Finite-Amplitude Perturbation in Plane Couette Flow
Résumé
A finite-amplitude perturbation, local in time and space, is created to destabilize a plane Couette flow, a shear flow asymptotically linearly stable for all values of the Reynolds number. When this perturbation leads to a turbulent spot, its survival depends on the amplitude of perturbation. A critical amplitude Ac (R) is defined and measured. Below this amplitude, the spot relaxes after a growth period, while above it the spot grows up to a spatially bounded turbulent state, persistent over times long compared to the typical growth time. The results show a critical behaviour of Ac (R) in the neighbourhood of RNL = 325 ± 5. Below RNL no destabilization occurs, whatever the amplitude is. These results shed light on the discrepancies previously observed between the measures of critical Reynolds numbers.