Finite amplitude perturbation and spots growth mechanism in plane Couette flow

Abstract

The plane Couette flow, a shear flow linearly stable for all values of the Reynolds number, R, is experimentally studied. A finite amplitude perturbation, local in both time and space, is created in order to destabilize the flow. A critical amplitude, Ac(R), below which disturbances are not sustained is measured. Above this amplitude, a turbulent spot grows to a spatially-bounded turbulent state, persistent over times long compared to its typical growth time. The critical amplitude, Ac(R), is seen to diverge when R approaches the nonlinear critical Reynolds number RNL=325±5 from above. Below this value of the Reynolds number, no destabilization occurs with this kind of perturbation, whatever its amplitude. The divergent behavior on approaching RNL is characterized in terms of a power law. This result sheds light on the discrepancies previously observed between critical Reynolds number measurements. The spot is then analyzed in terms of its 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 that 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.’’