Existence and direction of an inertial-range energy cascade with Kolmogorov scaling in BECs

Determine whether atomic Bose-Einstein condensates exhibit an inertial range of length scales in which kinetic energy cascades in accordance with Kolmogorov scaling, and ascertain whether the cascade is direct (from large to small scales) or inverse (from small to large scales).

Background

The paper highlights that, despite mature understanding in classical fluids, quantum turbulence remains less understood. A central issue is whether an inertial range exists in Bose-Einstein condensates (BECs) where Kolmogorov scaling holds and, if so, whether the energy cascade proceeds directly (as in 3D classical fluids) or inversely (as in 2D classical fluids).

This question is motivated by differences between classical 2D turbulence, where enstrophy conservation leads to inverse energy cascades, and 2D quantum fluids, where quantized vortices and their non-conservation complicate expectations. The authors develop a particle image velocimetry technique to access velocity structure functions, providing tools to address this open question.

References

While the understanding of classical turbulence has matured in the past century, that of quantum systems has many open questions. For example, in BECs, does there exist a range of length scales---the inertial scale---in which kinetic energy cascades from large to small scale (direct,'' as in 3D classical fluids) or from small scale to large (inverse,'' as for 2D classical fluids) in accordance with a Kolmogorov scaling law?

— Kolmogorov turbulence in atomic Bose-Einstein condensates (2408.04715 - Zhao et al., 8 Aug 2024) in Introduction (opening paragraphs)