Dynamics of the Direct Vortex Cascade in 2D Quantum Turbulence

Wei-Can Yang, Wang, Xin, Tsubota, Makoto

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.

Enrico Fonda, Katepalli R. Sreenivasan, Daniel Perry Lathrop

Andrew Forrester, Gary A. Williams

The dynamics of the forward vortex cascade in 2D turbulence in a superfluid film is investigated using analytic techniques. The cascade is formed by injecting pairs with the same initial seperation (the stirring code) at a constant rate. They move to smaller scales with constant current under the action of frictional forces, finally reaching the core size separation, where they annihilate and the energy is removed by a thermal bath. On switching off the injection, the pair distribution first decays starting from the initial stirring scale, with the total vortex density decreasing linearly in time at a rate equal to the initial injection rate. As pairs at smaller scales decay, the vortex density then falls off as a power law, the same power law found in recent exact solutions of quenched 2D superfluids.

Ryu Numasato, Makoto Tsubota

Ashton S. Bradley

Two-dimensional quantum vortex motion provides a minimal system exhibiting fluid turbulence. Quantum analogues of the classical inverse energy cascade and macroscopic energy condensation processes in 2d will be presented and linked to recent experimental work.

Michikazu Kobayashi, Makoto Tsubota