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

Florent Ravelet (1, 2) , Arnaud Chiffaudel (1) , François Daviaud (1)

1 SPEC - UMR3680 - Service de physique de l'état condensé
2 AHD - Laboratory for Aero and Hydrodynamics

We study the transition from basic state to fully developed turbulence for an inertially-driven von Karman flow between two counter-rotating large impellers fitted with curved blades. The laminar basic flow is very similar to the flow between smooth disks in an effective aspect ratio. The transition to turbulence in this closed flow is globally supercritical and is driven by the destabilisation of the azimuthal shear-layer, i.e. Kelvin--Helmholtz instability. Quasi-periodicity and chaos precedes the emergence of turbulent spectra. The energy of the velocity fluctuations can be used as an order parameter to characterize the transition. This quantity defines a critical Reynolds number Re_c for the appearance of time-dependence in the flow, and an upper threshold Re_t for the saturation of the instability cascade which can be viewed as a threshold for developed turbulence. The turbulent dissipation measured as a dimensionless drag coefficient reaches a plateau past this finite value Re_t, as expected for a "Kolmogorov" turbulence for infinite Re. The spectral analysis in temporal domain 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. The transformation of the time-spectrum from a peak-frequency spectrum to a continuous spectrum is described and discussed.

Mots clés: transition to turbulence; inertial stirring; von karman swirling flow

Domaines: Dynamique des Fluides [physics.flu-dyn]

Florent Ravelet, Arnaud Chiffaudel, François Daviaud. Supercritical transition to turbulence in an inertially-driven von Karman closed flow. 2006. ⟨hal-00118719v1⟩