Extending the reach of Lagrangian analysis in turbulence

Abstract

The hypothesis in the classical Kolmogorov picture of turbulence with perhaps the most far-reaching consequences is that of universality, the notion that small-scale turbulence dynamics are independent of the way the turbulence was generated. The assumption of universality can be evaluated by comparing measurements taken in many kinds of flows. However, up to now the range of flows that can be used to study universality from a Lagrangian viewpoint has been highly constrained, because large-scale Eulerian inhomogeneity manifests as Lagrangian non-stationarity. The recent work of Viggiano et al. (J. Fluid Mech., vol. 918, 2021, A25) significantly extends this range by showing how the dynamics along Lagrangian trajectories can be continuously renormalised using local Eulerian scales, at least in flows whose development is self-similar. They demonstrate their results on a turbulent jet, a classical flow that is well studied from the Eulerian perspective, though not in a Lagrangian sense. Their work provides an exciting roadmap for expanding the scope of Lagrangian analysis of turbulent flows.