Symmetry related slow processes in parallel shear flows: Extended abstract

Parallel shear flows, like plane Couette flow or the asymptotic suction boundary layer, come with continuous symmetries of translation in the downstream and spanwise direction. Flow states that differ in their spanwise or downstream location but are otherwise identical are dynamically equivalent. In the case of travelling waves, this trivial degree of freedom can be removed by going to a frame of reference that moves with the state, thereby turning the travelling wave in the laboratory frame to a fixed point in the co-moving frame of reference. Further exploration of the symmetry suggests a general method by which the trivial translational degrees of freedom can be removed also for more complicated and dynamically active states. We will describe the method and explore its implications for the case of the asymptotic suction boundary layer. In the case of the long period oscillatory edge state, the method reveals the slow vortex dynamics underlying the periodic process, and captures the reduction in speed during the bursts. In addition, we find evidence for slow components in the spanwise direction.