Origin of separation-independent excess kurtosis in longitudinal velocity increments

Identify the physical mechanism responsible for the observed separation-independent excess kurtosis in the longitudinal velocity-increment distribution PDF(Δv^L) in turbulent two-dimensional atomic Bose-Einstein condensates.

Background

The experiments and dissipative Gross-Pitaevskii simulations show non-Gaussian, fat-tailed velocity-increment distributions consistent with intermittency corrections, with transverse excess kurtosis increasing at smaller separations. However, both experiment and numerics show an unexpected feature: the longitudinal excess kurtosis remains approximately independent of separation.

Understanding this behavior is important for interpreting intermittency and anisotropy in quantum turbulence and for connecting PDF-based diagnostics with structure-function scaling in compressible superfluids.

References

Although our observations demonstrate Kolmogorov scaling behavior, our study leaves a range of open questions. A second question is why---both in experiment and numerics---does ${\rm PDF}(\Delta vL)$ have an excess kurtosis that is independent of separation?

— Kolmogorov turbulence in atomic Bose-Einstein condensates (2408.04715 - Zhao et al., 8 Aug 2024) in Discussion and outlook (first paragraph)