Three-Dimensional Coherent States in Plane Shear Flows

Three-dimensional steady states in plane Couette flow and traveling-wave solutions in plane Poiseuille flow are calculated for stress boundary conditions. The procedure is tied to a self-sustaining mechanism associated with the coherent structures that have been observed in turbulent shear flows. The exact states in both types of flow are remarkably similar to each other and to the coherent structures. They survive down to Reynolds numbers below the critical value for turbulence onset. These results suggest that the underlying process is generic and fundamental to both transitional and developed turbulence.