Supercritical transition to turbulence in an inertially-driven von Karman closed flow

TL;DR

This study investigates the transition to turbulence in an inertially-driven von Karman flow, identifying critical Reynolds numbers and characterizing the supercritical nature of the transition through spectral and global measurements.

Contribution

It provides new insights into the supercritical transition to turbulence in a closed flow, highlighting the role of azimuthal shear-layer destabilization and energy fluctuation dynamics.

Findings

Transition driven by Kelvin-Helmholtz instability with wave phenomena.

Identification of critical Reynolds number Rec and crossover Ret.

Turbulent dissipation reaches a plateau consistent with Kolmogorov turbulence.

Abstract

We study the transition from laminar flow to fully developed turbulence for an inertially-driven von Karman flow between two counter-rotating large impellers fitted with curved blades over a wide range of Reynolds number (100 - 1 000 000). The transition is driven by the destabilisation of the azimuthal shear-layer, i.e., Kelvin-Helmholtz instability which exhibits travelling/drifting waves, modulated travelling waves and chaos below the emergence of a turbulent spectrum. A local quantity -the energy of the velocity fluctuations at a given point- and a global quantity -the applied torque- are used to monitor the dynamics. The local quantity defines a critical Reynolds number Rec for the onset of time-dependence in the flow, and an upper threshold/crossover Ret for the saturation of the energy cascade. The dimensionless drag coefficient, i.e., the turbulent dissipation, reaches a plateau above this finite Ret, as expected for a "Kolmogorov"-like turbulence for Re -> infinity. Our observations suggest that the transition to turbulence in this closed flow is globally supercritical: the energy of the velocity fluctuations can be considered as an order parameter characterizing the dynamics from the first laminar time-dependence up to the fully developed turbulence. Spectral analysis in temporal domain moreover reveals that almost all of the fluctuations energy is stored in time-scales one or two orders of magnitude slower than the time-scale based on impeller frequency.