Minimal-energy perturbations rapidly approaching the edge state in Couette flow

Nonlinear optimal perturbations in a Couette flow: bursting and transition

Resolvent Estimates for 2 Dimensional Perturbations of Plane Couette Flow *

We present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing perturbations of the Couette flow. We prove estimates on the norm of the resolvent of this operator showing this norm to be proportional to the Reynolds number R for a region of the complex plane. Numerical approximations indicate that the same dependence is v...

Geometry of state space in plane Couette flow

A large conceptual gap separates the theory of low-dimensional chaotic dynamics from the infinite-dimensional nonlinear dynamics of turbulence. Recent advances in experimental imaging, computational methods, and dynamical systems theory suggest a way to bridge this gap in our understanding of turbulence. Recent discoveries show that recurrent coherent structures observed in wall-bounded shear f...

Nonequilibrium velocity fluctuations and energy amplification in planar Couette flow.

In this paper we investigate intrinsic thermally excited nonequilibrium velocity fluctuations in laminar planar Couette flow. For this purpose we have complemented the solution of the stochastic Orr-Sommerfeld equation for the intensity of the fluctuations of the wall-normal velocity, presented in a previous publication, with a solution of the stochastic Squire equation for the intensity of the...

1 Geometry of state space in plane Couette flow

A large conceptual gap separates the theory of low-dimensional chaotic dynamics from the infinite-dimensional nonlinear dynamics of turbulence. Recent advances in experimental imaging, computational methods, and dynamical systems theory suggest a way to bridge this gap in our understanding of turbulence. Recent discoveries show that recurrent coherent structures observed in wall-bounded shear f...