Exact Coherent State with Travelling Hairpin Vortex in Plane Couette Flow

A new type of travelling wave solution is obtained in plane Couette flow. The solution appears via a Hopf bifurcattion from the so-called stationary hairpin vortex state found recently by [1] and [2]. The most striking feature of the solution is an anti-symmetric mean flow profile. The fluctuating flow patterns propagate in the streamwise direction with the phase velocity being zero at its onset and increasing gradually as the Reynolds number is increased.