Boundary Layer Transition as Succession of Temporal and Spatial Symmetry Breaking

We show that both temporal and spatial symmetry breaking in canonical K-type transition arise as organized hydrodynamic structures rather than stochastic fluctuations. Before the skin-friction maximum, the flow is fully described by a periodic, spanwise symmetric, harmonic response to the Tollmien-Schlichting wave, forming a spatially compact coherent structure that produces hairpin packets. This fundamental harmonic response may visually resemble turbulence, but remains fully periodic and delimits the exact extent of the deterministic regime. A distinct regime change occurs after this point; a hierarchy of new (quasi-)periodic and aperiodic space-time structures emerges, followed shortly by anti-symmetric structures that develop similarly despite no anti-symmetric inputs, marking the onset of aperiodicity and spanwise asymmetry. We identify these structures as symmetry-decomposed spectral and space-time proper orthogonal modes that resolve the full progression from deterministic to broadband dynamics. The key insight is that laminar-turbulent transition can be viewed as a sequence of symmetry breaking events, each driven by energetically dominant, space-time coherent modes that gradually turn an initially harmonic flow into broadband turbulence.