Properties Of Turbulence Research Articles

Experimental characterization of turbulence properties in negative triangularity DIII-D plasmas

Abstract Negative Triangularity (NT) plasmas have demonstrated robustly ELM-free high-performance operation and provide a unique testbed to study how plasma shaping affects turbulent transport. The Beam Emission Spectroscopy (BES) diagnostic provides localized 2D measurements of low-k ($k_{\theta} \rho_s < 1$) density fluctuations. In a sweep of upper triangularity at fixed power, H-mode access is suppressed and an NT-edge is observed. The turbulence amplitude ($\tilde{n}/n$) is shown to decrease by $\sim50\%$ for $\rho<0.9$ in the NT-edge phase as compared to the H-mode phase. Additionally, low-velocity edge modes below 70 kHz are suppressed by triangularity and the dominant mode propagating in the electron diamagnetic direction is seen to broaden in wavenumber space in the NT-edge phase. In a strong NT plasma ($\delta_{avg}\sim-0.5$), low amplitude modes ($\tilde{n}/n <0.5\%$) propagating in the ion-diamagnetic direction with radially-poloidally symmetric eddy structure are identified for $\rho \sim 0.65-0.83$ consistent with Ion Temperature Gradient (ITG) turbulence. Modes consistent with Trapped Electron Mode (TEM) turbulence are observed propagating in the electron-diamagnetic direction for $\rho\gtrsim0.83$ with poloidally extended eddy structure and reduced amplitudes observed at the separatrix. The turbulence properties presented in this paper help validate our understanding of NT turbulence and help explain the improved confinement and unique edge features of NT plasmas.

Anisotropic diffusion of high-energy cosmic rays in magnetohydrodynamic turbulence

The origin of cosmic rays (CRs) and how they propagate remain unclear. Studying the propagation of CRs in magnetohydrodynamic (MHD) turbulence can help to comprehend many open issues related to CR origin and the role of turbulent magnetic fields. To comprehend the phenomenon of slow diffusion in the near-source region, we study the interactions of CRs with the ambient turbulent magnetic field to reveal their universal laws. We numerically study the interactions of CRs with the ambient turbulent magnetic field, considering pulsar wind nebula as a general research case. Taking the magnetization parameter and turbulence spectral index as free parameters, together with radiative losses, we perform three group simulations to analyze the CR spectral, spatial distributions, and possible CR diffusion types. Our studies demonstrate that (1) CR energy density decays with both its effective radius and kinetic energy in the form of power-law distributions; (2) the morphology of the CR spatial distribution strongly depends on the properties of magnetic turbulence and the viewing angle; (3) CRs suffer a slow diffusion near the source and a fast or normal diffusion away from the source; (4) the existence of a power-law relationship between the averaged CR energy density and the magnetization parameter is independent of both CR energy and radiative losses; and (5) radiative losses can suppress CR anisotropic diffusion and soften the power-law distribution of CR energy density. The distribution law established between turbulent magnetic fields and CRs presents an intrinsic property, providing a convenient way to understand complex astrophysical processes related to turbulence cascades.

Cosmic rays escape from their sources

Cosmic rays (CRs) are accelerated in diverse astrophysical objects like supernova remnants, massive star clusters, or pulsars. Fermi acceleration mechanisms built a power-law distribution controlled by the ratio of the acceleration to escape timescales in the acceleration site. Hence, escape is an essential mechanism to establish the particle distribution at cosmic-ray sources and to control the flux of cosmic rays injected into the galaxy. Different models have tried to account for the escape process. However, all show some limitations due to the complexity of the particle release mechanism, usually involving 3D geometry, with specific magnetic turbulence properties linked to the process itself. The escape process is also time dependent and results from the interplay of particle acceleration and injection efficiency in the astrophysical source. Once injected into the interstellar medium, freshly released particles are channelled by the ambient magnetic field, which is itself turbulent. In a simplified view, we mainly focus on the propagation of CRs along 1D magnetic flux tubes before turbulent motions start to mix them over a turbulent coherence length, and then we further question this assumption. Close to their sources, one can also expect cosmic rays to harbour higher pressure with respect to their mean value in the interstellar medium. This intermittency in the CR distribution is prone to trigger several types of kinetic and macro instabilities, among which the resonant streaming instability has been the most investigated. In this article, we review recent observational and theoretical studies treating cosmic-ray escape and propagation in the vicinity of their source. We will consider three main astrophysical contexts: association with massive star clusters, gamma-ray halos around pulsars, and, more specifically, supernova remnants. In particular, we discuss in some detail the cosmic-ray cloud (CRC) model, which has been widely used to investigate CR propagation in the environment of supernova remnants. The review also discusses recent studies on CR-induced feedback over the interstellar medium surrounding the sources associated with the release process, as well as alternative types of driven instabilities.

Radial Evolution of MHD Turbulence Anisotropy in Low Mach Number Solar Wind

Abstract The Parker Solar Probe (PSP) and Wind spacecraft observed the same plasma flow during PSP encounter 15. The solar wind evolves from a sub-Alfvénic flow at 0.08 au to become modestly super-Alfvénic at 1 au. We study the radial evolution of the turbulence properties and deduce the spectral anisotropy based on the nearly incompressible (NI) MHD theory. We find that the spectral index of the z + spectrum remains unchanged (∼−1.53), while the z − spectrum steepens, the index of which changes from −1.35 to −1.47. The fluctuating kinetic energy is on average greater than the fluctuating magnetic field energy in the sub-Alfvénic flow while smaller in the modestly super-Alfvénic flow. The NI MHD theory well interprets the observed Elsässer spectra. The contribution of 2D fluctuations is nonnegligible for the observed z − frequency spectra for both intervals. Particularly, the magnitudes of 2D and NI/slab fluctuations are comparable in the frequency domain for the modestly super-Alfvénic flow, resulting in a slightly concave shape of z − spectrum at 1 au. We show that, in the wavenumber domain, the power ratio of the observed forward NI/slab and 2D fluctuations is ∼15 at 0.08 au, while it decreases to ∼3 at 1 au, suggesting the growing significance of the 2D fluctuations as the turbulence evolves in low Mach number solar wind.

Effect of curvature on the hypersonic turbulent boundary over the curved compression ramp

Direct numerical simulation of the shock wave/turbulent boundary layer interaction on a compression ramp and curved compression ramps with different radii of the curvature at the Mach number Ma=5.0 and Reynolds number Re=16 800/mm is performed, and the purpose of the study is to investigate the impact of different radii of the curvature on the development of the flow. The flow structure and turbulence properties are analyzed. As the curved angle radius increases, the range of flow deceleration and the impact of the shock wave interaction on the turbulent boundary layer gradually decrease, and the peak value of turbulent pulsation amplification in the interaction zone becomes smaller. Mean skin friction decomposition is carried in upstream undisturbed region and reattachment region. The skin friction coefficient in the upstream is primarily composed of the viscous dissipation term Cf,V and the turbulent kinetic energy production term Cf,T. While in the reattachment zone, it is mainly balanced by the term Cf,T and the spatial growth term Cf,G. Bidimensional empirical mode decomposition is applied to further study the contribution of the turbulent motion at different scales to Cf,T, and the result shows that for the compression ramp, Cf,T is mainly contributed by the large-scale vortex structure generated in the interaction zone, while for the curved compression ramp, it is mainly contributed by the rapid amplification of turbulent pulsations caused by the shock wave interaction. This study is not only a new parametric study of the shock wave/turbulent boundary interaction but also provides a reference for the aerodynamic design of hypersonic vehicles.

Three-dimensional evolution and turbulent kinetic energy transport of tip vortex from an elliptical hydrofoil

A non-cavitating tip vortex generated by an elliptical hydrofoil is investigated utilizing tomographic particle image velocimetry (TPIV). Focus is placed on its three-dimensional evolution over a relatively large streamwise region, as well as the transport process of turbulent kinetic energy (TKE). Based on the variations in vortex structure and related vortex properties, three main stages of tip vortex evolution can be identified: formation stage, persistence stage, and decay stage. The boundary between the formation and persistence stages is the position where tip vortex cavitation (TVC) is more prone to incept, attributed to the rapid growth in vortex circulation and vortex-center axial velocity, along with high turbulent fluctuations. During the tip vortex evolution, its swirling momentum significantly influences the axial flow pattern, likely by altering the pressure gradient along the vortex path. TKE transport equation is employed to analyze the turbulent properties of the tip vortex. Flow near the hydrofoil tip is highly turbulent and unsteady, with the local TKE at an excessive level. The local high TKE tends to diffuse into surrounding flow rather than being concentrated within the tip vortex as it moves downstream. TKE is mainly produced on the suction side of hydrofoil, potentially due to local boundary-layer behaviors, and is subsequently transported into the vortex core. As the tip vortex propagates further downstream, the in-core TKE exhibits a decreasing trend, and a relaminarization process appears to occur in far wake region. The flow topology of the tip vortex is examined with the invariants of velocity gradient tensor, providing insights into the topological features during the vortex evolution.

Modal analysis of turbulent flows simulated with spectral element method

Leveraging the high-order nature of spectral element methods, this work introduces a methodology that enables instantaneous, local analysis of turbulent flows through a transformation to a modal space. It also introduces a dynamic explicit modal filter (DEMF) for removing the excess energy in large-eddy simulation of turbulent flows. The transformation is achieved through the application of the discrete Chebyshev transform to nodal solution values, and the resulting modes are employed to characterize and distinguish different turbulent flow properties. Implementing direct numerical simulation (DNS), a qualitative explanation of how modes can assess flow directionality and turbulence properties is provided by considering the modal representation at different locations for different turbulent flows. Additionally, reducing the resolution from DNS, it is shown how modes can qualitatively assess local flow resolvedness. A quantitative assessment of local flow resolvedness is conducted by calculating sequential energy levels from the modes and then comparing them between DNS and under-resolved cases. These energy levels correspond to different scales of motion and their behavior changes as turbulence intensifies and decays. It is observed that flow under-resolvedness manifests itself in the increased magnitudes of higher energy levels corresponding to small scales of motion. Finally, the new DEMF is discussed, which is triggered locally by comparing the local Kolmogorov length scale and the average grid spacing. The filter removes the excess energy in the detected under-resolved regions by selectively removing the energy of the modes that contribute to higher energy levels.

Comparing methods for reducing artificial pressure fluctuations using large eddy simulation in high-rise building wind load assessment

Reducing artificial pressure fluctuations (RAPF) is one of the key challenges in simulating atmospheric boundary layer turbulence. This study, based on the synthetic turbulence method, compares the performance of three RAPF methods: inlet mass correction (IMC), divergence-free correction (DFC), and local pressure correction (LPC). First, large eddy simulations of an empty domain show that the IMC and DFC methods effectively suppress unrealistic pressure fluctuations throughout the flow field. As the turbulence develops downstream, the pressure fluctuations decay rapidly and become almost insignificant. Conversely, the LPC method only reduces local nonphysical pressure fluctuations by adjusting the pressure reference location, but as the distance from the reference point increases, the pressure fluctuations gradually increase. Moreover, the IMC and DFC methods adjust the initial turbulent field to meet inlet mass balance or divergence-free conditions, which results in changes to the initial turbulence characteristics. However, the LPC method avoids modifying the initial turbulence, allowing it to better maintain the original turbulence properties. Finally, the simulations for wind loads on the high-rise building indicate that the application of the IMC, DFC, and LPC methods results in reasonable mean, standard deviation and peak values of pressures on the building surfaces, as well as accurate calculations of the integrated base forces and moments.

Turbulence and flapping pivot axis effects on torsional flutter harvester efficiency by closed-form formula

This “Short Communication” investigates the dynamics of a torsional-flutter energy harvester in atmospheric winds with stationary turbulence. This apparatus is an example of a flutter mill, which operates by exploiting aeroelastic instability as a competitive alternative and as a renewable energy supply for one or few housing units. The apparatus has a rigid blade-airfoil that rotates about a pivot to generate flapping motion. Contrary to recent studies by the second author, the effect of random stationary turbulence on flutter onset is examined by an analytical approach, employed by Scanlan (1997) for bridge flutter analysis. Turbulence effect is simulated by suitably modifying the span-wise coherence equation of the aeroelastic load. The incipient flutter threshold is found as a function of turbulence properties. Various configurations are studied, i.e., pivot position, aspect ratio, turbulence coherence decay parameter and structural damping. The objective is to perform a thorough sensitivity analysis as the necessary premise for the planned, future examination of post-critical instability and operational efficiency of the harvester by suitable modeling and wind tunnel tests.

Self-adaptive turbulence eddy simulation of a supersonic cavity-ramp flow

High Reynolds number supersonic wall-bounded turbulent flow is common in the aviation industry. However, accurately predicting this flow remains a long-standing challenge for turbulence modeling, particularly in separation cases. This study presents a numerical investigation of a Mach 2.92 turbulent cavity-ramp flow employing a new hybrid turbulence modeling approach, denoted as the self-adaptive turbulence eddy simulation (SATES) method. The results are compared with experimental data, as well as with outcomes from the conventional Reynolds-averaged Navier–Stokes (RANS) method and the previous delayed detached eddy simulation (DDES). The SATES model demonstrates a satisfactory prediction of time-averaged and fluctuating quantities in the free shear layer, redeveloping boundary layer, and ramp, showing better accuracy than the RANS results. Notably, the SATES results from the medium grid exhibit similarities to the DDES results from the extremely fine grid which is about 26 times compared with the SATES mesh. Furthermore, the significant features of the supersonic reattached flow, including turbulent properties, vortex structures, and unsteadiness characteristics, are analysed in detail, including the Reynolds stresses anisotropy invariant maps, transport process of vorticity, and frequency spectra. This work confirms that accurate numerical predictions of high Reynolds number supersonic separated and reattached flows are achievable using the SATES method with a relatively coarse mesh maintaining an affordable computational cost.

Forecasting Constraints from Surface Brightness Fluctuations in Galaxy Clusters

Studies of surface brightness (SB) fluctuations in the intracluster medium present an indirect estimate of turbulent pressure support and associated Mach numbers. While high-resolution X-ray spectroscopy can directly constrain line-of-sight gas motions, including those due to turbulence, such observations are relatively expensive and will be limited to nearby, bright clusters. In this respect, SB fluctuations are the most economical means to constrain turbulent motions at large cluster radii across a range of redshifts and masses. To forecast what current and future X-ray and Sunyaev–Zel’dovich facilities may achieve in SB fluctuation studies, I review and synthesize matters of accuracy and precision with respect to calculating power spectra of SB fluctuations, from which turbulent properties are derived. Balancing concerns of power spectrum accuracy and precision across a range of spatial scales, I propose the use of three annuli with [0, 0.4]R 500, [0.4, 1]R 500, and [1, 1.5]R 500. Adopting these three regions, I calculate the uncertainty in the hydrostatic mass bias, σbM , that can be achieved for various instruments in several scenarios. I find that Lynx and AtLAST are competitive in their constraints at R 500, while AtLAST should perform better when constraining σbM at R 200.

Spectrally decomposed denoising diffusion probabilistic models for generative turbulence super-resolution

We investigate the statistical recovery of missing physics and turbulent phenomena in fluid flows using generative machine learning. Here, we develop and test a two-stage super-resolution method using spectral filtering to restore the high-wavenumber components of two flows: Kolmogorov flow and Rayleigh–Bénard convection. We include a rigorous examination of the generated samples via systematic assessment of the statistical properties of turbulence. The present approach extends prior methods to augment an initial super-resolution with a conditional high-wavenumber generation stage. We demonstrate recovery of fields with statistically accurate turbulence on an 8× upsampling task for both the Kolmogorov flow and the Rayleigh–Bénard convection, significantly increasing the range of recovered wavenumbers from the initial super-resolution.

An Experimental Study of Flow and Turbulence Properties near the Rising Sector Gate Mouth Considering the Gate Opening with a PIV Measuring System

Hydraulic structures, such as movable weir gates, are widely installed in rivers and streams for various purposes. Among these is the rising sector gate, which is the focus of this study. This research investigated how different gate openings affect flow velocity and turbulence distributions at the gate mouth. A hydraulic analysis of flow and turbulence characteristics near the mouth of a rising sector gate model was conducted through laboratory experiments with various flow conditions and gate openings utilizing a Particle Image Velocimetry (PIV) system. Experimental tests were carried out with two gate-opening angles (30 and 45 degrees). The PIV measurements revealed significant variations in flow velocity and turbulence properties in response to the gate openings and flow conditions. Notably, in the vicinity of the gate mouth, where the flow regime changes rapidly between the upstream and downstream regions, the turbulence properties in the upstream part of the gate mouth were more than twice those in the downstream part. Additionally, the streamwise distribution of depth-averaged relative turbulence intensity was analyzed. The results showed that the depth-averaged relative turbulence intensity decreased by nearly half as the gate opening increased from 30 to 45 degrees, with the lowest values observed at the gate mouth, followed by an increase downstream. A functional relationship between the maximum flow velocity at the gate mouth during underflow operation and the Froude number was established to guide practical gate operation in the field.

Impact of emergent vegetation on three-dimensional turbulent flow properties and bed morphology in a partially vegetated channel

The study aimed to explore three-dimensional turbulent flow properties and bed morphology in a partially vegetated channel with sand bed conditions. Presence of flexible vegetation in the river and its interaction with the flow are of great significance in understanding the momentum and mass transport in the flow. Experiments were conducted in a straight, tilting rectangular flume with staggered emergent vegetation covering half of the channel width. The results show that the presence of vegetation diverts streamwise velocity from the vegetated side to the non-vegetated side. The study reveals that the presence of vegetation leads to an increase in turbulent intensity, turbulent kinetic energy, and Reynolds shear stress at the transition area between the vegetated and non-vegetated sides of the channel. This increase is attributed to higher transverse flow and momentum exchange in the transition area between the vegetated and non-vegetated sides. In the vegetated side, the vegetation serves as an obstruction, reducing turbulent intensity, turbulent kinetic energy, and Reynolds shear stress compared to the transition area between the vegetated and non-vegetated sides. This reduction in turbulence supports the stability of bed materials and promotes sediment deposition. The presence of vegetation significantly alters the secondary current in the channel. Scour depth along the non-vegetated side was higher than the vegetated side, mainly because the flow concentrated in the centre and non-vegetated side of the channel. The investigation determines that the existence of vegetation on the vegetated side effectively protects against bed erosion and sediment transport. Understanding the impact of emergent flexible vegetation on flow properties and sediment transport can inform decisions about vegetation layouts in river ecosystems.

Turbulence with associated kinetic energy budget in the region of wave-blocking formed over an obstacle

Turbulence characteristics in the region of wave-blocking over a submerged forward-facing obstacle is explored, and the results are compared with those of base-flow over the obstacle. Wave-blocking over obstacle is setup, adjusting the strong incoming flow with counter-propagating waves, and confirmed by linear dispersion relation. A variation in the flow is detected in three distinct segments: flow from the upstream, wave-blocking over the obstacle and the waves propagating from the downstream. The instantaneous velocity is recorded using a three-dimensional micro-acoustic Doppler velocimeter along the flow. Turbulence properties such as the mean velocity, Reynolds stress, turbulent kinetic energy, and associated coherent structures around the wave-blocking are discussed. Moreover, power spectral density, kinetic energy budget, and turbulence length- and time-scales are examined. The stress fractions to the total shear stress contribute higher for only flow than those of wave-blocking over obstacle. The power-spectral peaks at a fixed frequency for wave-blocking along lee side are greater than those of base-flow over obstacle. Kinetic energy budget for only flow over the obstacle is much higher than that of wave-blocking, indicating loss of energy due to wave-blocking. In the near-bed region, length-scale increases indicating the higher momentum and energy transfer. Increase in anisotropy plays significant role in the production. Results are valuable to ship sailing, design of coastal structures, and sediment transport.

Gradient Technique Theory: Tracing Magnetic Field and Obtaining Magnetic Field Strength

The gradient technique is a promising tool with theoretical foundations based on the fundamental properties of MHD turbulence and turbulent reconnection. Its various incarnations use spectroscopic, synchrotron, and intensity data to trace the magnetic field and measure the media magnetization in terms of Alfvén Mach number. We provide an analytical theory of gradient measurements and quantify the effects of averaging gradients along the line of sight and over the plane of the sky. We derive analytical expressions that relate the properties of gradient distribution with the Alfvén Mach number M A. We show that these measurements can be combined with measures of sonic Mach number or line broadening to obtain the magnetic field strength. The corresponding technique has advantages to the Davis–Chandrasekhar–Fermi way of obtaining the magnetic field strength.

Effects of a spoiler attachment on the wake flow of a bed-mounted horizontal pipe

This research investigated the spatial flow field of a pipe with a spoiler attachment and the modifications in the wake flow field of a bed-mounted horizontal pipe due to the attachment of a spoiler to the pipe for two different approach flow conditions. To attain the above-mentioned objective, the spatial evolution of the mean and turbulence flow properties in the flow field of the cylinder with an attached spoiler was determined. In addition, the mean flow and turbulence properties of a pipe without a spoiler attachment were compared with the properties of a pipe with an attached spoiler of height 0.2 D. For this purpose, two approach flow Reynolds numbers based on the pipe's diameter (D) and the free-stream velocity (U∞), Re∞ = 8850 and 11650, were considered. Three-dimensional (3D) velocity measurements were recorded with an acoustic Doppler velocimetry (ADV) between locations 4 D upstream (u/s) and 12 D downstream (d/s) of the pipe. It is observed that the length of the recirculation region is increased extensively due to the spoiler on the pipe from 6 D and 6.4 D to 10.7 D. The peak streamwise velocities for both Reynolds numbers are located near the free-water surface, as separated flows are deflected upward and result in enhanced free-stream velocities, which are higher than their approach flow free-stream velocities. In addition to that, the strength of the backflow is enhanced by 23% due to the attachment of the spoiler as compared to that of the pipe without the spoiler. The streamwise and vertical turbulence intensities are increased by 24% and 36%, respectively, and the wake flow field is found to be highly anisotropic. The streamwise turbulence intensities, Reynolds shear stress (RSS), turbulent kinetic energy (TKE), and turbulence indicator are attaining their peaks near the top level of the spoiler in the wake region. The triple velocity correlations indicate that the switching of sweeps and ejection events takes place near the top level of the spoiler. Therefore, it can be concluded that the spoiler attachment has increased the turbulence level in the wake region, and their highest magnitudes are located near the top level of the spoiler.

Investigation of Coastal Winds and Turbulence Characteristics Using Doppler Lidar

AbstractSea ports play a major role in the transport of goods worldwide, and knowledge of wind characteristics in these areas is vital to maintaining safety. However, coastal wind flow can be highly complex and turbulent, necessitating additional analysis. A Doppler lidar providing continuous wind profiles is deployed in the Port of Genoa, Italy, to characterize the mean wind velocity and turbulence properties within the coastal surface layer (40–250 m above ground level). Weather conditions, reanalysis data, and transient wind profiles are combined to analyze wind field characteristics on a day which experienced a thunderstorm. We also utilize a method to identify and categorize sources of turbulence through analysis of lidar derived quantities such as wind shear, turbulent kinetic energy, and vertical skewness. Seasonal variations in the wind properties are investigated by selecting data from June (summer) and December (winter). Differences are found in dominant wind direction and the associated frequency of convective mixing, with onshore winds most common in summer and offshore winds in winter. The measured lidar velocity is also compared against Monin–Obukhov similarity theory predictions, showing satisfactory agreement at low heights but struggling to reproduce observations of the stable atmospheric conditions present during winter.

The Independence of Magnetic Turbulent Power Spectra to the Presence of Switchbacks in the Inner Heliosphere

An outstanding gap in our knowledge of the solar wind is the relationship between switchbacks and solar wind turbulence. Switchbacks are large fluctuations, even reversals, of the background magnetic field embedded in the solar wind flow. It has been proposed that switchbacks may form as a product of turbulence and decay via coupling with the turbulent cascade. In this work, we examine how properties of solar wind magnetic field turbulence vary in the presence or absence of switchbacks. Specifically, we use in situ particle and fields measurements from Parker Solar Probe to measure magnetic field turbulent wave power, separately in the inertial and kinetic ranges, as a function of switchback magnetic deflection angle. We demonstrate that the angle between the background magnetic field and the solar wind velocity in the spacecraft frame (θ vB ) strongly determines whether Parker Solar Probe samples wave power parallel or perpendicular to the background magnetic field. Further, we show that θ vB is strongly modulated by the switchback magnetic deflection angle. In this analysis, we demonstrate that switchback deflection angle does not correspond to any significant increase in wave power in either the inertial range or at kinetic scales. This result implies that switchbacks do not strongly couple to the turbulent cascade in the inertial or kinetic ranges via turbulent wave–particle interactions. Therefore, we do not expect switchbacks to contribute significantly to solar wind heating through this type of energy conversion pathway although contributions via other mechanisms, such as magnetic reconnection, may still be significant.

Spectral Properties of Turbulence in a Suburban Area of São Paulo Megacity

Spectral Properties of Turbulence in a Suburban Area of São Paulo Megacity