Size Distribution of Emission Vortex Rings in Turbulence Induced by Vibrating Wire in Superfluid $$^4$$ 4 He
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Size Distribution of Emission Vortex Rings in Turbulence Induced by Vibrating Wire in Superfluid 4 He H. Yano1,2
· K. Hamazaki2 · N. Koizumi2 · K. Sato2 · K. Obara2 · O. Ishikawa2
Received: 28 August 2019 / Accepted: 28 November 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract We report the spontaneous emission of vortex rings from turbulence induced by a vibrating wire in superfluid 4 He, and investigate the statistical behavior of quantum turbulence. Using a set of vibrating wires as a turbulence generator and vortex detectors, we measured the distribution of times of flights between the generator and the detectors for emission directions parallel and perpendicular to the vibration direction of the generator wire. We find that the times exhibit a single exponential distribution for emissions in both directions, indicating temporally random emission of vortex rings with a single mean emission rate. When a limit is set on the detection diameter of the vortex rings, the detection times exhibit a double exponential distribution for the perpendicular direction for ring diameters above 10 µm, suggesting that large vortex rings reach the detector with a high rate emission at later times. In the parallel emission direction, the emission rate during an equilibrium state exhibits a power law behavior with a minimum diameter of detected vortex rings, implying that a vortex tangle generated by an oscillating object has a self-similar structure of vortex lines. Keywords Superfluid 4 He · Quantum turbulence · Vortex ring
1 Introduction The statistical behavior of turbulence has been studied for both classical and quantum fluids in recent years. The laminar–turbulent transition for a classical fluid follows a Poisson process for pipe flow, suggesting random intermittent transitions [1]. The temporal and spatial characteristics of turbulence in channel flow have been studied with regard to directed percolation theory [2]. A self-similar structure of turbulent regions
B
H. Yano [email protected]
1
Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka City University, Osaka 558-8585, Japan
2
Graduate School of Science, Osaka City University, Osaka 558-8585, Japan
123
Journal of Low Temperature Physics
appears in classical turbulence [3]. The laminar–turbulent transition also exhibits randomness in quantum turbulence generated in superfluid 4 He [4,5]. This behavior is expected to be associated with the motion of vortices in turbulence. To explore the statistics of vortex motion in turbulence, we have studied the distribution of vortex rings emitted from quantum turbulence in superfluid 4 He. Quantum turbulence generated in superfluid 4 He consists only of quantized vortices, and is therefore suitable for studying the statistical behavior of vortex motion. Oscillating objects such as a vibrating wire or a micro-sphere are typically used to generate turbulence in superfluid helium, even at very low temperatures [6–9]. To investigate the statistical beha
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