Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence

Gorce, Jean-Baptiste; Falcon, Éric

doi:10.1103/physrevlett.129.054501

Cited by 10 publications

(5 citation statements)

References 47 publications

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“…These findings are also important from a practical perspective since they predict the mean value and statistics of the power injected by a large-scale force in turbulence. This could be experimentally investigated by adding a large-scale propeller in the experiment in which largescale equipartition was observed [24]. Moreover, since the proper variables of the system are identified, our work paves the way to use equilibrium statistical mechanics and maximum entropy techniques to model geophysical large scales, as already successfully done for the simpler 2D case [20].…”

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confidence: 77%

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Fluctuation relations at large scales in three-dimensional hydrodynamic turbulence

Alexakis,

Chibbaro,

Michel

2023

EPL

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It has long been conjectured that, in three-dimensional turbulence, velocity modes at scales larger than the forcing scale follow equilibrium dynamics. Recent numerical and experimental evidence shows that such modes share the same mean energy and therefore support this claim, but equilibrium dynamics does not reduce to equipartition of energy. In this work, a large set of direct numerical simulations is carried out to investigate if fluctuation-dissipation relations and the fluctuation theorem also apply at these scales. These two results link out-of-equilibrium properties of a forced system with its behavior at equilibrium. Both relations are verified quantitatively by the results of our simulations, further supporting that large-scale modes display equilibrium dynamics. They provide new tools to characterize both the mean value and the fluctuations of the injected energy by a large-scale force acting on turbulence driven by small scale random noise.

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mentioning

confidence: 77%

“…Recent numerical and experimental investigations report equipartition of energy at large scales [21][22][23][24], as predicted by the TEE, at least provided some constraints on the forcing mechanism are put [25,26]. TEE have also been found able to capture bifurcation between turbulent states [27][28][29].…”

mentioning

confidence: 89%

Fluctuation relations at large scales in three-dimensional hydrodynamic turbulence

Alexakis,

Chibbaro,

Michel

2023

EPL

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“…This article focuses on the statistics of velocity structure functions at separations larger than the forcing scale. Gorce & Falcon (2022) studied the second-and third-order structure functions and found that they are independent of separation r of two measured points, which we believe is a result of low resolution. This article shows that the probability density functions (p.d.f.s) of velocity difference at large separations are close to, but deviate from, the Gaussian distribution.…”

Section: Introductionmentioning

confidence: 88%

“…Numerical and experimental results have justified the large-scale statistical equilibrium in 3-D HIT (Cichowlas et al. 2005; Dallas, Fauve & Alexakis 2015; Cameron, Alexakis & Brachet 2017; Alexakis & Biferale 2018; Alexakis & Brachet 2019, 2020; Gorce & Falcon 2022; Hosking & Schekochihin 2023). The dynamics of scales larger than the forcing scale are of interest for many flows where the energy flux is zero, e.g.…”

Section: Introductionmentioning

confidence: 94%

Departure from the statistical equilibrium of large scales in forced three-dimensional homogeneous isotropic turbulence

Ding,

Xie,

Wang

2024

J. Fluid Mech.

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We study the statistically steady states of the forced dissipative three-dimensional homogeneous isotropic turbulence at scales larger than the forcing scale in real separation space. The probability density functions (p.d.f.s) of longitudinal velocity difference at large separations are close to, but deviate from, Gaussian, measured by their non-zero odd parts. The analytical expressions of the third-order longitudinal structure functions derived from the Kármán–Howarth–Monin equation prove that the odd-part p.d.f.s of velocity differences at large separations are small but non-zero. Specifically, when the forcing effect in the displacement space decays exponentially as the displacement tends to infinity, the odd-order longitudinal structure functions have a power-law decay with an exponent of $-$ 2, implying a significant coupling between large and small scales. Under the assumption that forcing controls the large-scale dynamics, we propose a conjugate regime to Kolmogorov's inertial range, independent of the forcing scale, to capture the odd parts of p.d.f.s. Thus, dynamics of large scales departs from the absolute equilibrium, and we can partially recover small-scale information without explicitly resolving small-scale dynamics. The departure from the statistical equilibrium is quantified and found to be viscosity-independent. Even though this departure is small, it is significant and should be considered when studying the large scales of the forced three-dimensional homogeneous isotropic turbulence.

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“…The induced flows subsequently interact to form a central HIT region with small mean flow. Recent innovative techniques have also been developed to generate turbulence in laboratories via injection of vortex rings and magnetic particles (Gorce & Falcon 2022;Matsuzawa et al 2023). We note that some facilities use rotating elements (e.g.…”

Section: Synthetic Jets and Pointwise Energy Injectionmentioning

confidence: 99%

Laboratory generation of zero-mean-flow homogeneous isotropic turbulence: non-grid approaches

Ghazi Nezami,

Byron,

Johnson

2023

Flow

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Over the years, many facilities have been developed to study turbulent flow in the laboratory. Homogeneous isotropic turbulence (HIT) with zero mean flow provides a unique environment for investigating fundamental aspects and specific applications of turbulent flow. We provide an extensive overview of laboratory facilities that generate incompressible zero-mean-flow HIT using different types of actuators and configurations. Reviewed facilities cover a variety of geometries and sizes, as well as forcing style (e.g. symmetric versus asymmetric and unsteady versus steady). We divide facilities into four categories, highlighting links between their geometries and the statistics of the flows they generate. We then compare published data to uncover similarities and differences among various turbulence-generation mechanisms. We also compare the decay of turbulence in zero-mean-flow facilities with that observed in wind and water tunnels, and we analyse the connections between flow characteristics and physical aspects of the facilities. Our results emphasize the importance of considering facility geometry and size together with the strength and type of actuators when studying zero-mean-flow HIT. Overall, we provide insight into how to optimally design and build laboratory facilities that generate zero-mean-flow HIT.

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Statistical Equilibrium of Large Scales in Three-Dimensional Hydrodynamic Turbulence

Cited by 10 publications

References 47 publications

Fluctuation relations at large scales in three-dimensional hydrodynamic turbulence

Fluctuation relations at large scales in three-dimensional hydrodynamic turbulence

Departure from the statistical equilibrium of large scales in forced three-dimensional homogeneous isotropic turbulence

Laboratory generation of zero-mean-flow homogeneous isotropic turbulence: non-grid approaches

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