Influence of Reynolds number and forcing type in a turbulent von K\'arm\'an flow

TL;DR

This study investigates how Reynolds number and forcing type influence hysteresis and multistability in turbulent von Kármán flows, revealing new states and responses through combined experimental and theoretical analysis.

Contribution

It provides new experimental insights into hysteresis, multistability, and negative responses in turbulent flows under different forcing conditions, linking these phenomena to thermodynamics of long-range systems.

Findings

Hysteresis behavior increases with Reynolds number.

Torque control reveals multiple quasi-steady states and negative differential responses.

Analogies with electrical circuits help explain multistability phenomena.

Abstract

We present a detailed study of of a global bifurcation occuring in a turbulent von K\'arm\'an swirling flow. In this system, the statistically steady states progressively display hysteretic behaviour when the Reynolds number is increased above the transition to turbulence. We examine in detail this hysteresis using asymmetric forcing conditions --- rotating the impellers at different speeds. For very high Reynolds numbers, we study the sensitivity of the hysteresis cycle --- using complementary Particle Image Velocimetry (PIV) and global mechanical measurements --- to the forcing nature, imposing either the torque or the speed of the impellers. New mean states, displaying multiple quasi-steady states and negative differential responses, are experimentally observed in torque control. A simple analogy with electrical circuits is performed to understand the link between multi-stability and negative responses. The system is compared to other, similar "bulk" systems, to understand some relevant ingredients of negative differential responses, and studied in the framework of thermodynamics of long-range interacting systems. The experimental results are eventually compared to the related problem of Rayleigh-B\'enard turbulence.