Propelled micro-probes in turbulence

TL;DR

This study uses direct numerical simulations to analyze how self-propelled probes measure turbulence, revealing how their motion affects statistical properties of velocity and scalar fields, and illustrating the transition from Lagrangian to Eulerian perspectives.

Contribution

It introduces a detailed analysis of self-propelled probes in turbulence, highlighting the effects of propulsion speed on statistical measurements and the Lagrangian-Eulerian transition.

Findings

Acceleration statistics follow predictable trends with propulsion speed.

Scalar fluctuations exhibit similar trends to velocity statistics.

Lagrangian-to-Eulerian transition depends on propulsion velocity.

Abstract

The temporal statistics of incompressible fluid velocity and passive scalar fields in developed turbulent conditions is investigated by means of direct numerical simulations along the trajectories of self-propelled point-like probes drifting in a flow. Such probes are characterised by a propulsion velocity which is fixed in intensity and direction; however, like vessels in a flow they are continuously deviated by their intended course as the result of local sweeping of the fluid flow. The recorded time-series by these moving probes represent the simplest realisation of transect measurements in a fluid flow environment. We investigate the non trivial combination of Lagrangian and Eulerian statistical properties displayed by the transect time-series. We show that, as a result of the homogeneity and isotropy of the flow, the single-point acceleration statistics of the probes follows a predictable trend at varying the propulsion speed, a feature that is also present in the scalar time-derivative fluctuations. Further, by focusing on two-time statistics we characterize how the Lagrangian-to-Eulerian transition occurs at increasing the propulsion velocity. The analysis of intermittency of temporal increments highlights in a striking way the opposite trends displayed by the fluid velocity and passive scalars.