Dynamics of the vortex line density in superfluid counterflow turbulence

Abstract

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 L. The closure of such an equation for superfluid inhomogeneous flows requires additional inputs besides 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.

The phenomenon of magnetic vortices superconducting for (Sr2RuO4)

“…However, as the line scans displayed in 9(c) show, the contrast appears to have reversed after increasing the temperature to 4.5K. This would be a very interesting result but care needs to be taken, for instance the shift of ~1.75µm may have occurred due to thermal expansion; more evidence of this is needed [12] .…”

Dynamics of turbulent plugs in a superfluid He4 channel counterflow

“…Most of attempts to find equation of motion for the vortex line density so far dealt with steady-state tangles and represented P 1 and D in Eq. ( 10) as functions of L and V ns only for the homogeneous tangles, adding the curvature, the binormal, and their derivatives [17][18][19] in the inhomogeneous case. In the current situation of the inhomogeneous and growing tangle we can not expect a unique closure.…”

“…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.…”

“…[13][14][15] ). A microscopic theory by Schwarz 16 introduced additional structural properties of the tangle, such as root-mean-square curvature and var-ious anisotropy parameters, as important ingredients of the theory [17][18][19] . As was pointed out by Schwarz, the arguments leading to these equations for L apply only to the average time-dependent behavior near the steadystate, although are very often used in other situations.…”