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

Abstract

The quantization of vortex lines in superfluids requires the introduction of their density $\C L(\B r,t)$ in the description of quantum turbulence. The space homogeneous balance equation for $\C L(t)$, proposed by Vinen on the basis of dimensional and physical considerations, allows a number of competing forms for the production term $\C P$. Attempts to choose the correct one on the basis of time-dependent homogeneous experiments ended inconclusively. To overcome this difficulty we announce here an approach that employs an inhomogeneous channel flow which is excellently suitable to distinguish the implications of the various possible forms of the desired equation. We demonstrate that the originally selected form which was extensively used in the literature is in strong contradiction with our data. We therefore present a new inhomogeneous equation for $\C L(\B r,t)$ that is in agreement with our data and propose that it should be considered for further studies of superfluid turbulence.

6 pages, 3 figs, PRB submitted

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Cited by in corpus (8)

• Spherically symmetric formation of localized vortex tangle around a heat source in superfluid ${}^4$He
• Transition to turbulence and streamwise inhomogeneity of vortex tangle in thermal counterflow
• Coupled dynamics for superfluid ${}^4$He in the channel
• Large-scale normal fluid circulation in helium superflows
• Energy spectra and fluxes of turbulent rotating Bose-Einstein condensates in two dimensions
• Reply to Comment on "Dynamics of the Density of Quantized Vortex-Lines in Superfluid Turbulence"
• Dynamics of the vortex line density in superfluid counterflow turbulence
• Modelling turbulent flow of superfluid ${}^4$He past a rough solid wall in the $T=0$ limit