Dynamics of vortex tangle without mutual friction in superfluid4He

Abstract

A recent experiment has shown that a tangle of quantized vortices in superfluid 4 He decayed even at mK temperatures where the normal fluid was negligible and no mutual friction worked. Motivated by this experiment, this work studies numerically the dynamics of the vortex tangle without the mutual friction, thus showing that a self-similar cascade process, whereby large vortex loops break up to smaller ones, proceeds in the vortex tangle and is closely related with its free decay. This cascade process which may be covered with the mutual friction at higher temperatures is just the one at zero temperature Feynman proposed long ago. The full Biot-Savart calculation is made for dilute vortices, while the localized induction approximation is used for a dense tangle. The former finds the elementary scenario: the reconnection of the vortices excites vortex waves along them and makes them kinked, which could be suppressed if the mutual friction worked. The kinked parts reconnect with the vortex they belong to, dividing into small loops. The latter simulation under the localized induction approximation shows that such cascade process actually proceeds self-similarly in a dense tangle and continues to make small vortices. Considering that the vortices of the interatomic size no longer keep the picture of vortex, the cascade process leads to the decay of the vortex line density. The presence of the cascade process is supported also by investigating the classification of the reconnection type and the size distribution of vortices. The decay of the vortex line density is consistent with the solution of the Vinen's equation which was originally derived on the basis of the idea of homogeneous turbulence with the cascade process. The cascade process revealed by this work is an intrinsic process in the superfluid system free from the normal fluid. The obtained result is compared with the recent Vinen's theory which discusses the Kelvin wave cascade with sound radiation.67.40.Vs, 67.40.Bz

Evaporation of a Packet of Quantized Vorticity

“…In the case of superfluid turbulence, recent work indicates that generation of sound plays the role of 'sink' of kinetic energy [1]. Furthermore it appears that the generation of small scales occurs via creation of helical waves [2] of higher and higher wavenumbers on the quantized vortex filaments (Kelvin waves), and via creation of small vortex loops [3]. The nonlinear mechanism behind both processes is vortex reconnection, either indirectly (reconnections create cusps which relax into large amplitude Kelvin waves) or directly (reconnections create small vortex loops).…”

Dynamics of Quantized Vortices in Superfluid Helium and Rotating Bose-Einstein Condensates

“…Here L = (1/Λ) dξ is the vortex line density, where ξ is the one-dimensional coordinate along the vortex filaments and the integral is taken along all vortices in the sample volume Λ. The parameter χ 2 depends on temperature, being about 0.3 at zero temperature [34]. A simple generalization of this equation for an inhomogeneous system may be obtained by adding a diffusion term, so that we have the inhomogeneous Vinen's equaion…”

“…As the vortex filament formulation cannot represent the reconnection process itself, we assume that two vortices reconnect when they approach within the space resolution ∆ξ. The detail of this procedure is discussed in our paper [34].…”

“…The method used in the numerical simulation is similar to that of Schwarz [14] and described in detail in our paper [34]. A vortex filament is represented by a single string of points with a distance ∆ξ.…”

“…Our present main interest is to understand if a tangle of such quantized vortex filaments can still create the statistical law such as the Kolmogorov spectrum. This subsection is devoted to the description of the vortex filament formulation [14,34], followed by a discussion of the energy spectrum in the next subsection.…”