Font Size: 

Quantum turbulence is a disordered phenomenon observed in BECs and superfluids such as He3​ ​and He4​, characterized by the presence of vortices with quantized circulation which form topological defects in an inviscid and compressible fluid. While three-dimensional (3D) quantum turbulence is characterized by a direct energy cascade that follows a Kolmogorov law, two-dimensional (2D) quantum turbulence presents an inverse energy cascade as in its classical counterpart. In this work we show a sharp transition between 2D and 3D behavior as we vary either the size of the domain, or the strength of a 3D perturbation to an initial 2D flow. The evolution of the flows are studied  numerically using the Gross-Pitaevskii equation, and the direction of the cascade is determined using a new method to measure energy fluxes. To two explorations of parameter space are done by varying the aspect ratio of the domain L​z/​ L​perp in the former case, and by defining proper 2D and 3D initial conditions in the latter case. For both cases a critical transition is found, as reported before in classical turbulence. Finally, numerical resolution effects are considered and discussed.