Local and nonlocal dynamics in superfluid turbulence

Abstract

In turbulent superfluid He II, the quantized vortex lines interact via the classical Biot-Savart law to form a complicated vortex tangle. We show that vortex tangles with the same vortex line density will have different energy spectra, depending on the normal fluid which feeds energy into the superfluid component, and identify the spectral signature of two forms of superfluid turbulence: Kolmogorov tangles and Vinen tangles. By decomposing the superfluid velocity field into local and nonlocal contributions, we find that in Vinen tangles the motion of vortex lines depends mainly on the local curvature, whereas in Kolmogorov tangles the long-range vortex interaction is dominant and leads to the formation of clustering of lines, in analogy to the 'worms' of ordinary turbulence.

A new self-consistent approach of quantum turbulence in superfluid helium

“…This local kinematic approach has been extensively employed in past studies to shed light on fundamental aspects of superfluid turbulence. In particular, various models of imposed normal flow V n have been studied: uniform [51,[56][57][58], parabolic [59][60][61][62][63], Hagen-Poiseuille and tail-flattened flows [64], vortex tubes [65], ABC flows [66], frozen normal fluid vortex tangles [67], random waves [58], time-frozen snapshots of turbulent solutions of Navier-Stokes equations [58,60,63] and time-dependent homogeneous and isotropic turbulent solutions of linearly forced Navier-Stokes equations [68]. (iii) Self-consistent local friction…”

Coupled normal fluid and superfluid profiles of turbulent helium II in channels

“…Unfortunately, most numerical simulations of superfluid turbulence in the literature have determined the superfluid vortex tangle in the presence of a prescribed normal fluid, without taking into account the back reaction of the vortex lines on the normal fluid. Various models of the imposed normal fluid have been studied: uniform, [32][33][34][35] parabolic, [36][37][38][39] Hagen-Poiseuille and tail-flattened flows, 40 vortex tubes, 41 ABC flows, 42 frozen normal fluid vortex tangles 43 , random waves 35 , time-frozen snapshots of the turbulent solution of the Navier-Stokes equations 35,37,39 and time-dependent homogeneous and isotropic turbulent solutions of linearly forced Navier-Stokes equations. 44 Moreover, most calculations were performed in open or periodic domains, avoiding the difficulty of the boundary.…”

Visualization of quantum turbulence in superfluid He3−B : Combined numerical and experimental study of Andreev reflection

“…In Refs. 40,41 , both the counterflow turbulence and the vortex tangle driven by the synthetic turbulence in the normal fluid were simulated starting from an arbitrary seeding initial condition and then letting L grow and saturate to a statistically steady state. An important advantage is that in both cases the vortex line density was changing within the same interval from L = 0 until saturation at L ≈ 2.2 × 10 8 m −2 .…”

“…For three realizations of the counterflow turbulence with different values of the counterflow velocity, and for three realizations of the mechanically driven turbulence with different values of the rms normal fluid velocity (see Refs. 40,41 for details and values of parameters), we calculated the Andreev reflection from the unstructured ("ultraquantum") and structured ("quasiclassical") tangles. These calculations were performed for different values of the vortex line density corresponding to different stages of the tangle's evolution from L = 0 to the saturated, statistically steady state.…”