Size Distribution of Emission Vortex Rings in Turbulence Induced by Vibrating Wire in Superfluid $$^4$$He

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 $$\upmu \hbox {m}$$ , 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.