Flexible fiber reveals the two-point statistical properties of turbulence

TL;DR

This paper introduces a phenomenological theory and numerical validation showing that a flexible fiber in turbulence can serve as a tool to measure two-point statistical properties of turbulent flows, including energy flux and structure function scaling.

Contribution

The study presents a new theoretical framework and numerical validation demonstrating how flexible fibers can be used to measure turbulence statistics, revealing a regime where fibers are slaved to turbulent fluctuations.

Findings

Identification of two distinct flapping regimes in turbulent flow.

Validation of the theory through Direct Numerical Simulations.

Proposal of a new method to measure turbulence statistics using fibers.

Abstract

We study the dynamics of a flexible fiber freely moving in a three-dimensional fully-developed turbulent field and present a phenomenological theory to describe the interaction between the fiber elasticity and the turbulent flow. This theory leads to the identification of two distinct regimes of flapping, which we validate against Direct Numerical Simulations (DNS) fully resolving the fiber dynamics. The main result of our analysis is the identification of a flapping regime where the fiber, despite its elasticity, is slaved to the turbulent fluctuations. In this regime the fiber can be used to measure two-point statistical observables of turbulence, including scaling exponents of velocity structure functions, the sign of the energy cascade and the energy flux of turbulence, as well as the characteristic times of the eddies within the inertial range of scales. Our results are expected to have a deep impact on the experimental turbulence research as a new way, accurate and efficient, to measure two-point, and more generally multi-point, statistics of turbulence.