Journal of Low Temperature Physics

, Volume 171, Issue 5, pp 563-570

Open Access This content is freely available online to anyone, anywhere at any time.

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

  • T. KusumuraAffiliated withDepartment of Physics, Osaka City University Email author 
  • , H. TakeuchiAffiliated withGraduate school of Integrated Arts and Sciences, Hiroshima University
  • , M. TsubotaAffiliated withDepartment of Physics, Osaka City UniversityThe OCU Advanced Research Institute for Natural Science and Technology (OCSARINA), Osaka City University


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 uncorrelated turbulence and the correlated turbulence. We decompose the energy spectrum into two terms, namely the self-energy spectrum E self (k) made by individual vortices and the interactive energy spectrum E int (k) made by interference of two vortices. The uncorrelated turbulence is defined as turbulence with E int (k)≪E self (k), while the correlated turbulence is turbulence where E int (k) is not much smaller than E self (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 correlated turbulence.


Bose-Einstein condensate Quantum turbulence Quantum vortices