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

TL;DR

This paper explores how quantum turbulence transitions from two-dimensional to three-dimensional behavior by varying system height, revealing the roles of Kelvin waves and energy cascades in this dimensional crossover.

Contribution

It provides a systematic analysis of the dimensional transition in quantum turbulence, highlighting the role of Kelvin waves and identifying the critical scales for the transition.

Findings

Distinct vortex behaviors in 2D and 3D turbulence

Kelvin waves mediate energy transfer and dissipation

Transition characterized by changes in decay rates and vortex correlations

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.