Eulerian and Lagrangian secondorder statistics of superfluid ^{4}He grid turbulence
Abstract
We use particletracking velocimetry to study Eulerian and Lagrangian secondorder statistics of superfluid ^{4}He grid turbulence. The Eulerian energy spectra at scales larger than the mean distance between quantum vortex lines behave classically with close to Kolmogorov1941 scaling and are almost isotropic. The Lagrangian secondorder structure functions and frequency power spectra, measured at scales comparable with the intervortex distance, demonstrate a sharp transition from nearly classical behavior to a regime dominated by the motion of quantum vortex lines. Employing the homogeneity of the flow, we verify a set of relations that connect various secondorder statistical objects that stress different aspects of turbulent behavior, allowing a multifaceted analysis. We use the twoway bridge relations between Eulerian energy spectra and secondorder structure functions to reconstruct the energy spectrum from the known secondorder velocity structure function and vice versa. The Lagrangian frequency spectrum reconstructed from the measured Eulerian spectrum using the EulerianLagrangian bridge differs from the measured Lagrangian spectrum in the quasiclassical range, which calls for further investigation.
 Publication:

Physical Review B
 Pub Date:
 April 2021
 DOI:
 10.1103/PhysRevB.103.144506
 arXiv:
 arXiv:2012.05663
 Bibcode:
 2021PhRvB.103n4506T
 Keywords:

 Condensed Matter  Other Condensed Matter;
 Physics  Fluid Dynamics
 EPrint:
 15 pages, 8 figures