Parameterization of travelling waves in plane Poiseuille flow

The first finite-dimensional parameterization of a subset of the phase space of the Navier–Stokes equations is presented. Travelling waves in two-dimensional plane Poiseuille flow are numerically shown to approximate maximum-entropy configurations. In a coordinate system moving with the phase velocity, the enclosed body of the flow exhibits a hyperbolic sinusoidal relationship between the vorticity and stream function. The phase velocity and two-amplitude parameters describe the stable manifold on the slow viscous time scale. This original parameterization provides a valuable visualization of this subset of the phase space of the Navier–Stokes equations. These new results provide physical insight into an important intermediate stage in the instability process of plane Poiseuille flow.