Turbulence Integral Scale Research Articles

Turbulence Revealed by Wavelet Transform: Power Spectrum and Intermittency for the Velocity Field of the Cosmic Baryonic Fluid

We use continuous wavelet transform techniques to construct the global and environment-dependent wavelet statistics, such as energy spectrum and kurtosis, to study the fluctuation and intermittency of the turbulent motion in the cosmic fluid velocity field with the IllustrisTNG simulation data. We find that the peak scale of the energy spectrum defines a characteristic scale, which can be regarded as the integral scale of turbulence, and the Nyquist wavenumber can be regarded as the dissipation scale. With these two characteristic scales, the energy spectrum can be divided into the energy-containing range, the inertial range, and the dissipation range of turbulence. The wavelet kurtosis is an increasing function of the wavenumber k, which first grows rapidly then slowly with k, indicating that the cosmic fluid becomes increasingly intermittent with k. In the energy-containing range, the energy spectrum increases significantly from z = 2 to 1, but remains almost unchanged from z = 1 to 0. We find that both the environment-dependent spectrum and kurtosis are similar to the global ones, and the magnitude of the spectrum is smallest in the lowest-density and largest in the highest-density environment, suggesting that the cosmic fluid is more turbulent in a high-density than in a low-density environment. In the inertial range, the energy spectrum’s exponent is steeper than both the Kolmogorov and Burgers exponents, indicating more efficient energy transfer compared to Kolmogorov or Burgers turbulence.

Effect of three-dimensionality of turbulence on the along-wind loads of square cross-sectional structures

The existing theories for along-wind loads on slender structures, based on the “strip assumption” overlook the three-dimensionality of turbulence. However, numerous experimental phenomena contradicting the “strip assumption” highlight the need to consider the effects of three-dimensional turbulence (3D effect). This study develops an analysis model that considers the three-dimensionality of turbulence and derives a function containing the section-shape-dependent characteristic parameters to represent the 3D effect. A method for identifying the parameters through a wind tunnel test is proposed to solve this function. The parameters for the square cross section are then identified in two different turbulence fields, revealing that the identification parameters of both cases are nearly identical. This similarity indicates that the parameters are independent of the turbulence validating the proposed theories. Finally, the 3D effect on square cross-sectional structures with different aspect ratios under various turbulence integral scales is analyzed. The results showed that as the ratio of the turbulence integral scale to the windward width of the structures increases, the 3D effect reduces, but the rate of reduction slows down. In addition, increasing the aspect ratios of structures further mitigates the 3D effect, enhancing the accuracy of the “strip assumption.” These results can be a reference for evaluating the accuracy of the “strip assumption” theory for square cross-sectional high-rise buildings in atmospheric boundary layer turbulence. The proposed method can be applied to investigate the 3D effect on along-wind loads of slender structures with various cross-sectional shapes.

Effects of turbulence integral scale on the fluctuating pressures on side face of the standard tall building model

Effects of turbulence integral scale on the fluctuating pressures on side face of the standard tall building model

Mathematical Analysis of the Wind Field Characteristics at a Towering Peak Protruding out of a Steep Mountainside

Wind field characteristics in a complex topography are significantly influenced by the nature of the surrounding terrains. This study employs onsite measurements to investigate the wind field characteristics at a towering peak protruding out of a steep mountainside, where butterfly−lookalike landscape platform will be constructed; the impact of the surrounding topography on the wind flow is highlighted. The results showed that the blocking effect of the mountains in the mountainous side of the valley caused a significant drop in the mean wind speed from that direction. The stationary test (reverse arrangement test) indicated that the wind speed had a strong nonstationary characteristic, necessitating the employment of a steady and nonstationary wind speed model to assess the wind turbulence characteristics. The three directions’ wind turbulence integral scales were critically influenced by the occurrence of the wind speedup effect, unexpectedly resulting in the vertical turbulence integral scale being the greatest of the three. Furthermore, the measured wind turbulence properties under both wind speed models showed certain variations from the recommended specifications. Consequently, the impact of the local terrain and the speedup effect on the wind characteristics must be thoroughly evaluated to ensure the structural stability of structures installed at a similar topography.

Analysis of the Near-Ground Wind Field Characteristics during Typhoon Soulik

In 2013, during Typhoon Soulik, wind data were collected at various heights above the ground (15, 27, 53, 67, and 82 m) on the 550 kV 52# pole transmission tower in Ningde City, Fujian Province. The wind speed profile, turbulence intensity, gust factor, crest factor, and power spectrum were analyzed using 10 min interval wind speed records. The results show the following: (1) the average wind velocity of Typhoon Soulik varies in accordance with both the power law and the logarithmic law, but the Deaves–Harris model exhibits significant discrepancies; (2) the turbulence intensity in u, v, and w orientations decreases with the average wind velocity at each height. Exponential fitting is conducted on the strength of turbulence and gust factor profiles in each direction based on the standards of different countries, resulting in the derivation of empirical expressions; (3) the integral scale components of turbulence in u, v, and w orientations exhibit a positive correlation with both average wind velocity and height. The turbulence integral scale ratios in the longitudinal, transverse, and vertical directions at heights of 15, 53, and 82 m are 1:0.68:0.11, 1:0.67:0.27, and 1:0.67:0.30, respectively; (4) the Von Karman empirical spectrum and the modified Kaimal cross-spectrum model closely match the observed wind power spectrum of Typhoon Soulik. The presented results contribute to furthering references for wind-resistant design of structures in typhoon-prone areas and prevention of typhoon-related disasters.

Effect of turbulent integral scale on non-Gaussian characteristics of surface wind pressure on square cylinder

This study investigated the statistical properties of the pressure fluctuations on a square cylinder across three distinct turbulence fields characterized by varying turbulent integral scales. The effect of turbulent integral scale on the non-Gaussian characteristics and extreme surface wind pressure acting on square cylinders beneath the separating flow were studied in detail. The findings indicated that the pressure distribution on the windward surface generally conformed to a Gaussian distribution, whereas notable non-Gaussian characteristics were observed in the pressure distribution on the side and leeward surfaces. The fluctuating pressure, skewness, kurtosis, peak factor, and extreme pressure increase with an increasing ratio of turbulent integral scale to structural depth (Lux/D), whereas the mean pressure remains unaffected by variations in Lux/D. As Lux increased, the energy of the internal vortices in the shear layer also increased. As a result, the non-Gaussian features of the pressure caused by vortex breakdown become more pronounced. Compared with Lux/D = 1.96, the underestimated value of the extreme pressure on the square cylinder had a maximum difference of up to 15.4% at Lux/D = 0.53. Therefore, the corresponding turbulent integral scale should be accurately simulated when measuring wind loading on a structure through wind tunnel tests.

Theoretical and experimental study of the spanwise effect of turbulence on the aerodynamic lift on a wing with different aspect ratios

In this paper, a combined theoretical and experimental study is carried out to investigate the spanwise effect of turbulence on the aerodynamic lift on a wing with different aspect ratios. The ratio of the mean square variance of the aerodynamic lift calculated by the commonly used strip theory and the two-wavenumber buffeting theory is analyzed comprehensively for the wings with different aspect ratios in turbulence with various integral scales. To validate the theoretical analysis and achieve a deeper understanding of the spanwise effects of turbulence, wind tunnel experiments are performed on National Advisory Committee for Aeronautics 0015 airfoils in grid-generated turbulent flows with different integral scales. The results demonstrate that it is essential to use the two-wavenumber buffeting theory to account for the spanwise effect of turbulence when calculating the aerodynamic lifts on wings with small aspect ratios, especially when in small-scale turbulence. The deviations between the equivalent two-wavenumber coherence function and the spanwise effect influence function at low reduced streamwise wavenumbers are the underlying causes for spanwise effects of turbulence. To achieve reliable wind tunnel testing results, appropriate simulations of the ratio of the turbulence integral scale to the chord are very important in the measurements of aerodynamic lifts on finite-span wing sections, especially for those with small aspect ratios.

Accelerations of large inertial particles in turbulence

Understanding the dynamics of material objects advected by turbulent flows is a long-standing question in fluid dynamics. In this perspective article we focus on the characterization of the statistical properties of non-interacting finite-sized massive spherical particles advected by a vigorous turbulent flow. We study the fluctuations and temporal correlations of particle accelerations and explore their behaviours with respect to the particle size and the particle mass density by means of fully resolved numerical simulations. We observe that the measured trends cannot be interpreted as the simple multiplicative combination of the two dominant effects: the spatial filtering of fluid accelerations and the added-mass–adjusted fluid-to-particle density ratio. We argue that other hydrodynamical forces or effects, e.g., preferential flow sampling, have still a significant role even at the largest particle sizes, which reach here the integral scale of turbulence.

Experimental and numerical study on buffeting force characteristics of the π -shaped bridge deck

In this study, a π-shaped main beam with typical geometric characteristic parameters was selected for conducting wind tunnel tests, and the characteristics of the buffeting force were measured. Based on the measured results, numerical expansion research was conducted using the narrowband synthetic random flow generation (NSRFG) turbulent inlet method, and a grid strategy was provided. By changing the geometric characteristic parameters of the π-shaped girder, a comparative study was conducted using proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods, revealing the influence of cross-sectional geometric characteristic parameters on the buffeting force characteristics and analyzing their mechanism of action. The results indicate that the inlet wind parameters of the NSRFG need to be adapted to the grid size. The grid filter size at the front end of the model should be smaller than 0.193 of the along-wind turbulence integral scale, which can then be used to solve for 80% of the turbulent kinetic energy. The smaller the aspect ratio is, the larger the buffeting force spectrum is, and the smaller the opening ratio is, the smaller the buffeting force spectrum is. The opening ratio strongly influences the buffeting lift spectrum, and the aspect ratio strongly influences the buffeting drag spectrum. The POD decomposition indicates that the geometric characteristic parameters affect the shape, strength, position, and direction of vortices at the section opening. DMD decomposition indicates that geometric feature parameters affect the frequency and growth rate of dominant modes as well as the directionality and regularity of vortex distribution.

Prediction and Early Warning of Extreme Winds for High-Speed Railway Bridge Construction Using Machine-Learning Methods

Measuring the impact of extreme winds is important in high-speed railway bridge construction to avoid the risk of engineering accidents. This study presents an early-warning framework for high-speed railway (HSR) bridge construction under extreme wind conditions, using a long-span continuous beam bridge constructed in a typhoon-prone area as a case study. Specifically, on-site wind environment measurements during a typhoon are utilized, and parameters such as fluctuating wind turbulence intensity, gust factor, turbulence integral scale, and power spectral density are employed to characterize the wind environment. Multi-step prediction of gust wind speed during the bridge construction is performed using the hybrid Back Propagation-Genetic Algorithm (BP-GA). Hierarchical warnings and control actions are proposed and implemented based on the prediction results. The analysis results of wind parameters revealed a discrepancy between the measured and specified typhoon turbulence intensities, with the windward turbulence intensity being lower than specified. The longitudinal average gust factor exceeded the transverse value. The prediction curve based on the BP-GA algorithm closely resembles the actual curve, meeting accuracy requirements. Notably, the one-step prediction provided the most accurate results. Based on the predicted wind speed trend for the upcoming half-hour, appropriate hierarchical warnings and control measures were conducted.

How do crosswinds from two turbulent generators affect the aerodynamic loads of running trains at tunnel entrances?

In order to investigate the effect of natural turbulent crosswinds on the aerodynamic loads of a high-speed train (HST) running through a tunnel entrance of high-speed railways, the new contribution is that the changing law of the HST's aerodynamic loads under the incoming turbulence with actual turbulence integral scale is revealed when the HST running in tunnel-flat ground-tunnel scenes, based on two types of turbulence generators with size scaled up by 8 times. The train surface pressure coefficients of the numerical model are compared with the corresponding results of wind tunnel experiments to verify the computational fluid dynamics method. The primary results show that the incoming turbulent flow generated by the spire is consistent with the characteristics of the measured wind. The peak aerodynamic load coefficients of the head carriage increase 1.12–1.5 and 1.06–2.0 times, respectively, under the incoming turbulent flow by the spire and fence, compared to the incoming flow of 11.50 m/s.

Integral Turbulent Length and Time Scales of Higher Order Moments

Turbulent length and time scales represent a fundamental quantity for analysing and modelling turbulent flows. Although higher order statistical moments have been conveniently used for decades to describe the mean behaviour of turbulent fluid flow, the definition of the integral turbulent scales seems to be limited to the velocity or its fluctuation itself (i.e. the first moment). Higher order moments are characterized by smaller integral scales and a framework is proposed for estimating autocorrelation functions and integral turbulent length or time scales of higher order moments under the assumption that the probability distribution of the velocity field is Gaussian. The new relations are tested for synthetic turbulence as well as for DNS data of a turbulent plane jet at Reynolds number 10000. The present results in particular suggest that the length or time scales of higher order moments can be markedly smaller than those of the turbulent variable itself, which has implications for statistical uncertainty estimates of higher order moments.

A physics-driven Σ-Y atomization model for heavy-duty engine simulations

The atomization of a liquid jet is a multi-scale and multi-physics problem of interest for many engineering applications. Particularly, it drives the fuel-oxidizer mixing and dictates the efficiency of combustion engines. High-fidelity multi-phase simulations remain challenging due to the excessive computational cost required to capture all the atomization scales. Thus, atomization models are necessary to represent sub-grid liquid structures. In this work, a modified Σ-Y model in the context of Eulerian-Lagrangian Spray Atomization (ELSA) is used to transport the surface area density of the spray. The model's predictive performance is assessed under various operating conditions relevant to heavy-duty engines using the Engine Combustion Network (ECN) Spray C and Spray D research-grade injectors. The classic droplet collision formulation of the Σ-Y model alone does not replicate the response of the measured spray surface area to changes in injector, ambient pressure, and injection pressure, requiring individual tuning of the model's parameters. Instead, a transition between dense and dilute spray breakup mechanisms is proposed in terms of the average droplet spacing. The collision breakup mechanism represents the dilute spray, whereas the droplet size in the dense spray is driven by a competition between the integral scale of turbulence and the balance between the turbulent kinetic energy and the surface energy of the droplets. Such an approach minimizes the requirements for model tuning. Moreover, the role of the constants of a compressible standard k-ε RANS model is assessed in the injector's internal flow and external spray simulation framework, and an updated set is proposed. The results are validated against x-ray radiography and Ultra-Small Angle X-ray Scattering (USAXS) data and highlight the predictive capabilities of the proposed physics-driven Σ-Y model, which is compatible with engine simulation turnaround times.

Three distinct scales dominate the role of eolian electric fields in dust turbulent transport

Although previous studies have shown that eolian electric fields significantly alter the lifting and dynamics of dust particles, they are limited to mean fields. The effects of eolian electric fields on the dust turbulent transport have not been reported before. Here, by combing the observational data and wavelet-based spectral analysis, we find that eolian electric fields enhance the vertical turbulent transport of dust particles in the near-surface layer and exhibit three distinct crucial scales. Specifically, the eolian electric fields exhibit a dominant promoting effect at the kilometer-sized synoptic scale, a secondary suppressive effect at the hectometer-sized very-large-scale motion scale, and a negligible effect at the decameter-sized turbulent integral scale. Such scale-dependent electrical effects can be explained by the fact that the linear coupling between vertical eolian electric field and dust concentration is strongest at the synoptic scale, followed by the very-large-scale motion scale, and is weakest at the turbulent integral scale.

Aerodynamic characteristics of a streamlined box girder under shear flow considering oncoming turbulence

Non-synoptic winds, such as typhoons and downbursts, are frequently characterized by shear flow associated with turbulence, which affects the aerodynamic performance of long-span bridges. To reveal the aerodynamic characteristics of streamlined box girders under non-synoptic winds, multi-fan wind tunnel (MFWT) tests were used to investigate the aerodynamic effect around a streamlined box girder considering the action of shear flow with different velocity gradients, turbulence intensities, and integral scales. In the MFWT tests, the high shear rate and large turbulence intensity were observed to magnify the mean wind pressure coefficient, whereas the variation in the turbulence integral scale had a slight effect on the mean wind pressure coefficient distribution. An increase in the shear rate was observed to be beneficial in reducing the drag and moment coefficients, as well as in increasing the lift coefficient. The empirical aerodynamic prediction relationships revealed that the influence of turbulence intensity on the aerodynamic coefficient is non-linear, whereas that of the turbulence integral scale and shear rate on the aerodynamic coefficient is linear. Additionally, the large eddy simulation (LES) method was used to study the vortex-shedding behaviors and aerodynamic spectrum characteristics of the streamlined box girder under shear flow. The LES results showed that larger shear parameters amplify the amplitudes of high-frequency aerodynamic forces. The vortex frequently begins from the low-velocity side of the streamlined box girder, which induces a suction effect on the low-velocity side that is greater than that on the high-velocity side.

Identification of two-dimensional aerodynamic admittance of a central-slotted box girder based on force-balance measurements

This paper presents an experimental investigation of buffeting lift forces on a central-slotted box girder in turbulent flow, and aims to identify the corresponding generalized aerodynamic admittance (generalized-AAF) and two-dimensional aerodynamic admittance (2D-AAF). The generalized-AAF is obtained using the one-wavenumber spectra of lift and wind fluctuations, while the 2D-AAF is obtained using an improved method based on force-balance measurement. The key to this improved method is separating out the three-dimensional effect of turbulence (3D-effect) from the generalized-AAF while considering the segment length of the force measurement and turbulence integral scale. The results indicate that the generalized-AAF of the central-slotted box girder is much less than the Sears function, which is consistent with most previous studies. However, the values of 2D-AAF decay more slowly in comparison with the Sears function. An empirical formula for the 2D-AAF of the central-slotted box girder is given based on the experimental data. Additionally, the study finds that the ratio of the turbulent integral scale to the characteristic dimension of the model plays a significant role in determining the 3D-effect of turbulence, resulting in the difference between the generalized-AAF and 2D-AAF. Therefore, the 2D-AAF is particularly useful for estimating the buffeting force of a bridge deck when the turbulence scale does not match the size of the model.

Experimental investigation on two-dimensional aerodynamic admittances of rectangular cylinders in various turbulent flows

This paper conducts an experimental investigation of two-dimensional aerodynamic admittances (2D AAFs) for rectangular 5:1 cylinders within various turbulent flow fields. The determination of 2D AAF is achieved by removing the influence of the three-dimensional effect (3D effect) from the traditional AAF, wherein the traditional AAF can be straightly derived based on the ratio of the one-dimensional fluctuating force spectrum to the one-dimensional turbulent wind spectrum. In line with prior research, the values of traditional AAFs show variations in response to the 3D effect in different turbulent flow fields. Moreover, within homo-turbulence conditions, or more specifically, under similar turbulence intensity, the traditional AAFs differ depending on the turbulent integral scale to the model characteristic width ratios (dimensionless turbulent integral scale). Compared to the traditional AAF, the 2D AAF effectively cuts down on the discrepancies arising from the dimensionless turbulent integral scale. In cases where different dimensionless turbulent integral scales are present but the turbulence intensity remains constant, the 2D AAFs are almost consistent. Nevertheless, it can be observed that the 2D AAF of the rectangular 5:1 cylinder is still affected by turbulence intensity. For different turbulence intensities, the 2D AAFs have certain changes. When there is less turbulence intensity, it frequently approaches the quasi-steady value, and as the turbulence intensity increases, it gradually approaches the Sears function.

Effects of Bubble Plumes on Lake Dynamics, Near‐Bottom Turbulence, and Transfer of Dissolved Oxygen at the Sediment‐Water Interface

AbstractWe quantify the lake dynamics, near‐bottom turbulence, flux of dissolved oxygen (DO) across the sediment‐water interface (SWI) and their interactions during oxygenation in two lakes. Field observations show that the lake dynamics were modified by the bubble plumes, showing enhanced mixing in the near‐field of the plumes. The interaction of the bubble‐induced flow with the internal density structure resulted in downwelling of warm water into the hypolimnion in the far‐field of the plumes. Within the bottom boundary layer (BBL), both lakes show weak oscillating flows primarily induced by seiching. The vertical profile of mean velocity within 0.4 m above the bed follows a logarithmic scaling. One lake shows a larger drag coefficient than those in stationary BBLs, where the classic law‐of‐the‐wall is valid. The injection of oxygen elevated the water column DO and hence, altered the DO flux across the SWI. The gas transfer velocity is driven by turbulence and is correlated with the bottom shear velocity. The thickness of the diffusive boundary layer was found to be consistent with the Batchelor length scale. The dynamics of the surface renewal time follow a log‐normal distribution, and the turbulent integral time scale is comparable to the surface renewal time. The analyses suggest that the effect of bubble plumes on the BBL turbulence is limited and that the canonical scales of turbulence emerge for the time‐average statistics, validating the turbulence scaling of gas transfer velocity in low‐energy lakes.

Numerical study of the effects of ventilation rates on supercavity dynamics and acoustic characteristics

This paper presents a numerical simulation investigation of the hydrodynamic and acoustic characteristics of ventilated supercavities that operate at various ventilation rates. The large eddy simulation (LES) and Ffowcs Williams–Hawkings (FW-H) methods are used to solve the unsteady flow field and noise. The results show that the ventilation rate plays an important role in cavity closure forms and can improve hydrodynamic performance. There is a transition from re-entrant flow closure to a stable double-vortex tube closure form at the supercavity tail as the ventilation rate increases. Meanwhile, under the condition of a high ventilation rate, the re-entrant flow region in the cavity gradually shrinks and hairpin vortices appear, the body length of the cavity increases,and the unsteadiness at the supercavity tail is weakened. However, the turbulence intensity and integral scale both increase with the ventilation rate. Moreover, it is found that the noise is closely related to supercavity closure form. Ventilated supercavities with closure forms of double-vortex tubes have better noise performance. Interestingly, as the ventilation rate increases, the total sound pressure levels are improved. The wavenumber-frequency spectra of supercavity turbulent pulsating pressures under studied ventilation rates are similar, but there are some differences in some local areas.

A strategy for modifying the effect of turbulence integral scale on fluctuating pressures of rectangular prisms

The turbulence integral scale has a significant effect on the fluctuating pressures encountered by prisms. At present, the turbulence integral scale cannot be adequately simulated, leading to errors in the fluctuating pressure. Based on the two-wavenumber aerodynamic admittance function of fluctuating pressure, this paper describes a strategy for modifying the fluctuating pressure of rectangular prisms in turbulent flows. Using the three-dimensional theory of lift, a three-dimensional model of fluctuating pressure is established, in which the two-wavenumber power spectrum of fluctuating pressure is the product of the two-wavenumber coherence and the one-wavenumber power spectrum of fluctuating pressure, and is also the product of the two-wavenumber aerodynamic admittance function and the two-wavenumber power spectrum of oncoming velocity. An empirical form of the-wavenumber coherence of fluctuating pressure is derived, allowing the two-wavenumber power spectrum of fluctuating pressure to be calculated, and the two-wavenumber aerodynamic admittance function of fluctuating pressure to be obtained. The two-wavenumber aerodynamic admittance function of fluctuating pressure on a given body is almost independent of the turbulence, indicating that only one test is needed to modify the simulated error of fluctuating pressure. Finally, the results for a prism with a 1:3 side-ratio show that the simulated error of fluctuating pressure can be ignored when the simulated turbulence integral scale is 0.5 or 1.1 times the target value, and the simulated error is reduced from 24% to around 10% when the simulated turbulence integral scale is 0.25 times the target value.