Freely Decaying Saffman Turbulence Experimentally Generated by Magnetic Stirrers

TL;DR

This study experimentally investigates the decay of homogeneous isotropic turbulence generated by magnetic stirrers, providing evidence supporting Saffman's model and revealing the relationship between the Saffman invariant and the large-scale energy spectrum.

Contribution

First experimental validation of the connection between the Saffman invariant and the $k^{2}$ energy spectrum in freely decaying turbulence.

Findings

Energy spectrum scales as $k^{2}$ at large scales

Saffman invariant is conserved during early decay

Decay behavior aligns with Saffman's model in large containers

Abstract

We investigate experimentally the decay of three-dimensional hydrodynamic turbulence, initially generated by the erratic motions of centimeter-size magnetic stirrers in a closed container. Such zero-mean-flow homogeneous isotropic turbulence is well suited to test Saffman's model and Batchelor's model of freely decaying turbulence. Here, we report a consistent set of experimental measurements (temporal decay of the turbulent kinetic energy, of the energy dissipation rate, and growth of the integral scale) strongly supporting the Saffman model. We also measure the conservation of the Saffman invariant at early times of the decay and show that the energy spectrum scales as $k^{2}$ at large scales and keeps its self-similar shape during the decay. This letter thus presents the first experimental evidence of the validity of the connection between the Saffman invariant and the $k^{2}$-energy spectrum of the large scales. The final decay regime closely corresponds to Saffman's model when the container size is sufficiently large.