Symbolic dynamics and chaos in plane Couette flow

The dynamics of transition to turbulence in plane Couette flow

In plane Couette flow, the incompressible fluid between two plane parallel walls is driven by the motion of those walls. The laminar solution, in which the streamwise velocity varies linearly in the wall-normal direction, is known to be linearly stable at all Reynolds numbers (Re). Yet, in both experiments and computations, turbulence is observed for Re & 360. In this article, we show that when...

Instability of Plane Couette Flow

The energy gradient theory has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow. In this theory, it is suggested that the transition to turbulence depends on the relative magnitudes of the energy gradient amplifying the disturbance and the viscous friction damping that disturbance. For a given flow geometry and fluid propert...

Modeling transitional plane Couette flow

The Galerkin method is used to derive a realistic model of plane Couette flow in terms of partial differential equations governing the space-time dependence of the amplitude of a few cross-stream modes. Numerical simulations show that it reproduces the globally sub-critical behavior typical of this flow. In particular, the statistics of turbulent transients at decay from turbulent to laminar fl...

Convective Instabilities in Plane Couette Flow

Stability Analysis of Perturbed Plane Couette Flow

Plane Couette ow perturbed by a spanwise oriented ribbon, similar to a con guration investigated experimentally at CEA-Saclay, is investigated numerically using a spectral-element code. 2D steady states are computed for the perturbed con guration; these di er from the unperturbed ows mainly by a region of counter-circulation surrounding the ribbon. The 2D steady ow loses stability to 3D eigenmo...