Multiscaling in superfluid turbulence: A shell-model study

Abstract

We examine the multiscaling behavior of the normal- and superfluid-velocity structure functions in three-dimensional superfluid turbulence by using a shell model for the three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) equations. Our 3D-HVBK shell model is based on the Gledzer-Okhitani-Yamada shell model. We examine the dependence of the multiscaling exponents on the normal-fluid fraction and the mutual-friction coefficients. Our extensive study of the 3D-HVBK shell model shows that the multiscaling behavior of the velocity structure functions in superfluid turbulence is more complicated than it is in fluid turbulence.

Intermittency of quantum turbulence with superfluid fractions from 0% to 96%

“…Still, due to the strong coupling between the two fluids, they are nearly locked together in the inertial range (V s V n V ), which implies that the normal and superfluid exponents are similar. This is indeed the case in the numerics as illustrated in Fig.10 , in the supplemental materials of [14] (see the G1-G21 subsets, which are obtained using the fluid properties of He-II) and by the figure 1 from [12] which shows similar normal and superfluid structure functions in the inertial range, implying similar intermittency exponents. Table III are not plotted because there are smaller than the size of the circle symbols.…”

“…Indeed, the absolute value of ζ N S 2 results from an arbitrary choice of model parameters in shell simulation (as recalled in [12]) and it is biased by use of the ESS method in experiments, as already ex- three studies. Interestingly, the exponents ζ 2 obtained in the simulations by Shukla et al [14] both exceed and fall short of their classical limit ζ N S 2 , which could be interpreted respectively as an intermittency enhancement and reduction. In Boué et al simulations [12], the exponents ζ 2 have a minimum below Kolmogorov 1941 value ζ 2 = 2/3, which corresponds itself to an absence of intermittency.…”

“…But they also reported a significant enhancement of intermittency at intermediate temperature, corresponding to the window ρ s /ρ 20 − 90% (yet the exponent of the second order structure function reaches values corresponding to an absence of intermittency) [12]. In 2016, numerical studies by Shukla et Pandit [14] using a different variant of shell model (respectively Sabra version and a GOY variant) TABLE I. Experimental and numerical studies of quantum turbulence intermittency.…”

Intermittency enhancement in quantum turbulence in superfluidHe4

“…Small-scale intermittency results in corrections to the energy spectrum and velocity structure functions that are nearly universal across a wide range of turbulent flows in classical fluids [6,7]. A question that has attracted increasing interest in recent years is whether this universality can be extended to quantum fluids such as superfluid 4 He whose hydrodynamic behavior is strongly affected by quantum effects and cannot be described by the Navier-Stokes equation [8][9][10][11][12][13].…”

Scaling laws of wave-cascading superfluid turbulence

“…A slope of 5/3 is often obtained for the energy spectrum of superfluid turbulence forced at a length scale much larger than the inter-vortex distance. There is an increasing amount of evidence for a substantial hydrodynamic-like inertial range from the laboratory experiments [10][11][12] and the numerical simulations using the Biot-Savart law, 11,[13][14][15][16][17] the multi-fluid equation, 18,19 and the Gross-Pitaevskii equation. 20 Naively speaking, on short wavelength scales, fluctuation amplitudes are sufficiently small and the picture of linear mode waves should be valid to describe the turbulent fluctuations.…”