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Register a new userDynamics of the Density of Quantized Vortex-Lines in Superfluid Turbulence
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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.
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This is a Reply to Nemirovskii Comment [Phys. Rev. B 94, 146501 (2016)] on the Khomenko et al, [Phys.Rev. B v.91, 180504(2016)], in which a new form of the production term in Vinens equation for the evolution of the vortex-line density $cal L$ in the thermal counterflow of superfluid $^4$He in a channel was suggested. To further substantiate the suggested form which was questioned in the Comment, we present a physical explanation for the improvement of the closure suggested in Khomenko et al [Phys.Rev. B v. 91, 180504(2016)] in comparison to the form proposed by Vinen. We also discuss the closure for the flux term, which agrees well with the numerical results without any fitting parameters.
Describing superfluid turbulence at intermediate scales between the inter-vortex distance and the macroscale requires an acceptable equation of motion for the density of quantized vortex lines $cal{L}$. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides $cal{L}$ and the normal and superfluid velocity fields. In this paper we offer a minimal closure using one additional anisotropy parameter $I_{l0}$. Using the example of counterflow superfluid turbulence we derive two coupled closure equations for the vortex line density and the anisotropy parameter $I_{l0}$ with an input of the normal and superfluid velocity fields. The various closure assumptions and the predictions of the resulting theory are tested against numerical simulations.
We have theoretically investigated Kelvin waves of quantized vortex lines in trapped Bose-Einstein condensates. Counterrotating perturbation induces an elliptical instability to the initially straight vortex line, driven by a parametric resonance between a quadrupole mode and a pair of Kelvin modes of opposite momenta. Subsequently, Kelvin waves rapidly decay to longer wavelengths emitting sound waves in the process. We present a modified Kelvin wave dispersion relation for trapped superfluids and propose a simple method to excite Kelvin waves of specific wave number.
Collisions in a beam of unidirectional quantized vortex rings of nearly identical radii $R$ in superfluid $^4$He in the limit of zero temperature (0.05 K) were studied using time-of-flight spectroscopy. Reconnections between two primary rings result in secondary vortex loops of both smaller and larger radii. Discrete steps in the distribution of flight times, due to the limits on the earliest possible arrival times of secondary loops created after either one or two consecutive reconnections, are observed. The density of primary rings was found to be capped at the value $500{rm ,cm}^{-2} R^{-1}$ independent of the injected density. This is due to collisions between rings causing piling-up of many other vortex rings. Both observations are in quantitative agreement with our theory.
Formation of vortex rings around moving spherical objects in superfluid He-4 at 0 K is modeled by time-dependent density functional theory. The simulations provide detailed information of the microscopic events that lead to vortex ring emission through characteristic observables such as liquid current circulation, drag force, and hydrodynamic mass. A series of simulations were performed to determine velocity thresholds for the onset of dissipation as a function of the sphere radius up to 1.8 nm and at external pressures of zero and 1 bar. The threshold was observed to decrease with the sphere radius and increase with pressure thus showing that the onset of dissipation does not involve roton emission events (Landau critical velocity), but rather vortex emission (Feynman critical velocity), which is also confirmed by the observed periodic response of the hydrodynamic observables as well as visualization of the liquid current circulation. An empirical model, which considers the ratio between the boundary layer kinetic and vortex ring formation energies, is presented for extrapolating the current results to larger length scales. The calculated critical velocity value at zero pressure for a sphere that mimics an electron bubble is in good agreement with the previous experimental observations at low temperatures. The stability of the system against symmetry breaking was linked to its ability to excite quantized Kelvin waves around the vortex rings during the vortex shedding process. At high vortex ring emission rates, the downstream dynamics showed complex vortex ring fission and reconnection events that appear similar to those seen in previous Gross-Pitaevskii theory-based calculations, and which mark the onset of turbulent behavior.
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