Isotropic Turbulence Research Articles

Comparison of Upwind and Symmetric WENO Schemes in Large Eddy Simulation of Basic Turbulent Flows

The properties of modern WENO schemes are examined as applied to large eddy simulation (LES). The WENO-ZM5 scheme with modified smoothness indicators (“upwind”) and the WEN-O‑SYMBOO6 scheme on a symmetric stencil (“symmetric WENO scheme”) are chosen. The schemes are compared on one-dimensional test problems (advection, Hopf, and Burgers equations) with both smooth and discontinuous solutions. The decay of isotropic turbulence is modeled within LES and the results are discussed. The solutions produced by the new schemes are compared with those based on the central difference scheme, the classical WENO5 scheme, and a hybrid scheme. The level of dissipation of the schemes is compared by analyzing their energy spectra. A similar comparison is made between the LES computations of the temporal evolution of a mixing layer, where the profiles of mean velocity and Reynolds stresses are considered in addition to the energy spectrum.

Experimental investigation of pressure statistics in laboratory homogeneous isotropic turbulence

Pressure gradient and pressure play a key role in the evolution of structures and energy redistribution in turbulence. However, experimental investigations of pressure statistics in turbulent flows are difficult. With development in optical Lagrangian particle tracking (LPT) techniques over the past decades, it is now possible to obtain the pressure gradient fields with high accuracy from the measured acceleration fields, which gives an inspiration to study pressure statistics experimentally. In this work, we construct the instantaneous pressure and pressure gradient fields by the divergence curl correction method, using Lagrangian particle tracking data from laboratory turbulence generated in our turbulence exploration apparatus (TEA), which is newly developed with eight forcing elements arranged symmetrically in space. The measured velocity and acceleration statistics show that the laboratory turbulence in the TEA system is very close to be homogeneous and isotropic. The statistics of pressure gradient and velocity correlation conditioned on velocity confirm the interesting role of pressure gradient in the redistribution of energy in turbulence. In particular, these statistics of pressure gradient are not sensitive to spatial filtering with a filter size up to the lower end of the inertial range, indicating that these statistics capture the characteristics of the pressure gradient at scales in the inertial range or above.

Eddy viscosity enhanced temporal direct deconvolution models for temporal large-eddy simulation of turbulence

A dynamic eddy viscosity (DEV) model and a constant eddy viscosity (CEV) model are proposed for stabilizing the temporal direct deconvolution model (TDDM) in temporal large-eddy simulation of turbulence. Compared to the original unresolved subfilter-scale model used in TDDM, the new eddy viscosity models reduce the number of empirical coefficients and make TDDM more convenient to be applied in practice. The DEV model does not have any empirical coefficients, and the CEV model has only one constant model coefficient that is independent of the filter width and insensitive to the grid resolution. To solve the stability issue of TDDM, an algorithm called the variable filter-width method (VFM) is proposed. In VFM, the filter width is initialized by a small value or 0 and then grows linearly in a small number of time steps until it reaches the target filter width. The three dimensional homogeneous isotropic turbulence is applied to investigate the performance of the proposed models. In the a posteriori testing at different grid resolutions, eddy viscosity enhanced temporal direct deconvolution models show a good accuracy in predicting various statistics and instantaneous spatial structures of turbulence, and they perform better than the original model, especially in the prediction of subfilter-scale (SFS) stress and SFS energy flux. Moreover, the energy spectrum and other flow statistics predicted by the CEV model with a fixed model coefficient 0.03 are in a good agreement with the filtered DNS.

Effects of time-filtering the Navier–Stokes equations

The underlying premise of temporal large eddy simulation (TLES) is that the attenuation of high-frequency content also attenuates the high-wavenumber content. Yet, to date, the effect in wavenumber space of removing high-frequency oscillations by time-domain filtering is not well understood. In this work, we numerically investigate the relationship between the frequency and wavenumber with particular attention to the role of the temporal residual-stress in TLES. Moreover, since under-resolved simulations that use high-order, non-dissipative numerical methods require some measure of artificial dissipation for stabilization, we also discuss the regularization term with practical relevance to under-resolved applications of TLES. Specifically, we analyze the effects of Eulerian time-domain filtering with a causal exponential filter on homogeneous isotropic turbulence. The data are generated by direct numerical simulation of the Navier–Stokes equations, which are driven to maintain an average Reynolds number (Reλ) of 200. A priori, Fourier transformations of the velocity fields were performed in order to compute the unfiltered and filtered energy and dissipation spectra in both wavenumber space and wavenumber–frequency space. Furthermore, the amount of unresolved dissipation of an insufficiently resolved simulation was approximated in an attempt to estimate the required additional artificial dissipation. The results indicate that the numerically motivated stabilization term can be reduced due to temporal filtering. Moreover, it has been shown that a sharp cutoff in the frequency domain does not translate into a sharp cutoff in the wavenumber space. Thus, a hybrid model that combines temporal filtering for the residual-stress and spatial filtering for stabilization might be advantageous.

Experimental investigation of particle aggregation in a humid and turbulent environment

Aggregation of wetted particles in a turbulent flow is experimentally investigated. The particles settle through nearly isotropic turbulence inside a humid air chamber. The particles are pre-chilled so that wetting occurred even at sub-saturated humidity levels. Aggregates that fall out of the turbulent flow are physically sampled and their size distributions quantified to infer bulk sticking efficiencies at various humidity levels. Optical particle tracking techniques are used to detect individual time-resolved collision events, forming an independent measure of the sticking efficiency parameterized by a collision Stokes number. The two methods are contrasted and the limitations of each are discussed. The data are used to develop a new version of the early Costa sticking model, which is utilized by various volcanic ash transport codes. The key outcome of this work is a generalized Costa sticking model which incorporates the effect of the water film thickness coating the particles.

Grey area in embedded wall-modelled LES on a transonic nacelle-aircraft configuration

A scale-resolving hybrid RANS–LES technique is applied to an aircraft-nacelle configuration under transonic flow conditions using the unstructured, compressible TAU solver. In this regard, a wall-modelled LES methodology is locally applied to the nacelle lower surface to examine shock-induced separation. To circumvent the grey-area issue of delayed turbulence onset, a Synthetic Turbulence Generator (STG) is used at the RANS–LES interface. Prior to the actual examinations, fundamental features of the simulation technique are validated by simulations of decaying isotropic turbulence as well as flat plate flows. For the aircraft-nacelle configuration at a Reynolds number of 3.3 million, a sophisticated mesh with 420 million points was designed which refines 32 % of the outer casing surface of the nacelle. The results show a development of a well-resolved turbulent boundary layer with a broad spectrum of turbulent scales which demonstrates the applicability of the mesh and method for aircraft configurations. Furthermore, the necessity of a low-dissipation low-dispersion scheme is demonstrated. However, a noticeable drop of the surface skin friction downstream of the STG motivates further research on the impact of the interface modelling on the shock–boundary layer interaction.

The response of small-scale shear layers to perturbations in turbulence

The perturbation response of small-scale shear layers in turbulence is investigated with direct numerical simulations (DNS). The analysis of shear layers in isotropic turbulence suggests that the typical layer thickness is about four times the Kolmogorov scale $\eta$ . Response for sinusoidal perturbations is investigated for an isolated shear layer, which models a mean flow around the shear layers in turbulence. The vortex formation in the shear layer is optimally promoted by the perturbation whose wavelength divided by the layer thickness is about 7. These results indicate that the small-scale shear instability in turbulence is efficiently promoted by velocity fluctuations with a wavelength of about $30\eta$ . Furthermore, DNS are carried out for decaying turbulence initialised by the artificially modified velocity field of isotropic turbulence. The vortex formation from shear layers is accelerated under the influence of external perturbations with the efficient wavelength to promote the instability. When velocity fluctuations with this wavelength are eliminated by a band-cut filter, the shear layers tend to persist for a long time without producing vortices. These behaviours affect the number of vortices in turbulence, which increases and decreases when velocity perturbations with the unstable wavelength of the instability are artificially amplified and damped, respectively. The increase in the number of vortices results in the enhancement of kinetic energy dissipation, enstrophy production and strain self-amplification. These results indicate that the perturbation response of shear layers is important in the small-scale dynamics of turbulence as well as the modulation of small-scale turbulent motions by external disturbance.

Circulation in Quasi-2D Turbulence: Experimental Observation of the Area Rule and Bifractality.

We present an experimental study of the velocity circulation in a quasi-two-dimensional turbulent flow. We show that the area rule of circulation around simple loops holds in both the forward cascade enstrophy inertial range (ΩIR) and the inverse cascade energy inertial range (EIR): When the side lengths of a loop are all within the same inertial range, the circulation statistics depend on the loop area alone. It is also found that, for circulation around figure-eight loops, the area rule still holds in EIR but is not applicable in ΩIR. In ΩIR, the circulation is nonintermittent; whereas in EIR, the circulation is bifractal: space filling for moments of the order of 3 and below and a monofractal with a dimension of 1.42 for higher orders. Our results demonstrate, as in a numerical study of 3D turbulence [K. P. Iyer et al., Circulation in High Reynolds Number Isotropic Turbulence is a Bifractal, Phys. Rev. X 9, 041006 (2019).PRXHAE2160-330810.1103/PhysRevX.9.041006], that, in terms of circulation, turbulent flows exhibit a simpler behavior than velocity increments, as the latter are multifractals.

Parameterization of turbulence modulation by finite-size solid particles in forced homogeneous isotropic turbulence

Turbulence modulation by finite-size particles in homogeneous isotropic turbulence (HIT) has been investigated numerically and experimentally in many studies, but its controlling parameters are not fully clear. In this work, four non-dimensional parameters governing the turbulent modulation by non-settling particles, i.e. $Re_\lambda$ of the background HIT, the particle-to-fluid density ratio $\rho _p/\rho _f$ , the relative particle size $d_p/\eta$ and the particle volume fraction $\phi _v$ , are identified through dimensional analysis. Then, a parameterization study is conducted based on results from fully resolved direct numerical simulations to investigate the influence of the above non-dimensional parameters on the modulation of turbulent kinetic energy (TKE) and viscous dissipation rate. Empirical models that quantitatively predict the modulation of TKE and dissipation rate are then developed by fitting in the simulation results. These models are used to examine the turbulence modulation results reported in the literature. The model predictions and the data points of TKE modulation show reasonable agreement, but the model predicting the modulation of dissipation rate needs further deliberation as the credibility of the available data points is currently difficult to assess. The generality and the physics behind these empirical models also require further investigation.

New exact Betchov-like relation for the helicity flux in homogeneous turbulence

In homogeneous and isotropic turbulence, the relative contributions of different physical mechanisms to the energy cascade can be quantified by an exact decomposition of the energy flux (Johnson, Phys. Rev. Lett., vol. 124, 2020, 104501; J. Fluid Mech., vol. 922, 2021, A3). We extend the formalism to the transfer of kinetic helicity across scales, important in the presence of large-scale mirror‐breaking mechanisms, to identify physical processes resulting in helicity transfer and quantify their contributions to the mean flux in the inertial range. All subfluxes transfer helicity from large to small scales. Approximately 50 % of the mean flux is due to the scale-local vortex flattening and vortex twisting. We derive a new exact relation between these effects, similar to the Betchov relation for the energy flux, revealing that the mean contribution of the former is three times larger than that of the latter. Multi-scale effects account for the remaining 50 % of the mean flux, with approximate equipartition between multi-scale vortex flattening, twisting and entangling.

Impact of the turbulence wavenumber spectrum and probing beam geometry on Doppler reflectometry perpendicular velocity measurements

The perpendicular propagation velocity of turbulent density fluctuations is an important parameter in fusion plasmas, since sheared plasma flows are crucial for reducing turbulence, and thus an essential input parameter for turbulent transport simulations. In the recent past various fusion devices have observed poloidal asymmetry in this velocity using Doppler reflectometry (DR) and correlation reflectometry. In this work, the phase screen model is used to analytically explain and quantify the combined effect of finite wavenumber resolution due to plasma curvature and probing beam geometry in a realistic turbulence wavenumber spectrum, leading to a reduced dominantly back-scattered wavenumber and a further underestimation of the perpendicular propagation velocity determined by DR. The full-wave code IPF-FD3D, which simulates microwave propagation and scattering, is used as a synthetic DR to study the effects of this diagnostic effect in a circular geometry using various isotropic synthetic turbulence wavenumber spectra. Angular scans from the midplane and variations in the position of the probing antenna are shown to estimate the impact of the diagnostic effect on the poloidal asymmetries.

Neural-network-based mixed subgrid-scale model for turbulent flow

An artificial neural-network-based subgrid-scale (SGS) model, which is capable of predicting turbulent flows at untrained Reynolds numbers and on untrained grid resolution is developed. Providing the grid-scale strain-rate tensor alone as an input leads the model to predict a SGS stress tensor that aligns with the strain-rate tensor, and the model performs similarly to the dynamic Smagorinsky model. On the other hand, providing the resolved stress tensor as an input in addition to the strain-rate tensor is found to significantly improve the prediction of the SGS stress and dissipation, and thereby the accuracy and stability of the solution. In an attempt to apply the neural-network-based model trained for turbulent flows with a limited range of the Reynolds number and grid resolution to turbulent flows at untrained conditions on untrained grid resolution, special attention is given to the normalisation of the input and output tensors. It is found that the successful generalization of the model to turbulence for various untrained conditions and resolution is possible if distributions of the normalised inputs and outputs of the neural network remain unchanged as the Reynolds number and grid resolution vary. In a posteriori tests of the forced and the decaying homogeneous isotropic turbulence and turbulent channel flows, the developed neural-network model is found to predict turbulence statistics more accurately, maintain the numerical stability without ad hoc stabilisation such as clipping of the excessive backscatter, and to be computationally more efficient than the algebraic dynamic SGS models.

Assessing passive scalar dynamics in bubble-induced turbulence using direct numerical simulations

By using direct numerical simulations (DNS) of bubbly flows with passive scalars, we show a transition in the scalar spectra from a $k^{-5/3}$ to a $k^{-3}$ scaling with the wavenumber $k$ , in contrast with those of single-phase isotropic turbulence. For cases with a mean scalar gradient in the horizontal direction, the scalar spectrum decays faster than $k^{-3}$ at high wavenumbers. While the $k^{-3}$ scaling is well established in the bubbly flow velocity spectrum, the scalar spectrum behaviour is not fully understood. We find that the transition length scale of the scalar spectra is comparable to or below the bubble diameter and decreases with the molecular diffusivity of the scalar in the liquid. We use DNS to compute the scalar spectrum budget and show that the scalar fluctuations are produced by the mean scalar gradient at length scales above the bubble diameter, contrary to the velocity fluctuations. At length scales below the bubble diameter, the net scalar transfer scales as $k^{-1}$ inducing the $k^{-3}$ scaling of the scalar spectra. This finding is consistent with the hypothesis proposed by Dung et al. (J. Fluid Mech., vol. 958, 2023, p. A5) about the physical mechanism behind the $k^{-3}$ scaling. We also show dependencies of the bubble suspension's convective scalar diffusivity on the gas volume fraction and molecular diffusivity that differ based on the direction of the mean scalar gradient. For a mean scalar gradient in the vertical direction, we find and qualitatively explain a significant effect of the molecular diffusivity in the gas on the convective scalar diffusivity.

Fundamental time scales of bubble fragmentation in homogeneous isotropic turbulence

We investigate the fundamental time scales that characterise the statistics of fragmentation under homogeneous isotropic turbulence for air–water bubbly flows at moderate to large bubble Weber numbers, $We$ . We elucidate three time scales: $\tau _r$ , the characteristic age of bubbles when their subsequent statistics become stationary; $\tau _\ell$ , the expected lifetime of a bubble before further fragmentation; and $\tau _c$ , the expected time for the air within a bubble to reach the Hinze scale, radius $a_H$ , through the fragmentation cascade. The time scale $\tau _\ell$ is important to the population balance equation (PBE), $\tau _r$ is critical to evaluating the applicability of the PBE no-hysteresis assumption, and $\tau _c$ provides the characteristic time for fragmentation cascades to equilibrate. By identifying a non-dimensionalised average speed $\bar {s}$ at which air moves through the cascade, we derive $\tau _c=C_\tau \varepsilon ^{-1/3} a^{2/3} (1-(a_{max}/a_H)^{-2/3})$ , where $C_\tau =1/\bar {s}$ and $a_{max}$ is the largest bubble radius in the cascade. While $\bar {s}$ is a function of PBE fragmentation statistics, which depend on the measurement interval $T$ , $\bar {s}$ itself is independent of $T$ for $\tau _r \ll T \ll \tau _c$ . We verify the $T$ -independence of $\bar {s}$ and its direct relationship to $\tau _c$ using Monte Carlo simulations. We perform direct numerical simulations (DNS) at moderate to large bubble Weber numbers, $We$ , to measure fragmentation statistics over a range of $T$ . We establish that non-stationary effects decay exponentially with $T$ , independent of $We$ , and provide $\tau _r=C_{r} \varepsilon ^{-1/3} a^{2/3}$ with $C_{r}\approx 0.11$ . This gives $\tau _r\ll \tau _\ell$ , validating the PBE no-hysteresis assumption. From DNS, we measure $\bar {s}$ and find that for large Weber numbers ( $We>30$ ), $C_{\tau }\approx 9$ . In addition to providing $\tau _c$ , this obtains a new constraint on fragmentation models for PBE.

Settling behavior of polydisperse droplets in homogeneous isotropic turbulence

The settling behavior of polydisperse droplets in homogeneous and isotropic turbulence was measured by an ultra-high-resolution two-dimensional Particle Image Velocimetry. The aim of the present study is to provide new insight on the dependence of multi-scale particle settling behavior on characteristic parameters of two-phase turbulent flow via a sophisticate conditional analysis. The relative settling strength (defined as the ratio of mean droplet settling velocity to root mean square velocity of turbulence), whose effect on droplet settling behavior is of the primary interest, ranges as SvL=0.5–2.0. The turbulence Taylor Reynolds number is Reλ=200–300, and the droplet Stokes number is Stp=0.1–10. Voronoï analysis is performed to obtain the concentration field of discrete droplets from particle images. Particle structures including clusters or voids are detected, and the droplet settling velocities corresponding to various probing conditions, such as Stp, local particle concentration, and size of particle structures, were then analyzed. For the present configuration (droplet net sedimentation), there is a non-monotonic dependency of the settling velocity on local particle concentration. The negative correlation between them occurs in the moderate-concentration sub-regime and is insensitive to the variation of SvL, in which individual droplets interact with turbulent flow independently. It can be well explained by the commonly invoked preferential sweeping mechanisms. On the other hand, the dense-concentration regime, in which droplets prefer to accumulate into clusters, presents a positive correlation; namely, the conditional-averaged settling velocity decreases with the increase in local particle concentration. In this sub-regime, it is not the scale of single particles but the scale of particle clusters and the relative strength of turbulence (measured by SvL) that jointly determines the droplet settling behavior. Such a process, to our knowledge, is consistent with the so-called multi-scale preferential sweeping effect.

Spectral response between particle and fluid kinetic energy in decaying homogeneous isotropic turbulence

In particle-laden turbulence, the Fourier Lagrangian spectrum of each phase is regularly computed, and analytically derived response functions relate the Lagrangian spectrum of the fluid and the particle phase. However, due to the periodic nature of the Fourier basis, the analysis is restricted to statistically stationary flows. In the present work, utilizing the bases of time-focalized proper orthogonal decomposition (POD), this analysis is extended to temporally non-stationary turbulence. Studying two-way coupled particle-laden decaying homogeneous isotropic turbulence for various Stokes numbers, it is demonstrated that the temporal POD modes extracted from the dispersed phase may be used for the expansion of both fluid and particle velocities. The POD Lagrangian spectrum of each phase may thus be computed from the same set of modal building blocks, allowing the evaluation of response functions in a POD frame of reference. Based on empirical evaluations, a model for response functions in non-stationary flows is proposed. The related energies of the two phases is well approximated by simple analytical expressions dependent on the particle Stokes number. It is found that the analytical expressions closely resemble those derived through the Fourier analysis of statistically stationary flows. These results suggest the existence of an inherent spectral symmetry underlying the dynamical systems consisting of particle-laden turbulence, a symmetry which spans across stationary/non-stationary particle-laden flow states.

The effects of a spur dike location in a 90° sharp channel bend on flow field: Focus on anisotropy degree and anisotropy nature

In this research, the flow features around a spur dike located in a 90˚ sharp channel bend have been studied experimentally in detail. Results showed that the effects of the spur dike on upstream sections increased by increasing α (spur dike location from the beginning of the bend). In addition, by increasing α, the horseshoe vortex (C3) and secondary flow in the channel bend (C1) strengthened. The energy and the Reynolds shear stress in the C3 region decreased by increasing α. It is recommended to use a Barycenteric Map (BM) instead of the normal Reynolds stresses to find the anisotropy nature accurately. A strong anisotropic condition was detected at the border of the recirculation flow region and the main flow. However, in the C3 and the interaction regions, the isotropy condition improved. In the main flow region, by increasing α, the isotropy degree improved. However, by increasing α, an increase in the development of the region with a high anisotropy degree towards the recirculation region was observed. The anisotropy degree in the near-bed layer region and the shear layer region is comparable. However, the anisotropy nature is different. The maximum error of the numerical simulation based on isotropic turbulence occurred at the shear layer region where the severe cigar-shaped turbulence occurred.

РАДИОФИЗИЧЕСКИЕ ОСОБЕННОСТИ РАДИОЛОКАЦИОННЫХ ОТРАЖЕНИЙ ОТ ЯСНОГО НЕБА В МИЛЛИМЕТРОВОМ ДИАПАЗОНЕ ДЛИН ВОЛН

The features of the Doppler spectra of radar signals scattered by atmospheric inhomogeneities under clear sky conditions are studied. A technique for measuring the wind field in the millimeter wavelength range using a coherent radar is described. The results of measurements of the radar reflectivity Z under summer convection cannot be interpreted by the theory of Bragg scattering on inhomogeneities due to locally homogeneous isotropic turbulence. The experimental values can exceed the theoretical estimates by two orders of magnitude. An analysis of the fine structure of the Doppler spectra obtained under summer conditions indicates their large width, multi-peakedness, and spatial variability. The authors attribute these features to the formation of thermals, the structure of which is accompanied by closely spaced ascending and descending flows. The high level of radar reflectivity also confirms the convective version of signal generation, in which a large moisture difference in closely spaced ascending and descending layers at the thermal boundary forms eddies with large refractive index gradients.

Super-resolution reconstruction for the three-dimensional turbulence flows with a back-projection network

Recent attempts to employ deep learning technology for the super-resolution (SR) reconstruction of turbulence have focused chiefly on reconstructing two-dimensional (2D) slices of the three-dimensional (3D) flow fields. However, tomographic particle image velocimetry (Tomo-PIV) measurements yield 3D velocity fields. The resolutions of 3D velocity field data along three directions cannot be simultaneously enhanced using a 2D SR reconstruction model. Additionally, a 3D velocity flow field structure cannot be accurately reconstructed using a 2D model. Therefore, we present a 3D flow field SR reconstruction method (FSR-3D) based on a back-projection network. The FSR-3D model incorporates a multiscale convolutional residual block and an up-and-down projection module and establishes the mapping relationship between low-resolution features and high-resolution (HR) features through an iterative mechanism. The proposed model is validated using two experiments. First, the original velocity field is reconstructed from downsampled forced isotropic turbulence data. Second, the downsampled direct numerical simulation (DNS) data of a turbulent channel flow are used to reconstruct the HR flow field to verify the reconstruction capability of the FSR-3D model with respect to the flow field of the boundary layer. Third, Tomo-PIV measurements of the wake flow behind a circular cylinder are used to further verify the generalization ability of the model and the reconstruction effect of the measured data. The experimental results demonstrate that the proposed FSR-3D model can accurately reconstruct the HR 3D velocity field. At the same time, the properties of the reconstruction results, such as their vortex structure, kinetic energy spectrum, and Reynolds stress, are closer to the DNS results than those of the 2D model. The reconstruction results of the Tomo-PIV measurement data show that the FSR-3D model has good generalization ability.

Super-resolution reconstruction of turbulent flows with a transformer-based deep learning framework

Details of flow field are highly relevant to understand the mechanism of turbulence, but obtaining high-resolution turbulence often requires enormous computing resources. Although the super-resolution reconstruction of turbulent flow fields is an efficient way to obtain the details, the traditional interpolation methods are difficult to reconstruct small-scale structures, and the results are too smooth. In this paper, based on the transformer backbone architecture, we present a super-resolution transformer for turbulence to reconstruct turbulent flow fields with high quality. It is supervised and has a broader perceptual field for better extraction of deep-level features. The model is applied to forced isotropic turbulence and turbulent channel flow dataset, and the reconstructed instantaneous flow fields are comprehensively compared and analyzed. The results show that SRTT can recover the turbulent flow fields with high spatial resolution and capture small-scale details. It can obtain either the isotropic or the anisotropic turbulent properties even in complex flow configurations.