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
