Turbulent statistics and intermittency enhancement in coflowing superfluidHe4

Abstract

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.

Strong anisotropy of superfluid He4 counterflow turbulence

“…in Ref. 2,13,18,20 ). Here α is the dimensionless mutual friction parameter related 1 to γ 0 as αρ s κ = (1 + α 2 )γ 0 , L is the vortex line density.…”

“…The detailed study of the statistics of the coflow was reported in Ref. 20 . Other parameters of the simulations were chosen based on dimensionless numbers: i) the Reynolds numbers Re j = ∆u ν j k 0 , ii) the turbulent intensity U ns ∆u , and iii) the dimensionless cross-over scale…”

“…. (20) In the upper row of Fig.1 we plot the spectrum • E j (k), compensated by the classical scaling k 5/3 for different flow conditions. In the lower row we show the crosscorrelations Eq.…”

Inhomogeneous distribution of particles in coflow and counterflow quantum turbulence

“…In the opposite limit T → T λ , the superfluid fraction vanishes and the classical behavior discussed above is recovered. More interesting is the intermediate case where the two fluid densities and viscosities are similar, at T ≈ 1.9 K. In this case, in the absence of a mean counterflow, the two velocity fields are tightly coupled even at the smallest flow scales [23]. Hence, S n ≈ S s and Ω n ≈ Ω s , and the clustering behavior predicted by eq.…”

“…As in ref. [23], the latter is estimated as Ω 2 0 = |ω s | 2 /2, where ω s = ∇ × u s is the superfluid vorticity, and · denotes a space average. The two velocity fields are stirred by independent large-scale Gaussian random forces Φ s (x) and Φ n (x) of unit variance.…”