Incompressible Homogeneous Isotropic Turbulence

Sagaut, Pierre; Cambon, Claude

doi:10.1007/978-3-319-73162-9_4

Cited by 4 publications

(6 citation statements)

References 132 publications

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“…The pressure-strain correlation for an incompressible flow obeys energy conservation, and only redistributes energy among dierent components of the velocity correlation tensor [12,13]. This can be readily seen from equation (44) where, due to angular integral over the spherical angles, the three-dimensional pressure-velocity gradient spectrum E i pu,i (k) vanishes. Thus E i pu,i (k) = 0.…”

Section: Discussionmentioning

confidence: 96%

“…We would like to conclude by noting that the pressure-velocity and pressurestrain correlations in the strain dominated regime of homogeneous shear flows have been studied within the prescription of rapid distortion theory (RDT) [5,[41][42][43][44]. In RDT, the turbulence is subjected to a rapid distortion, and-such being the case-the slow pres sure and dissipation terms are absent in the evolution equation, resulting in a flow governed by a set of linear equations.…”

Section: J Stat Mech (2018) 023204mentioning

confidence: 99%

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Spectral calculations for pressure–velocity and pressure–strain correlations in homogeneous shear turbulence

Dutta¹

2018

J. Stat. Mech.

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Theoretical analyses of pressure related turbulent statistics are vital for a reliable and accurate modeling of turbulence. In the inertial subrange of turbulent shear flow, pressure–velocity and pressure–strain correlations are affected by anisotropy imposed at large scales. Recently, Tsuji and Kaneda (2012 J. Fluid Mech. 694 50) performed a set of experiments on homogeneous shear flow, and estimated various one-dimensional pressure related spectra and the associated non-dimensional universal numbers. Here, starting from the governing Navier–Stokes dynamics for the fluctuating velocity field and assuming the anisotropy at inertial scales as a weak perturbation of an otherwise isotropic dynamics, we analytically derive the form of the pressure–velocity and pressure–strain correlations. The associated universal numbers are calculated using the well-known renormalization-group results, and are compared with the experimental estimates of Tsuji and Kaneda. Approximations involved in the perturbative calculations are discussed.

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Section: Discussionmentioning

confidence: 96%

Section: J Stat Mech (2018) 023204mentioning

confidence: 99%

Spectral calculations for pressure–velocity and pressure–strain correlations in homogeneous shear turbulence

Dutta¹

2018

J. Stat. Mech.

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“…Plugging (2.12) into (2.11), , and according to the scaling of TKE spectrum, the scalar spectrum scales as where is the scaling constant. For a comprehensive overview of a variety of the spectral transfer models as well as the analysis of their dynamics and properties, interested readers are referred to Sagaut & Cambon (2018, § 4.7.1).…”

Section: Turbulent Transport Of Passive Scalarsmentioning

confidence: 99%

A non-local spectral transfer model and new scaling law for scalar turbulence

Akhavan-Safaei

Zayernouri

2023

J. Fluid Mech.

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In this study, we revisit the spectral transfer model for the turbulent intensity in passive scalar transport (under large-scale anisotropic forcing), and a subsequent modification to the scaling of scalar variance cascade is presented. From the modified spectral transfer model, we obtain a revised scalar transport model using a fractional-order Laplacian operator that facilitates the robust inclusion of the non-local effects originating from large-scale anisotropy transferred across the multitude of scales in the turbulent cascade. We provide an a priori estimate for the non-local model based on the scaling analysis of the scalar spectrum, and later examine our developed model through direct numerical simulation. We present a detailed analysis on the evolution of the scalar variance, high-order statistics of the scalar gradient and important two-point statistical metrics of the turbulent transport to make a comprehensive comparison between the non-local model and its standard version. Finally, we present an analysis that seamlessly reconciles the similarities between the developed model with the fractional-order subgrid-scale scalar flux model for large-eddy simulation (Akhavan-Safaei et al., J. Comput. Phys., vol. 446, 2021, 110571) when the filter scale approaches the dissipative scales of turbulent transport. In order to perform this task, we employ a Gaussian process regression model to predict the model coefficient for the fractional-order subgrid model.

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“…The studies of Qian (1997), Qian (1999), Lundgren (2002), Lundgren (2003), Antonia & Burattini (2006), Tchoufag, Sagaut & Cambon (2012), Antonia et al. (2019) and Meldi, Djenidi & Antonia (2021) have indicated that (1.2) is in fact approached very slowly, so that a very large value of (, where and is the fluid kinematic viscosity) may be required before the IR is unambiguously established (see figure 4.6 of Sagaut & Cambon (2018) which summarizes different predictions for ). In particular, the eddy damped quasinormal Markovian numerical simulations in both decaying and forced homogeneous isotropic turbulence (Meldi et al.…”

Section: Introductionmentioning

confidence: 99%

Dual scaling and the n-thirds law in grid turbulence

Tang,

Antonia,

Djenidi

2023

J. Fluid Mech.

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A dual scaling of the turbulent longitudinal velocity structure function $\overline {{(\delta u)}^n}$ , i.e. a scaling based on the Kolmogorov scales ( $u_K$ , $\eta$ ) and another based on ( $u'$ , $L$ ) representative of the large scale motion, is examined in the context of both the Kármán–Howarth equation and experimental grid turbulence data over a significant range of the Taylor microscale Reynolds number $Re_\lambda$ . As $Re_\lambda$ increases, the scaling based on ( $u'$ , $L$ ) extends to increasingly smaller values of $r/L$ while the scaling based on ( $u_K$ , $\eta$ ) extends to increasingly larger values of $r/\eta$ . The implication is that both scalings should eventually overlap in the so-called inertial range as $Re_\lambda$ continues to increase, thus leading to a power-law relation $\overline {{(\delta u)}^n} \sim r^{n/3}$ when the inertial range is rigorously established. The latter is likely to occur only when $Re_\lambda \to \infty$ . The use of an empirical model for $\overline {{(\delta u)}^n}$ , which complies with $\overline {{(\delta u)}^n} \sim r^{n/3}$ as $Re_\lambda \to \infty$ , shows that the finite Reynolds number effect may differ between even- and odd-orders of $\overline {{(\delta u)}^n}$ . This suggests that different values of $Re_\lambda$ may be required between even and odd values of $n$ for compliance with $\overline {{(\delta u)}^n} \sim r^{n/3}$ . The model describes adequately the dependence on $Re_\lambda$ of the available experimental data for $\overline {{(\delta u)}^n}$ and supports indirectly the extrapolation of these data to infinitely large $Re_\lambda$ .

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Incompressible Homogeneous Isotropic Turbulence

Cited by 4 publications

References 132 publications

Spectral calculations for pressure–velocity and pressure–strain correlations in homogeneous shear turbulence

Spectral calculations for pressure–velocity and pressure–strain correlations in homogeneous shear turbulence

A non-local spectral transfer model and new scaling law for scalar turbulence

Dual scaling and the n-thirds law in grid turbulence

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