77 research outputs found
Diffusion of an Inhomogeneous Vortex Tangle
The spatial diffusion of an inhomogeneous vortex tangle is studied
numerically with the vortex filament model. A localized initial tangle is
prepared by applying a counterflow, and the tangle is allowed to diffuse freely
after the counterflow is turned off. Comparison with the solution of a
generalization of the Vinen equation that takes diffusion into account leads to
a very small diffusion constant, as expected from simple theoretical
considerations. The relevance of this result to recent experiments on the
generation and decay of superfluid turbulence at very low temperatures is
discussed.Comment: 2 pages, 2 figure
Derivation of the transverse force on a moving vortex in a superfluid
We describe an exact derivation of the total nondissipative transverse force
acting on a quantized vortex moving in a uniform background. The derivation is
valid for neutral boson or fermion superfluids, provided the order parameter is
a complex scalar quantity. The force is determined by the one-particle density
matrix far away from the vortex core, and is found to be the Magnus force
proportional to the superfluid density.Comment: Latex, 6 page
The approach to vortex reconnection
We present numerical solutions of the Gross--Pitaevskii equation
corresponding to reconnecting vortex lines. We determine the separation of
vortices as a function of time during the approach to reconnection, and study
the formation of pyramidal vortex structures. Results are compared with
analytical work and numerical studies based on the vortex filament method.Comment: 11 pages, 9 figure
Decay of Counterflow Quantum Turbulence in Superfluid ^4He
We have simulated the decay of thermal counterflow quantum turbulence from a
statistically steady state at T=1.9[K], with the assumption that the normal
fluid is at rest during the decay. The results are consistent with the
predictions of the Vinen equation (in essence the vortex line density (VLD)
decays as t^{-1}). For the statistically steady state, we determine the
parameter c_2, which connects the curvature of the vortex lines and the mean
separation of vortices. A formula connecting the parameter \chi_2 of the Vinen
equation with c_2 is shown to agree with the results of the simulations.
Disagreement with experiment is discussed.Comment: 7 pages, 7 figure
Decay of quantised vorticity by sound emission
It is thought that in a quantum fluid sound generation is the ultimate sink
of turbulent kinetic energy in the absence of any other dissipation mechanism
near absolute zero. We show that a suitably trapped Bose-Einstein condensate
provides a model system to study the sound emitted by accelerating vortices in
a controlled way.Comment: 6 pages, 3 figure
Tree method for quantum vortex dynamics
We present a numerical method to compute the evolution of vortex filaments in
superfluid helium. The method is based on a tree algorithm which considerably
speeds up the calculation of Biot-Savart integrals. We show that the
computational cost scales as Nlog{(N) rather than N squared, where is the
number of discretization points. We test the method and its properties for a
variety of vortex configurations, ranging from simple vortex rings to a
counterflow vortex tangle, and compare results against the Local Induction
Approximation and the exact Biot-Savart law.Comment: 12 pages, 10 figure
Instability of vortex array and transitions to turbulent states in rotating helium II
We consider superfluid helium inside a container which rotates at constant
angular velocity and investigate numerically the stability of the array of
quantized vortices in the presence of an imposed axial counterflow. This
problem was studied experimentally by Swanson {\it et al.}, who reported
evidence of instabilities at increasing axial flow but were not able to explain
their nature. We find that Kelvin waves on individual vortices become unstable
and grow in amplitude, until the amplitude of the waves becomes large enough
that vortex reconnections take place and the vortex array is destabilized. The
eventual nonlinear saturation of the instability consists of a turbulent tangle
of quantized vortices which is strongly polarized. The computed results compare
well with the experiments. Finally we suggest a theoretical explanation for the
second instability which was observed at higher values of the axial flow
Modeling Kelvin wave cascades in superfluid helium
We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) and it is shown to possess the same scalings and the essential behaviour as the full Biot-Savart model, being much simpler than the later and, therefore, more amenable to theoretical and numerical investigations. The Truncated-LIA model supports six-wave interactions and dual cascades, which are clearly demonstrated via the direct numerical simulation of this model in the present paper. In particular, our simulations confirm presence of the weak turbulence regime and the theoretically predicted spectra for the direct energy cascade and the inverse wave action cascade. The second type of model we study, the Differential Approximation Model (DAM), takes a further drastic simplification by assuming locality of interactions in k-space via using a differential closure that preserves the main scalings of the Kelvin wave dynamics. DAMs are even more amenable to study and they form a useful tool by providing simple analytical solutions in the cases when extra physical effects are present, e.g. forcing by reconnections, friction dissipation and phonon radiation. We study these models numerically and test their theoretical predictions, in particular the formation of the stationary spectra, and closeness of numerics for the higher-order DAM to the analytical predictions for the lower-order DAM
Symmetries and Interaction coefficients of Kelvin waves
We considered symmetry restriction on the interaction coefficients of Kelvin
waves and demonstrated that linear in small wave vector asymptotic is not
forbidden, as one can expect by naive reasoning.Comment: 4 pages, submitted to J. of Low Temp. Phy
Identification of Kelvin waves: numerical challenges
Kelvin waves are expected to play an essential role in the energy dissipation
for quantized vortices. However, the identification of these helical
distortions is not straightforward, especially in case of vortex tangle. Here
we review several numerical methods that have been used to identify Kelvin
waves within the vortex filament model. We test their validity using several
examples and estimate whether these methods are accurate enough to verify the
correct Kelvin spectrum. We also illustrate how the correlation dimension is
related to different Kelvin spectra and remind that the 3D energy spectrum E(k)
takes the form 1/k in the high-k region, even in the presence of Kelvin waves.Comment: 6 pages, 5 figures. The final publication is available at
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