Dissipation in quantum turbulence in superfluid He4 above 1 K

Abstract

There are two commonly discussed forms of quantum turbulence in superfluid 4 He above 1K: in one there is a random tangle of quantizes vortex lines, existing in the presence of a non-turbulent normal fluid; in the second there is a coupled turbulent motion of the two fluids, often exhibiting quasi-classical characteristics on scales larger than the separation between the quantized vortex lines in the superfluid component. The decay of vortex line density, L, in the former case is often described by the equation dL/dt = −χ2(κ/2π)L 2 , where κ is the quantum of circulation, and χ2 is a dimensionless parameter of order unity. The decay of total turbulent energy, E, in the second case is often characterized by an effective kinematic viscosity, ν ′ , such that dE/dt = −ν ′ κ 2 L 2. We present new values of χ2 derived from numerical simulations and from experiment, which we compare with those derived from a theory developed by Vinen and Niemela. We summarise what is presently known about the values of ν ′ from experiment, and we present a brief introductory discussion of the relationship between χ2 and ν ′ , leaving a more detailed discussion to a later paper.

Inviscid diffusion of vorticity in low-temperature superfluid helium

“…This theory, as the modified Vinen equation, assumes (rather than infers) the existence of a diffusion process of vortex loops by postulating Brownian character of the vortex loops' dynamics. A superfluid's effective viscosity is also discussed in the different but related problem of the decay of superfluid turbulence, with experimental and numerical values [33][34][35][36] approximately in the range 0.01 < ν ′ /κ < 1 but more concentrated around 0.1.…”

“…Physically, in this zero temperature limit, χ 2 models a sink of vortex lines due to dissipation of kinetic energy through both vortex reconnections and phonon emission (induced by high frequency Kelvin waves [25]). It has been noted that χ 2 depends on the local vortex line density at finite temperatures [36]. We independently estimate values of χ 2 in the zero-temperature limit, using the full Biot-Savart law of Eq.…”

Characterizing vortex tangle properties in steady-state He II counterflow using particle tracking velocimetry

“…provided the counterflow velocity ρv n /ρ s exceeds a small critical velocity v 0 . To illustrate agreement with σ G1 , we computed v 2 L 1/2 using values for γ (a temperature-dependent parameter relating L to v ns ), v 0 , and the parameter c 2 reported in the recent work of Gao et al [27,28], and we approximated the mean vortex line spacing ℓ = L −1/2 across the entire parameter space. Since the agreement between σ G1 and v 2 L 1/2 appeared to be reasonable, we can use measured G1 velocity fluctuations to represent v 2 L 1/2 , and apply Eqn.…”

“…Since estimation of spatially-dependent c 2 is still beyond the capability of numerical simulations [28], and the traditional second sound method provides averaged information across the measurement volume, application of PTV to make whole-field measurements of G1 velocity fluctuations offers a unique opportunity to investigate the spatial dependence of c 2 .…”

Dynamics of turbulent plugs in a superfluid He4 channel counterflow

“…Recent advances in the experimental techniques, including flow visualization [22][23][24] , as well as increasing computing power, renewed the interest to the spatial inhomogeneity due to presence of channel walls 19,[25][26][27][28][29][30][31] and spatially-resolved investigations of the transient behavior in the thermal counterflow 32 . The latter work showed that the vortex tangle that eventually fills the whole channel, grows starting from a number of remnant vortex rings.…”