Investigation of intermittency in superfluid turbulence

Salort, Julien; Chabaud, Benoît; Lévêque, Emmanuel; Roche, Philippe-Emmanuel

doi:10.1088/1742-6596/318/4/042014

Cited by 28 publications

(43 citation statements)

References 9 publications

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“…The first numerical study of intermittent exponents (86) did not find any intermittent effect peculiar to superfluid turbulence neither at low temperature (T ' 0:5T λ , ρ s =ρ n = 40) nor at and high temperature (T ' 0:99T λ , ρ s =ρ n = 0:1), in agreement with experiments (17,86), all performed on the low-temperature side…”

Section: Theorysupporting

confidence: 79%

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Barenghi

L’vov

Roche

2014

Proc. Natl. Acad. Sci. U.S.A.

109

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Turbulence in superfluid helium is unusual and presents a challenge to fluid dynamicists because it consists of two coupled, interpenetrating turbulent fluids: the first is inviscid with quantized vorticity, and the second is viscous with continuous vorticity. Despite this double nature, the observed spectra of the superfluid turbulent velocity at sufficiently large length scales are similar to those of ordinary turbulence. We present experimental, numerical, and theoretical results that explain these similarities, and illustrate the limits of our present understanding of superfluid turbulence at smaller scales. He.) Besides the lack of viscosity, another major difference from ordinary (classical) fluids such as water or air is that, in helium, vorticity is constrained to vortex line singularities of fixed circulation κ = h=M, where h is Planck's constant, and M is the mass of the relevant boson (M = m 4 , the mass of He, the vortex core radius ξ ≈ 10 −10 m is comparable to the interatomic distance. Thus, quantization of circulation results in the appearance of another characteristic length scale: the mean separation between vortex lines, ℓ. In typical experiments (both in 4 He and 3 He), ℓ is orders of magnitude smaller than the scale D of the largest eddies but is also orders of magnitudes larger than ξ.There is a growing consensus (2) that superfluid turbulence at large scales R ℓ is similar to classical turbulence if excited similarly, for example by a moving grid. The idea is that motions at scales R ℓ should involve at least a partial polarization (3-5) of vortex lines and their organization into vortex bundles that, at such large scales, should mimic continuous hydrodynamic eddies. Therefore, one expects a classical Richardson-Kolmogorov energy cascade, with larger "eddies" breaking into smaller ones. The spectral signature of this classical cascade is indeed observed experimentally in superfluid helium. In the absence of viscosity, in superfluid turbulence the kinetic energy should cascade downscale without loss, until it reaches scales R ∼ ℓ, where the discreteness becomes important. It is also believed that the energy is further transferred downscales by the interacting Kelvin waves (helical perturbation of the individual vortex lines) where it is radiated away by thermal quasiparticles (phonons and rotons in 4 He). Although this scenario seems reasonable, crucial details are yet to be established. Our understanding of superfluid turbulence at scales of the order of ℓ is still at infancy stage, and what happens at scales below ℓ is a question of intensive debates. The "quasiclassical" region of scales, R ℓ, is better understood, but still less than classical hydrodynamic turbulence. The main reason is that at nonzero temperatures (but still below the critical temperature), superfluid helium is a two-fluid system. According to the theory of Landau and Tisza (6), it consists of two interpenetrating components: the inviscid superfluid, of density ρ s and velocity u s (associated to the quantum ground stat...

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Section: Theorysupporting

confidence: 79%

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Barenghi

L’vov

Roche

2014

Proc. Natl. Acad. Sci. U.S.A.

109

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“…We also expect similar inertial range behavior of classical and superfluid turbulence for T T λ , when ρ n ρ s , due to the inconsequential role played by the normal component, see, e.g. [4]. Moreover (and less trivially) the intermittent scaling exponents ξ p have to be the same in classical and low-temperature superfluid turbulence.…”

supporting

confidence: 57%

Enhancement of Intermittency in Superfluid Turbulence

et al. 2013

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We consider the intermittent behavior of superfluid turbulence in 4 He. Due to the similarity in the nonlinear structure of the two-fluid model of superfluidity and the Euler and Navier-Stokes equations one expects the scaling exponents of the structure functions to be the same as in classical turbulence for temperatures close to the superfluid transition T λ and also for T T λ . This is not the case when mutual friction becomes important. Using shell model simulations, we propose that for an intermediate regime of temperatures, such that the density of normal and superfluid components are comparable to each other, there exists a range of scales in which the effective exponents indicate stronger intermittency. We offer a bridge relation between these effective and the classical scaling exponents. Since this effect occurs at accessible temperatures and Reynolds numbers, we propose that experiments should be conducted to further assess the validity and implications of this prediction.Introduction. Non-equilibrium systems are often characterized by relatively quiescent periods which are interrupted by rare but violent changes of the physical observables. This phenomenon which is referred to as "intermittency" is very generic as it appears in many different stationary random processes.It is believed [1], that highly excited hydrodynamic turbulence possesses universal statistics in the inertial interval of scales L r η. Here L is the of energy input scale, e.g. due to instabilities of high velocity flows, and η is the viscous energy dissipation scale. The intermittent behavior of space homogeneous fully developed turbulence of incompressible fluids can be studied in terms of the velocity structure functions [1]

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“…This subject is thoroughly studied in the classical case, but much less so in the context of superfluid 4 He. The experiments [7][8][9] , conducted mostly at low temperatures and close to T λ , did not find deviations from the turbulent statistics of classical flows. A very recent experimental study 12 of turbulence in the wake of a disc was conducted in a wide range of temperatures; it also did not find any temperature dependence of the scaling exponent of the second order structure function.…”

Section: Introductionmentioning

confidence: 80%

Turbulent statistics and intermittency enhancement in coflowing superfluidHe4

et al. 2018

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The large scale turbulent statistics of mechanically driven superfluid 4 He was shown experimentally to follow the classical counterpart. In this paper we use direct numerical simulations to study the whole range of scales in a range of temperatures T ∈ [1.3, 2.1] K. The numerics employ selfconsistent and non-linearly coupled normal and superfluid components. The main results are that (i) the velocity fluctuations of normal and super components are well-correlated in the inertial range of scales, but decorrelate at small scales. (ii) The energy transfer by mutual friction between components is particulary efficient in the temperature range between 1.8 K and 2 K, leading to enhancement of small scales intermittency for these temperatures. (iii) At low T and close to T λ the scaling properties of the energy spectra and structure functions of the two components are approaching those of classical hydrodynamic turbulence.

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Investigation of intermittency in superfluid turbulence

Cited by 28 publications

References 9 publications

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Enhancement of Intermittency in Superfluid Turbulence

Turbulent statistics and intermittency enhancement in coflowing superfluidHe4

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