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Finite amplitude perturbation and spots growth mechanism in plane Couette flow

Olivier Dauchot 1 F. Daviaud 2, 1
1 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 : The plane Couette flow, a shear flow linearly stable for all values of the Reynolds number, is experimentally studied. A finite amplitude perturbation, local in time and space, is created in order to desstabilize the flow. For a Reynolds number R lower than R N L = 325±5, no destabilization occurs. When the Reynolds number is higher than R N L , a turbulent spot appears. A critical amplitude, A c (R), below which the spot growth and decay periods are roughly equal is measured. Above this amplitude, the spot grows up to a spatially bounded turbulent state, persistent over times long compared to the typical growth time. A power law for the asymptotic behaviour of A c (R) in the neighbourhood of R N L is made conspicuous. The spot is analyzed in terms of inside structure, spreading rates, as well as waves and velocity profiles close to the spot, in order to compare it to plane Poiseuille and boundary layer spots. The spot evolution appears to be very similar to the one observed for the plane Poiseuille spot. It is shown that the growth of the plane Couette spot can be described by the mechanism of " growth by destabilization " .
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Olivier Dauchot, F. Daviaud. Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Physics of Fluids, American Institute of Physics, 1995, 7, pp.335-343. ⟨10.1063/1.868631⟩. ⟨cea-01373989⟩

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