Mirror-symmetric exact coherent states in plane Poiseuille flow

Two new families of exact coherent states are found in plane Poiseuille flow. They are obtained from the stationary and the travelling-wave mirror-symmetric solutions in plane Couette flow by a homotopy continuation. They are characterized by the mirror symmetry inherited from those continued solutions in plane Couette flow. The first family arises from a saddle-node bifurcation and the second family bifurcates by breaking the top-bottom symmetry of the first family. We find that both families exist below the minimum saddle-node-point Reynolds number known to date Waleffe, Phys. Fluids, vol. 15, 2003, pp. 1517-1534).