Extended self-similarity in turbulent flows

Benzi, Roberto; Ciliberto, S.; Tripiccione, R.; Baudet, Christophe; Massaioli, F.; Succi, Sauro

doi:10.1103/physreve.48.r29

Cited by 959 publications

(987 citation statements)

References 5 publications

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“…In particular, the linear dependence ζ q ∝ q indicates self-similarity, while deviation from such linearity indicates intermittency. Due to the limited extension of the inertial range in the numerical simulations, extended self-similarity (ESS) (Benzi et al 1993) has been used, as customary. In this case, the structure functions S q are plotted as a function of the second-order moment S 2 .…”

Section: Resultsmentioning

confidence: 99%

Three-dimensional simulations of sheared current sheets: transition to turbulence?

et al. 2017

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Systems of multiple current sheets arise in various situations in natural plasmas, such as at the heliospheric current sheet in the solar wind and in the outer heliosphere in the heliosheath. Previous three-dimensional simulations have shown that such systems can develop turbulent-like fluctuations resulting from a forward and inverse cascade in wave vector space. We present a study of the transition to turbulence of such multiple current sheet systems, including the effects of adding a magnetic guide field and velocity shears across the current sheets. Three-dimensional hybrid simulations are performed of systems with eight narrow current sheets in a triply periodic geometry. We carry out a number of different analyses of the evolution of the fluctuations as the initially highly ordered state relaxes to one which resembles turbulence. Despite the evidence of a forward and inverse cascade in the fluctuation power spectra, we find that none of the simulated cases have evidence of intermittency after the initial period of fast reconnection associated with the ion tearing instability at the current sheets. Cancellation analysis confirms that the simulations have not evolved to a state which can be identified as fully developed turbulence. The addition of velocity shears across the current sheets slows the evolution in the properties of the fluctuations, but by the end of the simulation they are broadly similar. However, if the simulation is constrained to be two-dimensional, differences are found, indicating that fully three-dimensional simulations are important when studying the evolution of an ordered equilibrium towards a turbulent-like state.

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Section: Resultsmentioning

confidence: 99%

Three-dimensional simulations of sheared current sheets: transition to turbulence?

et al. 2017

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“…Unlike the logarithmic relationship (1.3) for the ECR, the ISR scaling has the form of a power-law. Hence, instead of (2.10), the classical ESS in the inertial range (Benzi et al 1993(Benzi et al , 1995 manifests itself as the ratio of the logarithms of the structure functions according to…”

Section: Extended Self-similarity For Structure Functionsmentioning

confidence: 99%

“…Moreover, comparison of singlepoint statistics in the ECR in turbulent boundary layers and channel flows (Sillero et al 2013) and the analysis of the second-order structure function in pipe flows (Chung et al 2015) suggest that differences with regard to (1.3) exist in different flow geometries. However, borrowing inspiration from the original ESS analysis of Benzi et al (1993Benzi et al ( , 1995, de Silva et al (2017) were recently able to demonstrate universality for the ECR Statistics of turbulence in the energy-containing range 3 scales in wall-bounded flows. In particular, they showed that when evaluating S p (s x ; u x ) with respect to a reference structure function S m (s x ; u x ) ≡ (∆u + x ) 2m 1/m of arbitrary order 2m, the 'ESS-form' of (1.3), given by 4) holds over a larger range of wall distances and at significantly lower Re τ than the direct representation (1.3).…”

Section: Introductionmentioning

confidence: 99%

“…Anselmet et al 1984;Frisch 1995). To firmly establish the universality of the ISR statistics, the so-called extended self-similarity (ESS) hypothesis of Benzi et al (1993Benzi et al ( , 1995 played a central role (Arneodo et al 1996;Belin et al 1996). In this framework, instead of evaluating the scaling of the structure functions directly as a function of distance, the relative scaling exponent is sought by plotting one structure function against another one of different order on log-log scales.…”

Section: Introductionmentioning

confidence: 99%

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Statistics of turbulence in the energy-containing range of Taylor–Couette compared to canonical wall-bounded flows

Krug¹,

Yang²,

Silva³

et al. 2017

J. Fluid Mech.

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Considering structure functions of the streamwise velocity component in a framework akin to the extended self-similarity hypothesis (ESS), de Silva et al. (J. Fluid Mech., vol. 823,2017, pp. 498-510) observed that remarkably the large-scale (energy-containing range) statistics in canonical wall bounded flows exhibit universal behaviour. In the present study, we extend this universality, which was seen to encompass also flows at moderate Reynolds number, to Taylor-Couette flow. In doing so, we find that also the transversal structure function of the spanwise velocity component exhibits the same universal behaviour across all flow types considered. We further demonstrate that these observations are consistent with predictions developed based on an attached-eddy hypothesis. These considerations also yield a possible explanation for the efficacy of the ESS framework by showing that it relaxes the self-similarity assumption for the attached eddy contributions. By taking the effect of streamwise alignment into account, the attached eddy model predicts different behaviour for structure functions in the streamwise and in the spanwise directions and that this effect cancels in the ESS-framework -both consistent with the data. Moreover, it is demonstrated here that also the additive constants, which were previously believed to be flow dependent, are indeed universal at least in turbulent boundary layers and pipe flow where high-Reynolds number data are currently available.

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“…Often the inertial range is quite limited in such studies. This range can be extended somewhat by using the extended-self-similarity (ESS) procedure [117] in which the slope of a log-log plots of the structure function S p versus S q yields the exponent ratio ζ p /ζ q ; this procedure is especially useful if q = 3 since ζ 3 = 1 for the 3D Navier-Stokes case. We illustrate the use of this ESS procedure in Sec.…”

Section: D Navier-stokes Turbulencementioning

confidence: 99%