Energy Spectrum of the Superfluid Velocity Made by Quantized Vortices in Two-Dimensional Quantum Turbulence

We discuss the configurations of vortices in two-dimensional quantum turbulence, studying energy spectrum of superfluid velocity and correlation functions with the distance between two vortices. We apply the above method to quantum turbulence described by Gross-Pitaevskii equation in Bose-Einstein condensates. We make two-dimensional quantum turbulence from many dark solitons through the dynamical instability. A dark soliton is unstable and decays into vortices in two- and three-dimensional systems. In our work, we propose a method of discriminating between the uncorrelatedturbulence and the correlatedturbulence. We decompose the energy spectrum into two terms, namely the self-energy spectrum Eself(k) made by individual vortices and the interactive energy spectrum Eint(k) made by interference of two vortices. The uncorrelatedturbulence is defined as turbulence with Eint(k)≪Eself(k), while the correlatedturbulence is turbulence where Eint(k) is not much smaller than Eself(k). Our simulations show that in the decay of dark solitons, the vortices created consist of correlated pairs of opposite circulation vortices, leading to the correlatedturbulence.