Quantum Turbulence Across Dimensions: Crossover from two- to three-dimension

Abstract: We investigate the dynamic transition of quantum turbulence (QT) in a confined potential field as the system evolves from purely two-dimensional (2D) to quasi-two-dimensional, and ultimately to three-dimensional (3D), by fixing the lateral dimensions of the trapping box while varying its height. In the 2DQT, distinct Onsager vortex cluster formation and inverse energy cascade are observed, while 3DQT exhibits a direct energy cascade consistent with the Vinen turbulence decay rate, which display striking differences. By systematically altering the system height, we explore how dimensionality drives the differentiation of turbulence types and find that this transition is closely related to the excitation of Kelvin waves. Kelvin waves not only introduce additional dissipation mechanisms but also serve as mediators for direct energy transfer across scales. When the wavelength of the permitted Kelvin waves exceeds the critical size of vortex clusters, turbulence begins transitioning to 3D type, culminating in fully developed 3DQT at the characteristic scale. In the transitional region, we observe continuous variations in the decay rate and vortex cluster correlation functions.