Turbulent Enstrophy Research Articles

Backscatter in energetically-constrained Leith parameterizations

This paper combines two strains in the literature on subgrid-scale parameterizations for eddying ocean models to develop six new parameterizations and test them in an idealized quasigeostrophic model. The first strain develops nonlinear, Smagorinsky-like Leith scalings for the viscous coefficient based on reasoning about the turbulent forward enstrophy cascade of geophysical turbulence. The second introduces backscatter whose amplitude is scaled to re-inject a portion of the energy dissipated by other parameterizations. In the new parameterizations developed here the backscatter and viscous coefficients depend on each other and are set to simultaneously absorb the forward enstrophy (or potential enstrophy) cascade and backscatter a portion of the dissipated energy. The addition of backscatter to Leith-scaled nonlinear viscosity improves the simulations at resolutions from 4 km to 24 km by increasing the total kinetic energy and by reducing the fraction of the total energy dissipation rate associated with the net effect of viscosity and backscatter. Versions that use biharmonic viscosity to absorb the enstrophy cascade perform better than versions using a harmonic viscosity, and purely viscous closures perform better than closures that dissipate both kinetic and potential energy. Stochastic and deterministic backscatter schemes are developed, and though similar, the deterministic schemes perform slightly better.

Effects of Lewis and Karlovitz numbers on transport equations for turbulent kinetic energy and enstrophy

Effects of Lewis and Karlovitz numbers on transport equations for turbulent kinetic energy and enstrophy

Statistical characteristics of turbulent mixing in spherical and cylindrical converging Richtmyer–Meshkov instabilities

In this paper, the Richtmyer–Meshkov instabilities in spherical and cylindrical converging geometries with a Mach number of approximately 1.5 are investigated by using the high resolution implicit large eddy simulation method, and the influence of the geometric effect on the turbulent mixing is investigated. The heavy fluid is sulphur hexafluoride (SF6), and the light fluid is nitrogen (N2). The shock wave converges from the heavy fluid into the light fluid. The Atwood number is 0.678. The total structured and uniform Cartesian grid node number in the main computational domain is 20483. In addition, to avoid the influence of boundary reflection, a sufficiently long sponge layer with 50 non-uniform coarse grids is added for each non-periodic boundary. Present numerical simulations have high and nonlinear initial perturbation levels, which rapidly lead to turbulent mixing in the mixing layers. Firstly, some physical-variable mean profiles, including mass fraction, Taylor Reynolds number, turbulent kinetic energy, enstrophy and helicity, are provided. Second, the mixing characteristics in the spherical and cylindrical turbulent mixing layers are investigated, such as molecular mixing fraction, efficiency Atwood number, turbulent mass-flux velocity and density self-correlation. Then, Reynolds stress and anisotropy are also investigated. Finally, the radial velocity, velocity divergence and enstrophy in the spherical and cylindrical turbulent mixing layers are studied using the method of conditional statistical analysis. Present numerical results show that the geometric effect has a great influence on the converging Richtmyer–Meshkov instability mixing layers.

Curved Surface Minijet Impingement Phenomena Analysed with ζ-f Turbulence Model

The jet impingement phenomenon plays an important role among the heat transfer intensification methods. Very often its application and analyses refer to simple flat surfaces, while there is a lack of information in the literature for cases addressing curved surfaces. In the present work, the single jet impingement on the non-flat (concave and convex) surface is studied for a wide range of geometries, which originate from the mini-jet heat-exchanger design. The numerical simulations were performed by an advanced ζ-f turbulence model implemented in the open-source OpenFOAM (ESI-OpenCFD Ltd, Bracknell, United Kingdom) code. Noticeable differences in the phenomena occurring on the convex and concave surfaces were identified in the stagnation zone. Besides, the existence and location of the secondary peak in the Nusselt number distribution differed between the cases. These distributions were influenced by the shape of geometry, which determined flow characteristics and resulting heat transfer performance. The origins of these differences were looked at in the turbulence characteristics close to the impinged surface of the stagnations zone and its vicinity, where turbulence kinetic energy and enstrophy were analysed. It was stated that the differences are already noticeable for the single jet impingement case, but they might sum up when multiple jets are considered. Therefore, here presented results would be important for the analysis of the overall unit of mentioned mini-jets heat-exchanger.

Bayesian approach to parameter estimation and model validation for nuclear fusion reactor mean-field edge turbulence modelling

This paper presents a Bayesian approach to infer about two mean-field plasma turbulence models, a first based on the turbulent kinetic energy k ⊥, and a second based on k ⊥ and the turbulent enstrophy ζ ⊥. These models contain several closure terms with unknown constants that have to be determined through fitting to reference data from turbulence simulations or experiments. In this paper, we compare two techniques to solve the Bayesian inference problem: the Laplace approximation and the adaptive Metropolis–Hastings (AMH) algorithm. Our Bayesian inference allows for parameter uncertainty quantification, identification of parameter cross-correlations and model comparison through the Bayesian evidence. Our results indicate that while a diffusive k ⊥–ζ ⊥ scaling for the anomalous diffusion coefficient provides a better approximation to the turbulent particle flux when based on exact turbulence simulation data, at present large modelling uncertainties and parameter cross-correlations in the full k ⊥–ζ ⊥ model make it less performant than the more simple k ⊥ model. For the cases studied here, the cross-correlations can be removed by a reparameterization of the k ⊥–ζ ⊥ model with fewer parameters. The results can form the basis for further development of the turbulence models.

Simulation and flow physics of a shocked and reshocked high-energy-density mixing layer

Abstract

Energy dissipation and enstrophy production/destruction at very low Reynolds numbers in the final stage of the transition period of decay in grid turbulence

Decay characteristics of turbulent kinetic energy and enstrophy in grid turbulence have been investigated in the far downstream region (x/M∼103: x is the downstream distance from the grid, M is the mesh size of the grid) through wind tunnel experiments using hot-wire anemometry, with the lowest turbulent Reynolds number Reλ≈5. The non-dimensional dissipation rate Cε increases rapidly toward the final stage of the transition period of decay and the profile agrees well with previous direct numerical simulation [W. D. McComb et al., “Taylor's (1935) dissipation surrogate reinterpreted,” Phys. Fluids 22, 061704 (2010)] and theoretical estimation [D. Lohse, “Crossover from high to low Reynolds number turbulence,” Phys. Rev. Lett. 73, 3223 (1994)] at very low Reλ in decaying and stationary isotropic turbulence. The present result of Cε is an update on the experimental data in grid turbulence toward a very low Reλ, where measurements have been absent. The energy spectrum in the dissipation range at very low Reλ deviates from a universal form observed at high Reynolds numbers. The decay rate of enstrophy is proportional to S+2G/Reλ (S is the skewness of the longitudinal velocity derivative and G is the destruction coefficient). It is shown that G and S+2G/Reλ increase rapidly with decreasing Reλ at very low Reλ, indicating that the effect of enstrophy destruction is dominant in the final stage of the transition period of decay. The profiles of S+2G/Reλ against Reλ is well fitted by a power-law function even in the final stage of the transition period of decay.

Bayesian analysis of turbulent transport coefficients in 2D interchange dominated ExB turbulence involving flow shear

While turbulent transport is known to dominate the radial particle and energy transport in the plasma edge, a self-consistent description of turbulent transport in mean-field transport codes remains lacking. Mean-field closure models based on the turbulent kinetic energy (k ⊥) and turbulent enstrophy (ζ⊥) have recently been proposed to self-consistently model this transport. This contribution analyses the diffusive particle transport relations of these models by means of the Bayesian framework for parameter estimation and model comparison. The reference data includes a set of isothermal simulations that not only include the scrape-off layer (SOL) but also the outer core region (in which a drift wave-like model is activated) and a set of anisothermal SOL simulations, both obtained with the TOKAM2D turbulence code. This analysis shows that the k ⊥(–ζ⊥) model does not appropriately capture the diffusion coefficients for these new data sets, presumably due to the strong flows in the diamagnetic direction that appear in these new cases. While flow shear is expected to quench the turbulence and the turbulent transport, its effect was not explicitly taken into account in the earlier k ⊥(–ζ⊥) transport models. As flow shear provides a new mechanism for the decorrelation of the turbulence, we propose to introduce an additional time scale in the diffusive transport relation as . Inspiration is drawn from shear decorrelation times reported in literature to propose several new candidate models, which are then analysed in a Bayesian setting. This allowed identifying irrelevant terms for certain models and to rank all models according to the Bayesian evidence. While the new models accounting for shear do improve the match to the data, significant errors still remain. Also, no single model could be identified that performs best for all data sets.

Deep learning for in situ data compression of large turbulent flow simulations

Large turbulent flow simulations can lead to information bottlenecks as data is generated faster than it can be processed and saved. Innovative in-situ data compression techniques are needed. Here we examine a deep learning approach to in-situ compression using a novel autoencoder architecture customized for three-dimensional turbulent flows. We compare it to a randomized single-pass singular value decomposition method and demonstrate improved compression and reconstruction, particularly with respect to important statistical quantities such as turbulent kinetic energy, enstrophy, and Reynolds stresses, at lower computational cost.

Vorticity gradient stretching in the direct enstrophy transfer process of two-dimensional turbulence

In two-dimensional turbulence enstrophy is injected at the forcing scale and transferred down to the dissipative scale where viscosity dominates. On intermediate scales the forward enstrophy cascade is accompanied by a stretching of the vorticity gradient (VG) at the strain rate (SR), resulting in a preferential orthogonality between the VG and the stretching direction. In a coordinate system formed by the SR eigenvectors at a fixed time, we find that the VG statistically turns toward the direction perpendicular to the eigenvector corresponding to the stretching, as shown in the figure.

A new mean‐field plasma edge transport model based on turbulent kinetic energy and enstrophy

AbstractThe predictive capabilities of mean‐field plasma edge transport codes are significantly reduced by the empirically determined radial diffusion coefficients commonly used to account for the turbulent transport. This paper aims to assess a two‐equation model including both turbulent kinetic energy and turbulent enstrophy for an improved description of the mean‐field turbulent transport. A turbulent enstrophy equation is analytically derived for isothermal, electrostatic, two‐dimensional, interchange‐dominated ExB turbulence in the scrape‐off layer. Evaluation of this equation shows that interchange is the dominant source, while the sheath loss and viscous terms provide the main sinks of turbulent enstrophy. Transport effects turn out to be of minor importance. A model for the combined turbulent kinetic energy and enstrophy equations and the particle transport is constructed starting from a one‐equation model for the turbulent kinetic energy. The resulting two‐equation model is shown to retain the dominant dynamics of the latter while improving its scalings.

Clustering of rapidly settling, low-inertia particle pairs in isotropic turbulence. Part 1. Drift and diffusion flux closures

In this two-part study, we present the development and analysis of a stochastic theory for characterizing the relative positions of monodisperse, low-inertia particle pairs that are settling rapidly in homogeneous isotropic turbulence. In the limits of small Stokes number and Froude number such that $Fr\ll St_{\unicode[STIX]{x1D702}}\ll 1$, closures are developed for the drift and diffusion fluxes in the probability density function (p.d.f.) equation for the pair relative positions. The theory focuses on the relative motion of particle pairs in the dissipation regime of turbulence, i.e. for pair separations smaller than the Kolmogorov length scale. In this regime, the theory approximates the fluid velocity field in a reference frame following the primary particle as locally linear. In this part 1 paper, we present the derivation of closure approximations for the drift and diffusion fluxes in the p.d.f. equation for pair relative positions $\boldsymbol{r}$. The drift flux contains the time integral of the third and fourth moments of the ‘seen’ fluid velocity gradients along the trajectories of primary particles. These moments may be analytically resolved by making approximations regarding the ‘seen’ velocity gradient. Accordingly, two closure forms are derived specifically for the drift flux. The first invokes the assumption that the fluid velocity gradient along particle trajectories has a Gaussian distribution. In the second drift closure, we account for the correlation time scales of dissipation rate and enstrophy by decomposing the velocity gradient into the strain-rate and rotation-rate tensors scaled by the turbulent dissipation rate and enstrophy, respectively. An analytical solution to the p.d.f. $\langle P\rangle (r,\unicode[STIX]{x1D703})$ is then derived, where $\unicode[STIX]{x1D703}$ is the spherical polar angle. It is seen that the p.d.f. has a power-law dependence on separation $r$ of the form $\langle P\rangle (r,\unicode[STIX]{x1D703})\sim r^{\unicode[STIX]{x1D6FD}}$ with $\unicode[STIX]{x1D6FD}\sim St_{\unicode[STIX]{x1D702}}^{2}$ and $\unicode[STIX]{x1D6FD}<0$, analogous to that for the radial distribution function of non-settling pairs. An explicit expression is derived for $\unicode[STIX]{x1D6FD}$ in terms of the drift and diffusion closures. The $\langle P\rangle (r,\unicode[STIX]{x1D703})$ solution also shows that, for a given $r$, the clustering of $St_{\unicode[STIX]{x1D702}}\ll 1$ particles is only weakly anisotropic, which is in conformity with prior observations from direct numerical simulations of isotropic turbulence containing settling particles.

A comparative study of the velocity and vorticity structure in pipes and boundary layers at friction Reynolds numbers up to

This study presents findings from a first-of-its-kind measurement campaign that includes simultaneous measurements of the full velocity and vorticity vectors in both pipe and boundary layer flows under matched spatial resolution and Reynolds number conditions. Comparison of canonical turbulent flows offers insight into the role(s) played by features that are unique to one or the other. Pipe and zero pressure gradient boundary layer flows are often compared with the goal of elucidating the roles of geometry and a free boundary condition on turbulent wall flows. Prior experimental efforts towards this end have focused primarily on the streamwise component of velocity, while direct numerical simulations are at relatively low Reynolds numbers. In contrast, this study presents experimental measurements of all three components of both velocity and vorticity for friction Reynolds numbers$Re_{\unicode[STIX]{x1D70F}}$ranging from 5000 to 10 000. Differences in the two transverse Reynolds normal stresses are shown to exist throughout the log layer and wake layer at Reynolds numbers that exceed those of existing numerical data sets. The turbulence enstrophy profiles are also shown to exhibit differences spanning from the outer edge of the log layer to the outer flow boundary. Skewness and kurtosis profiles of the velocity and vorticity components imply the existence of a ‘quiescent core’ in pipe flow, as described by Kwonet al. (J. Fluid Mech., vol. 751, 2014, pp. 228–254) for channel flow at lower$Re_{\unicode[STIX]{x1D70F}}$, and characterize the extent of its influence in the pipe. Observed differences between statistical profiles of velocity and vorticity are then discussed in the context of a structural difference between free-stream intermittency in the boundary layer and ‘quiescent core’ intermittency in the pipe that is detectable to wall distances as small as 5 % of the layer thickness.

Vorticity in the turbulent flow above variously rough surfaces

Highly turbulent flows above variously rough surfaces were investigated by means of Time-Resolved Particle Image Velocimetry in a wind tunnel. Proper Orthogonal Decomposition was applied to both velocity and vorticity data in order to detect dominant features in the flow based on turbulent kinetic energy and enstrophy, respectively. While both the shape and location of the POD patterns exhibited similarity with other studies, a systematic inconsistency in terms of contribution from the features to the enstrophy between the previously published papers and our results were found.

Turbulent dynamics of sinusoidal oscillatory flow over a wavy bottom

A direct numerical simulation study is conducted to investigate sinusoidal oscillatory flow over a two-dimensional wavy wall. The height and wavelength of the bottom profile, and the period and amplitude of the free-stream oscillation, are selected to mimic a wave-driven boundary layer over vortex ripples on a sandy seabed. Two cases with different Reynolds numbers$(Re)$are considered, and the higher-$Re$case achieves a fully developed turbulent state with a wide separation between the energy-containing and dissipative scales. The oscillatory flow is characterized by coherent columnar vortices, which are the main transport agents of turbulent kinetic energy and enstrophy. Two classes of coherent vortices are observed: (i) a primary vortex formed at the lee side of the ripple by flow separation at the crest; (ii) a secondary vortex formed beneath the primary vortex by vortex-induced separation. When the free-stream velocity weakens, these vortices form a counter-rotating vortex dipole and eject themselves over the crest with their mutual induction. Turbulence production peaks twice in a half-cycle; during the formation of the primary vortex and during the ejection of the vortex dipole. The intensity of the former peak remains low in the lower-$Re$case, as the vortex dipole follows a higher altitude trajectory limiting its interactions with the bottom, and leaving minimal residual turbulence around the ripples for the subsequent half-cycle. Flow snapshots and spectral analysis reveal two dominant three-dimensional features: (i) an energetic vortex mode with a preferred spanwise wavelength close to the ripple wavelength; (ii) streamwise vortical structures in near-wall regions with a relatively shorter spanwise spacing influenced by viscous effects. The vortex mode becomes strong when the cores of the vortices are strained to an elliptical form while moving towards the crest. Following the detachment of the vortices from the ripple, the vortex mode in the higher-$Re$case breaks down the spanwise coherence of the columnar vortices and decomposes them into intermittent patches of turbulent vortex clusters. The distribution of wall shear stress over the ripple is also analysed in detail. The peak values are observed near the ripple crest around the ejection of the vortex dipole and the maximum free-stream velocity. In the former, both the vortex mode and streamwise vortices have strong footprints on the wall, yielding a bimodal wall-shear-stress spectrum with two distinctive peaks. In the second high-stress regime, decaying coherent vortices impose strong inhomogeneity on the wall shear stress as their wall-attached parts sweep the ripples. These spanwise variations in the wall shear provide insights into the instability of two-dimensional sand ripples.

Dynamics of zonal shear collapse with hydrodynamic electrons

This paper presents a theory for the collapse of the edge zonal shear layer, as observed at the density limit at low β. This paper investigates the scaling of the transport and mean profiles with the adiabaticity parameter α, with special emphasizes on fluxes relevant to zonal flow (ZF) generation. We show that the adiabaticity parameter characterizes the strength of production of zonal flows and so determines the state of turbulence. A 1D reduced model that self-consistently describes the spatiotemporal evolution of the mean density n¯, the azimuthal flow v¯y, and the turbulent potential enstrophy ε=⟨(ñ−∇2ϕ̃)2/2⟩—related to fluctuation intensity—is presented. Quasi-linear analysis determines how the particle flux Γn and vorticity flux Π=−χy∇2vy+Πres scale with α, in both hydrodynamic and adiabatic regimes. As the plasma response passes from adiabatic (α > 1) to hydrodynamic (α < 1), the particle flux Γn is enhanced and the turbulent viscosity χy increases. However, the residual flux Πres—which drives the flow—drops with α. As a result, the mean vorticity gradient ∇2v¯y=Πres/χy—representative of the strength of the shear—also drops. The shear layer then collapses and turbulence is enhanced. The collapse is due to a decrease in ZF production, not an increase in damping. A physical picture for the onset of collapse is presented. The findings of this paper are used to motivate an explanation of the phenomenology of low β density limit evolution. A change from adiabatic (α=kz2vth2/(|ω|νei)>1) to hydrodynamic (α < 1) electron dynamics is associated with the density limit.

Scalings of heat transport and energy spectra of turbulent Rayleigh-Bénard convection in a large-aspect-ratio box

Direct Numerical Simulations of turbulent convection in a large aspect-ratio box are carried out in the range of Rayleigh number 7 × 104 ≤ Ra ≤ 2 × 106 at Prandtl number Pr=0.71. A strong correlation between the vertical velocity and temperature is observed in the turbulent regime at almost all the length scales. Frequency spectra of all the velocities and temperature show a −5/3 law for a wide band of frequencies. The variances of horizontal velocities at different points in the flow yield a single power-law. Probability density functions of velocities and temperature are close to Gaussian only at higher Rayleigh numbers. The mean and variance of temperature clearly show boundary layers, surface layers and a near-homogeneous bulk region. The boundary layer thickness decreases and bulk-homogeneity is enhanced on increasing the Rayleigh numbers. The wave number spectra of the turbulent kinetic energy exhibit Kolmogorov like (E(k)∼k−5/3) and Bolginao-Obukhov like (E(k)∼k−11/5) behaviour respectively in the central and near-wall regions of the container. An approximate balance between the production due to buoyancy and the dissipation is found in the turbulent kinetic energy budget. Taylor’s approximate equation of the production due to turbulent stretching and the dissipation of turbulent enstrophy is modified by the inclusion of buoyancy production in the enstrophy budget. The present results support the previously proposed 2/7 power-law dependence of the average Nusselt number on the Rayleigh number by yielding an exponent of 0.272, but do not necessarily support the proposed classification of “soft” and “hard” turbulence on the basis of this exponent.

Response of turbulent enstrophy to sudden implementation of spanwise wall oscillation in channel flow

The response of turbulent enstrophy to a sudden implementation of spanwise wall oscillation (SWO) is studied in a turbulent channel flow via direct numerical simulation. In the beginning of the application of SWO, a significant correlation is formed between ωy′ and ωz′. A transient growth of turbulent enstrophy occurs, which directly enhances turbulent dissipation and drifts the turbulent flow towards a new lower-drag condition. Afterwards, the terms related to the stretching of vorticity (ωx, ωy′, and ωz), the inclination of ωy′ by \(\frac{\partial w}{\partial y}\), the turn of ωz by \(\frac{\partial v\prime}{\partial z}\), and the horizontal shear of ωz by \(\frac{\partial w\prime}{\partial x}\) are suppressed due to the presence of SWO, leading to attenuation of the turbulent enstrophy.

Modelling enhanced confinement in drift-wave turbulence

The results of modeling studies of an enhanced confinement in the drift wave turbulent plasma of the CSDX linear device are presented. The mechanism of enhanced confinement is investigated here using a reduced 1D, time-dependent model, which illustrates the exchange of enstrophy between two disparate scale structures: the mesoscale flow and profile, and the turbulence intensity fields. Mean density, mean vorticity, and turbulent potential enstrophy are the variables for this model. Total potential enstrophy is conserved in this model. Vorticity mixing occurs on a scale length related to an effective Rhines' scale of turbulence, and shrinks as both density and vorticity gradients steepen. Numerical results obtained from solution of the model agree well with the experimental data from CSDX showing: (i) a steepening of the mean density profile, indicating a radial transport barrier formation, (ii) the development of a radially sheared azimuthal flow velocity that coincides with the density steepening and initiates a turbulence quench, and (iii) negative Reynolds work values, indicating that fluctuations drive the shear flow. These observations as the magnitude of the magnetic field B increases are recovered using purely diffusive expressions for the vorticity and density fluxes. A new dimensionless turbulence parameter RDT-defined as the ratio of the integrated potential enstrophy transfer from turbulence to the flow, to the integrated potential enstrophy production due to relaxation of the density gradient is introduced as a turbulence collapse indicator that detects when the enhanced confinement state is triggered.

Large-eddy simulation of decaying isotropic turbulence using the flowfield dependent variation method

PurposeThe purpose of this study is to investigate the accuracy and applicability of the Flowfield Dependent Variation (FDV) method for large-eddy simulations (LES) of decaying isotropic turbulence.Design/methodology/approachIn an earlier paper, the FDV method was successfully demonstrated for simulations of laminar flows with speeds varying from low subsonic to high supersonic Mach numbers. In the current study, the FDV method, implemented in a finite element framework, is used to perform LESs of decaying isotropic turbulence. The FDV method is fundamentally derived from the Lax–Wendroff Scheme (LWS) by replacing the explicit time derivatives in LWS with a weighted combination of explicit and implicit time derivatives. The increased implicitness and the inherent numerical dissipation of FDV contribute to the scheme’s numerical stability and monotonicity. Understanding the role of numerical dissipation that is inherent to the FDV method is essential for the maturation of FDV into a robust scheme for LES of turbulent flows. Accordingly, three types of LES of decaying isotropic turbulence were performed. The first two types of LES utilized explicit subgrid scale (SGS) models, namely, the constant-coefficient Smagorinsky and dynamic Smagorinsky models. In the third, no explicit SGS model was employed; instead, the numerical dissipation inherent to FDV was used to emulate the role played by explicit SGS models. Such an approach is commonly known as Implicit LES (ILES). A new formulation was also developed for quantifying the FDV numerical viscosity that principally arises from the convective terms of the filtered Navier–Stokes equations.FindingsThe temporal variation of the turbulent kinetic energy and enstrophy and the energy spectra are presented and analyzed. At all grid resolutions, the temporal profiles of kinetic energy showed good agreement with t(−1.43) theoretical scaling in the fully developed turbulent flow regime, where t represents time. The energy spectra also showed reasonable agreement with the Kolmogorov’s k(−5/3) power law in the inertial subrange, with the spectra moving closer to the Kolmogorov scaling at higher-grid resolutions. The intrinsic numerical viscosity and the dissipation rate of the FDV scheme are quantified, both in physical and spectral spaces, and compared with those of the two SGS LES runs. Furthermore, at a finite number of flow realizations, the numerical viscosities of FDV and of the Streamline Upwind/Petrov–Galerkin (SUPG) finite element method are compared. In the initial stages of turbulence development, all three LES cases have similar viscosities. But, once the turbulence is fully developed, implicit LES is less dissipative compared to the two SGS LES runs. It was also observed that the SUPG method is significantly more dissipative than the three LES approaches.Research limitations/implicationsJust as any computational method, the limitations are based on the available computational resources.Practical implicationsSolving problems involving turbulent flows is by far the biggest challenge facing engineers and scientists in the twenty-first century, this is the road that the authors have embarked upon in this paper and the road ahead of is very long.Social implicationsUnderstanding turbulence is a very lofty goal and a challenging one as well; however, if the authors succeed, the rewards are limitless.Originality/valueThe derivation of an explicit expression for the numerical viscosity tensor of FDV is an important contribution of this study, and is a crucial step forward in elucidating the fundamental properties of the FDV method. The comparison of viscosities for the three LES cases and the SUPG method has important implications for the application of ILES approach for turbulent flow simulations.