines. However, the coherent structures appear to have the same shape for the main modes, although the tip vortex structures have a higher dynamic relevance for the NREL 15-MW turbine. This is due to the larger length scales imposed by the rotor and the lower turbulence intensity at the taller rotor height.

Wind tunnel investigation on the recovery and dynamics of the wake of a floating offshore wind turbine subjected to low inflow turbulence

Floating offshore wind turbines (FOWT) operate in various turbulent conditions, including low turbulence intensity situations (TI∞ ≤ 5%). In this paper, we investigate experimentally the wake of a model floating wind turbine subjected to inflow turbulence up to TI∞ ≈ 3%. We consider idealised surge platform motion and analyse wake measurements at different downstream positions x ∈ [4D, 8D]. The results show that rotor movements enhance wake recovery compared to the fixed wind turbine, especially for TI∞ ≤ 2%. The recovery of the moving wind turbine wake is progressively less affected by motion with increasing TI∞ . Both amplitude and frequency of motion are key parameters that drive wake recovery and dynamics. We found in the wake large coherent structures induced by the platform movements, which allow a faster transition to the far wake but may cause increased loading on downstream turbines.

Enhancing accuracy of surface wind sensors in wind tunnel Testing: A Physics-Guided neural network calibration approach

Irwin’s surface wind sensor is widely used in wind tunnel testing for urban and environmental aerodynamics studies. However, the conventional physics-based calibration of this sensor could result in reduced measurement accuracy in regions with low flow velocities and high turbulence intensity. To address this issue, this study proposes a novel physics-guided neural network (PGNN) calibration approach, which couples a physics-based calibration model, derived from extended Taylor series expansions of measured wind speed, with an adaptive, data-driven general regression neural network. Sensors are calibrated within the turbulent boundary layer of an empty flat plate, considering both mean and standard deviation of wind velocity measured by high-accuracy thermal anemometry. The accuracy of calibrated sensors is then assessed using a 1:400 benchmark urban model. Experimental results show significant improvement in measurement accuracy, reducing mean absolute percentage error for wind speed standard deviation from 92.3 % with the current model to 9.8 % using PGNN.

One-degree-of-freedom galloping instability of a 3D bluff body pendulum at high Reynolds number

The cross-flow swinging dynamics of a cube pendulum is studied experimentally in a flow at high Reynolds numbers (Re∼105) with a low free-stream turbulence intensity. A galloping instability is observed and results in the exponential growth of the swinging motion. The onset of galloping is found to be very sensitive to the static yaw angle of the cube. Despite the 3D geometry of the cube, flow mechanisms similar to the case of a square cylinder appear to govern the onset of the instability. A quasi-steady linear model of the motion is assessed to predict the stability of the pendulum.For the lowest reduced velocity investigated (U∗=18.5), unsteady phenomena arise during the saturation phase of the pendulum oscillations. From the analysis of the unsteady loads and the pressure distribution on the faces of the cube, an unsteady phase delay between the wake and the pendulum dynamics is identified. It produces an energy loss in the pendulum motion which favors its saturation.

Breathing in danger: Mapping microplastic migration in the human respiratory system

The abundance of air pollutants over the last few years, including the concentration of microplastics, has become an alarming concern across the world. Initially discovered in marine life, these toxic and inflammatory particles have recently been found in human lung tissues. When inhaled, these harmful particles settle down in the lung airways and, over time, lead to respiratory failures. A recent study analyzed the microplastic transport behavior in the mouth–throat airways. However, the knowledge of the microplastic migration in bifurcating tracheobronchial airways is missing in the literature. Therefore, this first-ever study analyzes in detail the transport behavior and settling patterns of microplastic particles of different sizes and shapes at different respiratory intensities in the tracheobronchial lung airways. A numerical technique based on discrete phase modeling is employed to simulate the flow of microplastic particles in a three-dimensional realistic lung geometry. The numerical model results indicate low velocity and turbulence intensity magnitudes with smooth flow in the trachea compared to the airways of left and right lobes, which experience higher velocities and generate secondary vortices. Lower lung lobes are the deposition hotspots for the harmful microplastic particles at a lower flow rate. These hotspots shift to upper lung lobes at a higher flow rate for the same particle size. Moreover, microplastic particle size and shape influence the overall deposition rate in the tracheobronchial lung airways. The results of the current study, including microplastic accumulation regions at different breathing intensities, will contribute to the updated knowledge of pollutant inhalation and facilitate relevant treatment measures.

Flow Characteristics in Partly Vegetated Channels: An Experimental Investigation

In this study, we attempt to experimentally investigate the flow turbulence structure in a partly vegetated channel. To achieve the objective of this study, we conducted extensive measurements of flow velocities within and outside the vegetated area, where the flow is fully developed. The experiments were conducted in a very large channel at the Coastal Engineering Laboratory of the Department of Civil, Environmental, Building Engineering and Chemistry at the Polytechnic University of Bari, Italy. The instantaneous three flow velocity components were accurately measured using a 3D-Acoustic Doppler Velocimeter (ADV)-Vectrino system at high frequency. Flow behaviors through the vegetated area, at the interface, and in the unobstructed area were analyzed via time-averaged velocities, turbulence intensity, correlation properties, spectral analysis, and vortex identification. Experimental results showed the development of three distinct characteristic flow zones: (i) a vegetated area of low streamwise velocity, high turbulence intensities, dominant inward interactions, and more intense power spectrum, (ii) a shear layer zone of increasing streamwise velocity, more enhanced transverse flow motion, exponential decrease in turbulence intensities, and frequent ejection and/or outward interaction events, and (iii) a free-stream zone of higher and almost constant streamwise velocity, lower turbulence intensities, frequent sweep and/or inward interaction events, and less intense streamwise power spectrum. The results brought further insights into the flow behaviors in these characteristic flow zones. The extensive and detailed measured data can provide a basis for improving and calibrating numerical simulations of partly vegetated channels.

Direct numerical simulation of channel flow with real surface roughness using a ghost cell immersed boundary method

This paper investigates the impact of real surface roughness on channel flow using direct numerical simulation assisted by a ghost cell immersed boundary method (DNS-GCIBM). The principles and implementations of DNS-GCIBM are first introduced. Two test cases, including the two-dimensional flow around a cylinder and the three-dimensional flow in a sinusoidal roughness channel are employed to demonstrate the practicability and accuracy of the proposed approach, especially in numerical studies on the rough wall-bounded flow. Using DNS-GCIBM, channel flows under conditions of Ma = 0.3 and Reτ≈300, with both the real-world and regular roughness surfaces are studied. The results are statistically analyzed using the triple decomposition technique. The outer layer similarity in the streamwise mean velocity and Reynolds stress profiles indicate that the impact of roughness on the boundary layer primarily localizes within roughness sub-layer. In the streamwise mean velocity profile, both regular and real-world roughness surfaces induce obvious increase to the roughness function ΔU+ as roughness height Ra increases, while discrepancy of ΔU+ between the two types of roughness can be found. Furthermore, turbulence statistics are sensitive to the variations of Ra. As Ra increases, it becomes challenging to organize coherent structures near the wall, resulting in the reduction of streamwise Reynolds stress intensity. In addition, although the skin friction coefficient and ΔU+ are almost the same, the real-world roughness and the corresponding equivalent regular roughness manifest different flow structures near the wall. The real-world roughness contributes greater spatial inhomogeneity but lower turbulence intensity.

Impact of yaw misalignment on turbine loads in the presence of wind farm blockage

SummaryWake steering is very effective in optimizing the power production of an array of turbines aligned with the wind direction. However, the wind farm behaves as a porous obstacle for the incoming flow, inducing a secondary flow in the lateral direction and a reduction of the upstream wind speed. This is normally referred to as blockage effect. Little is known on how the blockage and the secondary flow influence the loads on the turbines when an intentional yaw misalignment is applied to steer the wake. In this work, we assess the variation of the loads on a virtual 4 by 4 array of turbines with intentional yaw misalignment under different levels of turbulence intensity. We estimate the upstream distance at which the incoming wind is influenced by the wind farm, and we determine the wind farm blockage effect on the loads. In presence of low turbulence intensity in the incoming flow, the application of yaw misalignment was found to induce a significant increase of damage equivalent load (DEL) mainly in the most downstream row of turbines. We also found that the sign (positive or negative) of the yaw misalignment affects differently the dynamic loads and the DEL on the turbines. Thus, it is important to consider both the power production and the blade fatigue loads to evaluate the benefits of intentional yaw misalignment control especially in conditions with low turbulence intensity upstream of the wind farm.

Study of Paired Approach Wake Separation Based on Crosswinds

The effect of crosswinds on paired approach (PA) procedures for Closely Spaced Parallel Runways (CSPR) is investigated in this paper by fully utilizing the crosswind environment to implement a more efficient PA and increase runway capacity. An improved wake dissipation model is used to quickly predict the change in the wake velocity field for the PA procedures. The change in the width of the hazard zone is explored in detail using the roll moment coefficient as a determination index. The calculation method for the hazard zone of a wake encounter in a PA is designed considering the influence of crosswind, turbulence, and ground effect. The results show the diffusion rate of the hazard zone and a decrease in the width of the maximum hazard zone under a breezeless environment with increases in the turbulence intensity. The maximum hazard zone width decreases with an increase in crosswind speed. Favorable crosswinds can reduce wake separation and improve the efficiency of a PA. Lower turbulence intensity has a better crosswind effect under a normal PA. The 3-degree offset PA can accommodate larger unfavorable crosswinds, with a higher turbulence intensity having a better crosswind effect. The 3-degree offset PA can substantially increase the proportion of time when no wake affects the PA procedure.