Finite-Amplitude Perturbation in Plane Couette Flow

Olivier Dauchot 1 François Daviaud 2, 1
2 SPHYNX - Systèmes Physiques Hors-équilibre, hYdrodynamique, éNergie et compleXes
SPEC - UMR3680 - Service de physique de l'état condensé, IRAMIS - Institut Rayonnement Matière de Saclay
Abstract : 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.
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Olivier Dauchot, François Daviaud. Finite-Amplitude Perturbation in Plane Couette Flow. Europhys. Letters, 1994. ⟨cea-01378687⟩

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