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Physics Today

Quantum turbulence

William Frank Vinen, Russell James Donnelly

Published Apr 1, 2007• 52 citations
Publisher

Abstract

Because superfluid eddies can only be formed from quantized vortex lines, one might expect quantum turbulence to be very different from its classical counterpart. But that's not necessarily so.
DOI
10.1063/1.2731972

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ABSTRACT We theoretically study the line density of quantum vortices in a superfluid turbulent wake based on the conjecture of quantum turbulence of a pure superfluid in the zero temperature limit. The conjecture states that a collection of many quantum vortices can mimic a classical eddy in the continuum approximation. By straightforwardly relating the Kolmogorov's similarity to this conjecture, we can estimate that the effective viscosity of a pure superfluid turbulence is comparable to the circulation quantum , the minimum circulation of quantum vortices. This result naturally leads to a definition of the superfluid Reynolds number, with the characteristic size and velocity , supported by the fact that the equation of motion of a pure superfluid reduces to the Euler equation for high . By using the classical description of the rate of energy injection or dissipation, we quantitatively evaluate a characteristic density of vortex lines in a superfluid turbulent wake and its spatial profile of grid turbulence in terms of the superfluid Reynolds number.
The quantization of vortex lines in superfluids requires the introduction of their density $\mathcal{L}(\mathbit{r},t)$ in the description of quantum turbulence. The space homogeneous balance equation for L(t)\mathcal{L}(t)L(t), proposed by Vinen on the basis of dimensional and physical considerations, allows a number of competing forms for the production term P\mathcal{P}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 very 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 form of an inhomogeneous equation for $\mathcal{L}(\mathbit{r},t)$ that is in agreement with our data and propose that it should be considered for further studies of superfluid turbulence.