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

We study the transition from laminar flow to fully developed turbulence for an inertially-driven von Kármán flow between two counter-rotating large impellers fitted with curved blades over a wide range of Reynolds number (10 − 10). 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 → ∞. 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.