Chaotic quantized vortices and hydrodynamic processes in superfluid helium

Nemirovskii, Sergey K.; Fiszdon, W.

doi:10.1103/revmodphys.67.37

Cited by 138 publications

(142 citation statements)

References 135 publications

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“…Since the characteristic length k −1 2 ∼ 5 × 10 −5 cm for sound radiation is enough smaller than our numerical space resolution ∆ξ, our cut-off procedure may be considered to be used for the effect of the sound radiation, assuming the cascade process continues self-similarly also from ∆ξ tok −1 2 . We have to comment on how the nonlocal interaction acts on the VT. 3 In a VT, the local field is usually superior to the nonlocal field. As stated in Sec.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Dynamics of vortex tangle without mutual friction in superfluid4He

2000

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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

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Section: Conclusion and Discussionmentioning

confidence: 99%

Dynamics of vortex tangle without mutual friction in superfluid4He

2000

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“…If these tubes are narrow in cross section, then they look like strings, and if the initial conditions are such that the fluid starts off like this, then this string resemblance should persist for some period of time. There is an interesting connection between string theory and magnetohydrodynamics with narrow magnetic flux tubes, and also with vortex flux tubes in superfluid turbulence theory [45][46][47]. The observed stochastic vortex tangle in superfluid turbulence He II suggests a similar phenomenon should occur in the inviscid Burgers system.…”

Section: Possible Relationship To String Theorymentioning

confidence: 99%

The quark-gluon plasma and the stochastic interpretation of quantum mechanics

Davidson¹

2010

Physica E: Low-dimensional Systems and Nanostructures

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Quark-gluon plasmas formed in heavy ion collisions at high energies are well described by ideal classical fluid equations with nearly zero viscosity. It is believed that a similar fluid permeated the entire universe at about three microseconds after the big bang. The estimated Reynolds number for this quark-gluon plasma at 3 microseconds is approximately 10^19. The possibility that quantum mechanics may be an emergent property of a turbulent proto-fluid is tentatively explored. A simple relativistic fluid equation which is consistent with general relativity and is based on a cosmic dust model is studied. A proper time transformation transforms it into an inviscid Burgers equation. This is analyzed numerically using a spectral method. Soliton-like solutions are demonstrated for this system, and these interact with the known ergodic behavior of the fluid to yield a stochastic and chaotic system which is time reversible. Various similarities to quantum mechanics are explored.

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“…An interesting review of recent results on inhomogeneous superfluid turbulence is presented by Nemirovskii and Fiszdon. 10 …”

Section: Introductionmentioning

confidence: 99%

Simplified hydrodynamic analysis of superfluid turbulence in He II: Internal dynamics of inhomogeneous vortex tangle

Geurst

Beelen

1996

Phys. Rev. B

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The hydrodynamic theory of superfluid turbulence is presented in a new simplified form. It applies to flow situations frequently encountered in practice, in which the thermohydrodynamic environment of a superfluid turbulent tangle of quantized vortices may be considered, in a first order of approximation, as given. Flow quantities like the mass density, the entropy density, and the drift velocities of mass and elementary excitations act, accordingly, as external parameters with respect to the internal dynamics of the vortex tangle. The internal dynamics is completely specified by a kinematic equation governing the time evolution of the line-length density of the quantized vortices and a dynamic equation involving the impulse density of the vortex tangle. The derivation of these equations starts from a variational principle that is reminiscent of Hamilton's principle in classical mechanics and proceeds, in order to include dissipative effects, by using methods of the thermodynamics of irreversible processes. A new quantity called superfluid turbulent pressure is introduced which shows many properties that are familiar from the ordinary pressure in a classical fluid. Two important particular cases are considered in more detail, viz., homogeneous superfluid turbulent flow and flow situations in which the vortex tangle is in permanent internal equilibrium. When diffusion of the vortex-tangle impulse is taken into account and dispersive effects are disregarded, the dynamic equation of the vortex tangle assumes, in the case of internal equilibrium, the form of Burgers' equation with a nonlinear source term. This equation, which is new, may be considered as a natural generalization of Vinen's equation to inhomogeneous superfluid turbulence. Some exact solutions which represent uniformly propagating superfluid turbulence fronts are listed in the Appendix. ͓S0163-1829͑96͒01033-8͔

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Chaotic quantized vortices and hydrodynamic processes in superfluid helium

Cited by 138 publications

References 135 publications

Dynamics of vortex tangle without mutual friction in superfluid4He

Dynamics of vortex tangle without mutual friction in superfluid4He

The quark-gluon plasma and the stochastic interpretation of quantum mechanics

Simplified hydrodynamic analysis of superfluid turbulence in He II: Internal dynamics of inhomogeneous vortex tangle

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