Nonuniform quantum turbulence in superfluids

Abstract

The problem of quantum turbulence in a channel with an inhomogeneous counterflow of superfluid turbulent helium is studied. The counterflow velocity V x ns (y) along the channel is supposed to have a parabolic profile in the transverse direction y. Such statement corresponds to the recent numerical simulation by Khomenko et al. [Phys. Rev. B 91, 180504 (2015)]. The authors reported about a sophisticated behavior of the vortex line density (VLD) L(r, t), different from L ∝ V x ns (y) 2 , which follows from the naive, straightforward application of the conventional Vinen theory. It is clear, that Vinen theory should be refined by taking into account transverse effects and the way it ought to be done is the subject of active discussion in the literature. In the work we discuss several possible mechanisms of the transverse flux of VLD L(r, t) which should be incorporated in the standard Vinen equation to describe adequately the inhomogeneous quantum turbulence (QT). It is shown that the most effective among these mechanisms is the one that is related to the phase slippage phenomenon. The use of this flux in the modernized Vinen equation corrects the situation with an unusual distribution of the vortex line density, and satisfactory describes the behavior L(r, t) both in stationary and nonstationary situations. The general problem of the phenomenological Vinen theory in the case of nonuniform and nonstationary quantum turbulence is thoroughly discussed.

Dynamics of turbulent plugs in a superfluid He4 channel counterflow

“…The situation is different with the production term. Directly interpreting the model form as a product of average slowly-varying fields, we get for P 1 = α V x ns,nl s ×s x L ≈ αV 0 ns I ,x L. So far, the prob-lem of the closure for P 1 amounted to the question how to describe 6,16,[29][30][31] I ,x in terms of L and V ns . As it follows from the discussion in Sec.…”

“…(8). Although the transverse diffusion is negligible, the transverse VLD flux J y is an important factor in the inhomogeneous tangle dynamics [29][30][31] , moving VLD from the channel core towards the walls. We move it to RHS of Eq.…”

“…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.…”

K-ϵ-L model in turbulent superfluid helium

“…where ν = η/ρ is the classical kinematic viscosity (length The last equation in (2.4) is the equation for the vortex line density L, which was proposed for the first time by Vinen without the inertial term and then generalized by many authors. It has been extended to cover the diversity of the phenomenologies, to include the influence of the walls [18,32], the anisotropy of the vortex tangle [33], the influence of the transverse flow [34] and other situations of interest as in Ref. [35,36,37].…”

About the non-standard viewpoint on the dynamics of closed vortex filament

“…Topological and geometrical aspects of a quantum turbulent flow was studied in the work [12]. More complicated problems were also considered: quantum turbulence in a channel with an counterflow of superfluid turbulent helium was studied in the paper [13].…”