Cascades and wall-normal fluxes in turbulent channel flows

Cimarelli, Andrea; Angelis, E. De; Jiménez, Javier; Casciola, Carlo Massimo

doi:10.1017/jfm.2016.275

Cited by 76 publications

(124 citation statements)

References 38 publications

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“…transfer between modes with approximately the same wavenumber magnitude, but different orientation. This implies that one of the wavenumber components is smaller in the recipient region than the donor region, and is responsible for the apparent inverse energy transfer in one-dimensional spectra observed here and previously by others (Cimarelli et al 2013(Cimarelli et al , 2016Aulery et al 2016). Thus, this does not really represent energy transfer to larger scales.…”

Section: Discussionsupporting

confidence: 44%

“…Aulery et al (2016) performed spectral analysis of the TKE budget in anisothermal turbulent channel flow up to Re τ = 395, and also observed inverse energy transfers. Finally, Cimarelli et al (2013Cimarelli et al ( , 2015Cimarelli et al ( , 2016 studied the evolution equation of the second order structure function as a function (r, y) where r is the separation vector in the structure function and y is the distance from the wall. They observed two distinct production mechanism at different wall-normal distances and inverse energy transfers.…”

Section: Introductionmentioning

confidence: 99%

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Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number

2018

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The transport equations for the variances of the velocity components are investigated using data from direct numerical simulations of incompressible channel flows at friction Reynolds number (Re τ ) up to Re τ = 5200. Each term in the transport equation has been spectrally decomposed to expose the contribution of turbulence at different length scales to the processes governing the flow of energy in the wall-normal direction, in scale and among components.The outer-layer turbulence is dominated by very large-scale streamwise elongated modes, which are consistent with the very large-scale motions (VLSM) that have been observed by many others. The presence of these VLSMs drive many of the characteristics of the turbulent energy flows. Away from the wall, production occurs primarily in these large-scale streamwise-elongated modes in the streamwise velocity, but dissipation occurs nearly isotropically in both velocity components and scale. For this to happen, the energy is transferred from the streamwise elongated modes to modes with a range of orientations through non-linear interactions, and then transferred to other velocity components. This allows energy to be transferred more-or-less isotropically from these large scales to the small scales at which dissipation occurs. The VLSMs also transfer energy to the wallregion, resulting in a modulation of the autonomous near-wall dynamics and the observed Reynolds number dependence of the near-wall velocity variances.The near-wall energy flows are more complex, but are consistent with the wellknown autonomous near-wall dynamics that give rise to streaks and streamwise vortices. Through the overlap region between outer and inner layer turbulence, there is a selfsimilar structure to the energy flows. The VLSM production occurs at spanwise scales that grow with y. There is transport of energy away from the wall over a range of scales that grows with y. And, there is transfer of energy to small dissipative scales which grow like y 1/4 , as expected from Kolmogorov scaling. Finally, the small-scale near-wall processes characterised by wavelengths less that 1000 wall units are largely Reynolds number independent, while the larger-scale outer layer process are strongly Reynolds number dependent. The interaction between them appears to be relatively simple.

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Section: Discussionsupporting

confidence: 44%

Section: Introductionmentioning

confidence: 99%

Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number

2018

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“…On the contrary, the behaviour of the subgrid dissipation becomes more complex in the near-wall region due to the appearance of a double peak. As also shown in Härtel et al (1994); Cimarelli & De Angelis (2012), the near-wall region for large filter lengths, is characterized by a three layer structure where two peaks of high dissipation embed a low dissipative layer which eventually gives rise to a change of sign and, hence, to a reverse energy transfer from small to large scales, ǫ sgs > 0 (Cimarelli et al 2013(Cimarelli et al , 2015(Cimarelli et al , 2016. In this context, we observe that the contribution of stresses involving small scales in the energy transfer processes of the near-wall region becomes dominant.…”

Section: Properties Of the Subgrid Stress Decompositionsmentioning

confidence: 66%

General formalism for a reduced description and modelling of momentum and energy transfer in turbulence

2019

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Based on hierarchies of filter lengths, the large eddy decomposition and the related subgrid stresses are recognized to represent generalized central moments for the study and modelling of the different modes composing turbulence. In particular, the subgrid stresses and the subgrid dissipation are shown to be alternative observables for quantitatively assessing the scale-dependent properties of momentum flux (subgrid stresses) and the energy exchange between the large and small scales (subgrid dissipation). In this work we present a theoretical framework for the study of the subgrid stress and dissipation. Starting from an alternative decomposition of the turbulent stresses, a new formalism for their approximation and understanding is proposed which is based on a tensorial turbulent viscosity. The derived formalism highlights that every decomposition of the turbulent stresses is naturally approximated by a general form of turbulent viscosity tensor based on velocity increments which is then recognized to be a peculiar property of small-scale stresses in turbulence. The analysis in a turbulent channel shows the rich physics of the small-scale stresses which is unveiled by the tensorial formalism and usually missed in scalar approaches. To further exploit the formalism, we also show how it can be used to derive new modelling approaches. The proposed models are based on the second- and third-order inertial properties of the grid element. The basic idea is that the structure of the integration volume for filtering (either implicit or explicit) impacts the anisotropy and inhomogeneity of the filtered-out motions and, hence, this information could be leveraged to improve the prediction of the main unknown features of small-scale turbulence. The formalism provides also a rigorous definition of characteristic lengths for the turbulent stresses, which can be computed in every type of computational elements, thus overcoming the rather elusive definition of filter length commonly employed in more classical models. A preliminary analysis in a turbulent channel shows reasonable results. In order to solve numerical stability issues, a tensorial dynamic procedure for the evolution of the model constants is also developed. The generality of the procedure is such that it can be employed also in more conventional closures.

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“…An exact equation for δu 2 was derived first by Kolmogorov in [5] for isotropic turbulence, and has been later generalised to inhomogeneous flows. We follow Cimarelli et al [11] and write below the GKE in the specialised form valid for the indefinite plane channel flow. This form of the GKE was previously introduced in [9], and later refined with the addition of a couple missing terms.…”

Section: The Generalised Kolmogorov Equationmentioning

confidence: 99%

An efficient numerical method for the generalised Kolmogorov equation

Gatti

Remigi

Chiarini

et al. 2019

Journal of Turbulence

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An efficient algorithm for computing the terms appearing in the Generalised Kolmogorov Equation (GKE) written for the indefinite plane channel flow is presented. The algorithm, which features three distinct strategies for parallel computing, is designed such that CPU and memory requirements are kept to a minimum, so that high-Re wall-bounded flows can be afforded.Computational efficiency is mainly achieved by leveraging the Parseval's theorem for the two homogeneous directions available in the plane channel geometry. A speed-up of 3-4 orders of magnitude, depending on the problem size, is reported in comparison to a key implementation used in the literature. Validation of the code is demonstrated by computing the residual of the GKE, and example results are presented for channel flows at Reτ = 200 and Reτ = 1000, where for the first time they are observed in the whole four-dimensional domain. It is shown that the space and scale properties of the scale energy fluxes change for increasing values of the Reynolds number. Among all scale energy fluxes, the wall-normal flux is found to show the richest behaviour for increasing streamwise scales.

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Cascades and wall-normal fluxes in turbulent channel flows

Cited by 76 publications

References 38 publications

Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number

Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number

General formalism for a reduced description and modelling of momentum and energy transfer in turbulence

An efficient numerical method for the generalised Kolmogorov equation

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