Vortex Emission from Quantum Turbulence Generated by Vibrating Wire in Superfluid ${}^4\text{He}$

To investigate the formation of quantum turbulence in superfluid ${}^4\text{He}$, we have studied the vortex emission from a turbulence region generated by a vibrating wire. The time of flight of vortex rings emitted from a generator to a detector exhibits a single exponential distribution, suggesting that vortex detection is a Poisson process. This means that the detector observes vortex rings at irregular intervals with a mean interval time. Therefore, the single exponential distribution suggests a constant emission rate of vortex rings during turbulence generation, which is proportional to the mean detection rate. By setting a limit on the diameter of detected vortex rings, we find that the emission rate exhibits a power law relationship with the ring diameter. Since the diameter of a vortex ring is related to the vortex line spacing within turbulence when reconnection occurs, the distribution of vortex line spacings is considered to be reflected in the size distribution of the emission rate. Therefore, the power law dependence of the emission rate suggests that the vortex lines within turbulence have a self-similar fractal structure.