Self-organization of vortex line length distribution in dilute quantum turbulence

There has been an exponential growth of interest in scale-free structure of quantum turbulence in recent years. Recent studies revealed that the vortex length distribution (VLD), meaning the size distribution of the vortices, in decaying quantum turbulence at zero temperature obeys a power law. This power law is very important because it means that there is a kind of self-similarity in quantum turbulence during the decay. Unfortunately, however, there has been no practical study that answers the important question; why can the quantum turbulence acquire power law VLD? In this paper, we first propose that the nature of quantized vortices allows us to describe the decay of quantum turbulence with a simple model without loosing physical validity. This simple model well reproduces the observed power law and suggests that the emergence of power law VLD is a consequence of two mechanisms; Richardson cascade and dynamical scaling law of vortex dynamics.