New exact coherent states in channel flow

Three spatially periodic travelling wave exact coherent states are presented for channel flow. Two of the flows, which are asymmetric with respect to the channel centreplane, are derived by homotopy from solutions for channel flow subject to a spanwise rotation investigated by [1]. The third flow satisfies a half-turn rotational symmetry about a point on the channel centreplane, and turns out to be the flow from which one of the asymmetric flows bifurcates in a symmetry breaking bifurcation. One of the asymmetric flows is found to substantially reduce the value of the lowest Reynolds number at which exact solutions are known to exist down to 665.