D. Khomenko

Dynamics of the Density of Quantized Vortex-Lines in Superfluid Turbulence

Institute of Thermophysics, Novosibirsk, RussiaThe quantization of vortex lines in superfluids requires the introduction of their density L(r,t) inthe description of quantum turbulence. The space homogeneous balance equation for L(t), proposedby Vinen on the basis of dimensional and physical considerations, allows a number of competingforms for the production term P. Attempts to choose the correct one on the basis of time-dependenthomogeneous experiments ended inconclusively. To overcome this difficulty we announce here anapproach that employs an inhomogeneous channel flow which is excellently suitable to distinguishthe implications of the various possible forms of the desired equation. We demonstrate that theoriginally selected form which was extensively used in the literature is in strong contradiction withour data. We therefore present a new inhomogeneous equation for L(r,t) that is in agreement withour data and propose that it should be considered for further studies of superfluid turbulence.

Analytic Solution of the Approach of Quantum Vortices Towards Reconnection

Experimental and simulational studies of the dynamics of vortex reconnections in quantum fluids showed that the distance d between the reconnecting vortices is close to a universal time dependence d=D[κ|t(0)-t|](α) with α fluctuating around 1/2 and κ=h/m is the quantum of circulation. Dimensional analysis, based on the assumption that the quantum of circulation κ=h/m is the only relevant parameter in the problem, predicts α=1/2. The theoretical calculation of the dimensionless coefficient D in this formula remained an open problem. In this Letter we present an analytic calculation of D in terms of the given geometry of the reconnecting vortices. We start from the numerically observed generic geometry on the way to vortex reconnection and demonstrate that the dynamics is well described by a self-similar analytic solution which provides the wanted information.

Local and nonlocal energy spectra of superfluid He3 turbulence

Below the phase transition temperature Tc ≃ 10 K He-B has a mixture of normal and superfluid components. Turbulence in this material is carried predominantly by the superfluid component. We explore the statistical properties of this quantum turbulence, stressing the differences from the better known classical counterpart. To this aim we study the time-honored Hall-Vinen-BekarevichKhalatnikov coarse-grained equations of superfluid turbulence. We combine pseudo-spectral direct numerical simulations with analytic considerations based on an integral closure for the energy flux. We avoid the assumption of locality of the energy transfer which was used previously in both analytic and numerical studies of the superfluid He-B turbulence. For T < 0.37 Tc, with relatively weak mutual friction, we confirm the previously found “subcritical” energy spectrum E(k), given by a superposition of two power laws that can be approximated as E(k) ∝ k with an apparent scaling exponent 5 3 < x(k) < 3. For T > 0.37 Tc and with strong mutual friction, we observed numerically and confirmed analytically the scale-invariant spectrum E(k) ∝ k with a (k-independent) exponent x > 3 that gradually increases with the temperature and reaches a value x ∼ 9 for T ≈ 0.72 Tc. In the near-critical regimes we discover a strong enhancement of intermittency which exceeds by an order of magnitude the corresponding level in classical hydrodynamic turbulence.

Coupled Dynamics for Superfluid \(^4\hbox {He}\) in a Channel

We study the coupled dynamics of normal and superfluid components of superfluid

^4

^4\hbox {He}

Reply to “Comment on ‘Dynamics of the density of quantized vortex lines in superfluid turbulence’ ”

4He in a channel considering the counterflow turbulence with laminar normal component. In particular, we calculated profiles of the normal velocity, the mutual friction, the vortex line density and other flow properties and compared them to the case where the dynamic of the normal component is “frozen.” We have found that the coupling between the normal and superfluid components leads to flattening of the normal velocity profile, increasingly more pronounced with temperature, as the mutual friction, and therefore, coupling becomes stronger. The commonly measured flow properties also change when the coupling between the two components is taken into account.

Dynamics of the vortex line density in superfluid counterflow turbulence

We study the coupled dynamics of normal and superfluid components of superfluid