Turbulence as a Problem in Non-equilibrium Statistical Mechanics

Goldenfeld, Nigel; Shih, Hong Yan

doi:10.1007/s10955-016-1682-x

Cited by 51 publications

(42 citation statements)

References 91 publications

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“…For η=0.1, 0.2 and 0.3, the PDF looks reasonably Gaussian. This excludes statistically [21] with an almost vanishing radial average. For increasing values of η ≥ 0.3, the tendency for the PDF to flatten away from zero becomes stronger, thereby enlarging the range of values of |U θ |.…”

Section: Statistics Of Transverse Large-scale Flowsmentioning

confidence: 99%

Turbulent bifurcations in intermittent shear flows: From puffs to oblique stripes

2017

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Localised turbulent structures such as puffs or oblique stripes are building blocks of the intermittency regimes in subcritical wall-bounded shear flows. These turbulent structures are investigated in incompressible pressure-driven annular pipe flow using direct numerical simulations in long domains. For low enough radius ratio η, these coherent structures have a dynamics comparable to that of puffs in cylindrical pipe flow. For η larger than 0.5, they take the shape of helical stripes inclined with respect to the axial direction. The transition from puffs to stripes is analysed statistically by focusing on the axisymmetry properties of the associated large-scale flows. It is shown that the transition is gradual : as the azimuthal confinement relaxes, allowing for an azimuthal large-scale component, oblique stripes emerge as predicted in the planar limit. The generality of this transition mechanism is discussed in the context of subcritical shear flows.2

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Section: Statistics Of Transverse Large-scale Flowsmentioning

confidence: 99%

Turbulent bifurcations in intermittent shear flows: From puffs to oblique stripes

2017

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“…The study of the turbulent-laminar transition is difficult around Re c , because the puffs are weakly unstable [14], and splitting and decaying are observed as rare events. In fact a super-exponential increase of the puffdecaying time scale has been observed as a function of the Reynolds number [8,9] and its origin has been discussed using the extreme value statistics [15][16][17][18] and directed percolation models [19,20], but it is still unclear if this is an effective law observed only around Re c or if it can be observed beyond. The goal of this paper is to introduce a sampling method to help this situation by accelerating the measurement of the puff decaying.…”

Section: Introductionmentioning

confidence: 99%

Method to measure efficiently rare fluctuations of turbulence intensity for turbulent-laminar transitions in pipe flows

Nemoto

Alexakis

2018

Phys. Rev. E

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The fluctuations of turbulence intensity in a pipe flow around the critical Reynolds number is difficult to study but important because they are related to turbulent-laminar transitions. We here propose a rare-event sampling method to study such fluctuations in order to measure the time-scale of the transition efficiently. The method is composed of two parts: (i) the measurement of typical fluctuations (the bulk part of an accumulative probability function) and (ii) the measurement of rare fluctuations (the tail part of the probability function) by employing dynamics where a feedback control of the Reynolds number is implemented. We apply this method to a chaotic model of turbulent puffs proposed by Barkley and confirm that the time-scale of turbulence decay increases super-exponentially even for high Reynolds numbers up to Re = 2500, where getting enough statistics by brute-force calculations is difficult. The method uses a simple procedure of changing Reynolds number that can be applied even to experiments.

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“…We observe a significant inverse cascade of kinetic energy at early stages. As time progresses, the kinetic energy flux becomes weaker and gets concentrated in the wavenumber band k ∈ [1,8]. This feature is compatible with the strongly vortical quasi-2D structure of the flow.…”

Section: Energy and Enstrophy Fluxes And Spectramentioning

confidence: 61%

Statistical features of rapidly rotating decaying turbulence: Enstrophy and energy spectra and coherent structures

et al. 2018

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In this paper we investigate the properties of rapidly rotating decaying turbulence using numerical simulations and phenomenological modelling. We find that as the turbulent flow evolves in time, the Rossby number decreases to ∼ 10 −3 , and the flow becomes quasi-two-dimensional with strong coherent columnar structures arising due to the inverse cascade of energy. We establish that a major fraction of energy is confined in Fourier modes (±1, 0, 0) and (0, ±1, 0) that correspond to the largest columnar structure in the flow. For wavenumbers (k) greater than the enstrophy dissipation wavenumber (k d ), our phenomenological arguments and numerical study show that the enstrophy flux and spectrum of a horizontal cross-section perpendicular to the axis of rotation are given by ω exp(−C(k/k d ) 2 ) and C 2/3 ω k −1 exp(−C(k/k d ) 2 ) respectively; for this 2D flow, ω is the enstrophy dissipation rate, and C is a constant. Using these results, we propose a new form for the energy spectrum of rapidly rotating decaying turbulence: E(k) = C 2/3 ω k −3 exp(−C(k/k d ) 2 ). This model of the energy spectrum is based on wavenumber-dependent enstrophy flux, and it deviates significantly from power law energy spectrum reported earlier.

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Turbulence as a Problem in Non-equilibrium Statistical Mechanics

Cited by 51 publications

References 91 publications

Turbulent bifurcations in intermittent shear flows: From puffs to oblique stripes

Turbulent bifurcations in intermittent shear flows: From puffs to oblique stripes

Method to measure efficiently rare fluctuations of turbulence intensity for turbulent-laminar transitions in pipe flows

Statistical features of rapidly rotating decaying turbulence: Enstrophy and energy spectra and coherent structures

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