I have worked on the coherent structures of the 3D Navier-Stokes equations for incompressible flow that arise through saddle-node bifurcations. They come in pairs with an upper branch and a lower branch. We study the steady state solutions and the time evolution of the perturbed solutions in phase space to capture the characteristics of turbulent shear flows and understand the nature of transition to turbulence.


Exact Coherent Structures in Turbulent Shear Flows

Lower Branch Asymptotic Theory

Lower Branch Unstable Manifold

Flow Motions



Fabian WaleffeJohn F. GibsonPredrag CvitanovićDivakar Viswanath

ChannelFlow

ARPACK - Arnoldi Package

FFTW library