Emergence of Invariant Solutions underlying Oblique Turbulent-Laminar Stripes in Plane Couette Flow

In subcritical shear flows laminar and turbulent regions may coexist giving rise to spatial patterns. A specific example pattern are oblique stripes of alternating turbulent and laminar bands. Understanding the large-scale periodicity of turbulent-laminar stripes and its oblique orientation to the base flow remains an open problem.
We present an invariant solution underlying the turbulent-laminar stripe pattern in plane Couette flow. The new solution emerges from the well-known Nagata-type solution of wavy velocity streaks in a sequence of symmetry-breaking bifurcations. The bifurcations shift the spatial phase relation between invariant velocity streaks and induce oblique amplitude modulations forming the pattern. Existence and emergence of this invariant solution opens up new possibilities to understand the oblique stripe pattern within a dynamical systems framework.