Heteroclinic connections in plane Couette flow

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...

Resolvent Estimates for Plane Couette Flow

We discuss the problem of deriving estimates for the resolvent of the linear operator associated with three dimensional perturbations of plane Couette flow, and determining its dependence on the Reynolds number R. Depending on the values of the parameters involved, we derive estimates analytically. For the remaining values of the parameters, we prove that deriving estimates for the resolvent ca...