A stochastic view of isotropic turbulence decay

Meldi, Marcello; Sagaut, Pierre; Lucor, Didier

doi:10.1017/s0022112010005793

Cited by 31 publications

(11 citation statements)

References 29 publications

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“…The main features of the generalized polynomial chaos approach are briefly recalled here; for more details we refer to Ghanem & Spanos [7] and Le Maître & Knio [17]. In the last years, this stochastic approach has been applied to turbulent flow analysis with satisfying results [18,20].…”

Section: Generalized Polynomial Chaosmentioning

confidence: 99%

Quantification of errors in large-eddy simulations of a spatially evolving mixing layer using polynomial chaos

2012

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A stochastic approach based on generalized polynomial chaos (gPC) is used to quantify the error in large-eddy simulation (LES) of a spatially evolving mixing layer flow and its sensitivity to different simulation parameters, viz., the grid stretching in the streamwise and lateral directions and the subgrid-scale (SGS) Smagorinsky model constant (CS). The error is evaluated with respect to the results of a highly resolved LES and for different quantities of interest, namely, the mean streamwise velocity, the momentum thickness, and the shear stress. A typical feature of the considered spatially evolving flow is the progressive transition from a laminar regime, highly dependent on the inlet conditions, to a fully developed turbulent one. Therefore, the computational domain is divided in two different zones (inlet dependent and fully turbulent) and the gPC error analysis is carried out for these two zones separately. An optimization of the parameters is also carried out for both these zones. For all the considered quantities, the results point out that the error is mainly governed by the value of the CS constant. At the end of the inlet-dependent zone, a strong coupling between the normal stretching ratio and the CS value is observed. The error sensitivity to the parameter values is significantly larger in the inlet-dependent upstream region; however, low-error values can be obtained in this region for all the considered physical quantities by an ad hoc tuning of the parameters. Conversely, in the turbulent regime the error is globally lower and less sensitive to the parameter variations, but it is more difficult to find a set of parameter values leading to optimal results for all the analyzed physical quantities. A similar analysis is also carried out for the dynamic Smagorinsky model, by varying the grid stretching ratios. Comparing the databases generated with the different subgrid-scale models, it is possible to observe that the error cost function computed for the streamwise velocity and for the momentum thickness is not significantly sensitive to the used SGS closure. Conversely, the prediction of the shear stress is much more accurate when using a dynamic subgrid-scale model and the variance of the error is lower in magnitude

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Section: Generalized Polynomial Chaosmentioning

confidence: 99%

Quantification of errors in large-eddy simulations of a spatially evolving mixing layer using polynomial chaos

2012

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“…One theoretical framework predicts that the decay rate depends on the large-scale structure of the flow, and not on the Reynolds number once turbulence is fully developed [2,[10][11][12][13]. As the Reynolds numbers diverge to infinity, the scale at which energy is dissipated grows arbitrarily small, but these scales continue to dissipate energy as quickly as it is transferred to them by the large scales.…”

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confidence: 99%

Decay of Turbulence at High Reynolds Numbers

2015

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Turbulent motions in a fluid relax at a certain rate once stirring has stopped. The role of the most basic parameter in fluid mechanics, the Reynolds number, in setting the relaxation rate is not generally known. This paper concerns the high-Reynolds-number limit of the process. In a classical grid-turbulence wind-tunnel experiment that both reached higher Reynolds numbers than ever before and covered a wide range of them (10 4 < Re = U M ν < 5 × 10 6 ), we measured the relaxation rate with the unprecedented precision of about 2%. Here U is the mean speed of the flow, M the forcing scale, and ν the kinematic viscosity of the fluid. We observed that the relaxation rate was Reynolds-number independent, which contradicts some models and supports others.PACS numbers: 47.27. Gs, 47.27.Jv Turbulence dissipates kinetic energy, and the easiest way to see this is to let turbulence relax, or freely decay, by removing the agitation that initially set the fluid in motion. In so doing, one observes qualitatively that the fluid comes to rest. The rate at which that happens is the subject at hand, and underlies general turbulence phenomena and modeling. To simplify the problem, the statistics of the turbulent fluctuations are often arranged to be spatially homogeneous and isotropic [1,2]. Even under these conditions, it is not possible quantitatively to predict the decay rate; it is even difficult precisely to measure the decay rate [3][4][5][6]. Yet empirical constraints on the properties of decaying turbulence are what is needed to advance the knowledge of the subject.The physics that control the decay are not fully understood, to the extent that the role of the most basic parameter in fluid mechanics, the Reynolds number, is not clear. What is known is that toward very low Reynolds numbers, the decay rate increases [7,8], as it also does when the spatial structure of the turbulence grows to the size of its container [4,9]. Here, we study the rate of decay in the limit of large Reynolds numbers for turbulence free from boundary effects, a rate which cannot be determined from the previous data.One theoretical framework predicts that the decay rate depends on the large-scale structure of the flow, and not on the Reynolds number once turbulence is fully developed [2, 10-13]. As the Reynolds numbers diverge to infinity, the scale at which energy is dissipated grows arbitrarily small, but these scales continue to dissipate energy as quickly as it is transferred to them by the large scales. This picture is compatible with an emerging consensus that the initial structure of the turbulence sets its decay rate, even when the flow is homogeneous [14][15][16][17].There is also, however, a line of thinking that an elegant and fully self-similar decay emerges in the limit of high Reynolds number [14,15,[18][19][20][21][22][23]. In this description, turbulence tends to become statistically similar to itself, when appropriately rescaled, even as it decays. Observation of a tendency toward slower decay with increasing Reynolds numbers wo...

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“…Experimentally, the focus of attention was on grid-induced turbulence [8][9][10][11][12][13][14][15], whereas in numerical simulations periodic boundary conditions were used [16][17][18][19]. To what degree the decay of the turbulence depends on the initial conditions [20][21][22] and whether or not it is selfsimilar has controversially been debated [5,11,16,[23][24][25][26][27]. We note that for HIT, already from dimensional analysis one obtains power laws for the temporal evolution of the vorticity and kinetic energy in decaying turbulence, namely ω(t) ∝ t −3/2 and k(t) ∝ t −2 , respectively, in good agreement with many measurements [10,12,28].…”

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Self-similar decay of high Reynolds number Taylor-Couette turbulence

et al. 2016

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We study the decay of high-Reynolds number Taylor-Couette turbulence, i.e. the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder (Rei = 2×10 6 , the outer cylinder is at rest) is stopped within 12 s, thus fully removing the energy input to the system. Using a combination of laser Doppler anemometry and particle image velocimetry measurements, six decay decades of the kinetic energy could be captured. First, in the absence of cylinder rotation, the flow-velocity during the decay does not develop any height dependence in contrast to the well-known Taylor vortex state. Second, the radial profile of the azimuthal velocity is found to be self-similar. Nonetheless, the decay of this wall-bounded inhomogeneous turbulent flow does not follow a strict power law as for decaying turbulent homogeneous isotropic flows, but it is faster, due to the strong viscous drag applied by the bounding walls. We theoretically describe the decay in a quantitative way by taking the effects of additional friction at the walls into account.Turbulence is a phenomenon far from equilibrium: Turbulent flow is driven in one or the other way by some energy input and at the same time energy is dissipated, predominantly (but not exclusively) at the smaller scales. For statistically stationary turbulence, this balance is reflected in the famous picture of the Richardson-Kolmogorov energy cascade [1,2]. While the driving on large scales clearly is non-universal, depending on the flow geometry and stirring mechanism, the energy dissipation mechanism has been hypothesized to be self-similar [3][4][5][6][7][8].How exactly is the energy taken out of the system? A good way to find out is to turn off the driving and follow the then decaying turbulence, as then all scales are probed during the decay process. This has been done in various studies over the last decades for homogeneous isotropic turbulence (HIT). Experimentally, the focus of attention was on grid-induced turbulence [8][9][10][11][12][13][14][15], whereas in numerical simulations periodic boundary conditions were used [16][17][18][19]. To what degree the decay of the turbulence depends on the initial conditions [20][21][22] and whether or not it is selfsimilar has controversially been debated [5,11,16,[23][24][25][26][27]. We note that for HIT, already from dimensional analysis one obtains power laws for the temporal evolution of the vorticity and kinetic energy in decaying turbulence, namely ω(t) ∝ t −3/2 and k(t) ∝ t −2 , respectively, in good agreement with many measurements [10,12,28]. These scaling laws are also obtained [29] when employing the 'variable range mean field theory' of Ref. [30], developed for HIT. In that way, the late-time behavior, when the flow is already viscosity dominated, can also be calculated, allowing for the calculation of the lifetime of the decaying turbulence [29].However, real turbulence is neither homogeneous nor isotropic, but it has anisotropies and is wall-bounded, with a considerable fraction of the dissipa...

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A stochastic view of isotropic turbulence decay

Cited by 31 publications

References 29 publications

Quantification of errors in large-eddy simulations of a spatially evolving mixing layer using polynomial chaos

Quantification of errors in large-eddy simulations of a spatially evolving mixing layer using polynomial chaos

Decay of Turbulence at High Reynolds Numbers

Self-similar decay of high Reynolds number Taylor-Couette turbulence

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