Turbulent-laminar Patterns in Plane Couette Flow
The greatest mystery in fluid dynamics is probably transition to turbulence. The simplest shear flow, plane Couette flow -- the flow between parallel plates moving at different velocities -- is linearly stable for all Reynolds numbers, but nevertheless undergoes sudden transition to 3D turbulence at Re near 325. At just these Reynolds numbers, it was recently discovered experimentally at CEA-Saclay that the flow takes the form of a steady and regular pattern of alternating wide turbulent and laminar bands, tilted at an angle with respect to the streamwise direction.
We have been able to reproduce these remarkable flows in numerical simulations of the Navier-Stokes equations. Simulations display a rich variety of variants of these patterns, including spatio-temporal intermittency, branching and travelling states, and localized states analogous to spots. Quantitative analysis of the Reynolds-averaged equations reveals that both the mean flow and the turbulent force are centrosymmetric and can be described by only three trigonometric functions, leading to a model of 6 ODEs. We find that the transition is best described as a bifurcation in the probability distribution function of the power spectrum.
Laurette S. Tuckerman, École Supérieure de Physique et de Chimie Industrielles, France