Temporal & Spatial Symmetry Breaking in K-type Boundary Layer Transition

We uncover the key symmetry breaking mechanisms in time and space within deterministic K-type boundary layer transition using a suite of techniques from modal decomposition and dynamical systems. Specifically, we employ space-time proper orthogonal decomposition (STPOD), spectral POD (SPOD), and D1 symmetry decomposition to identify coherent space-time structures with distinct optimality properties. Our analysis of the early transitional regime identifies a prototypical transition scenario characterized by dynamics on a periodic limit cycle, where all early pre-turbulence mechanisms are reproducible by a varying number of modes at the fundamental frequency and its harmonics. Our investigation in the late transitional and turbulent regimes beyond the skin friction maximum reveals the emergence of periodic and non-periodic, as well as symmetric and anti-symmetric, structures. We extract modes associated with the variance and instability of the fundamental limit cycle and demonstrate that it is their phase space dynamics and streamwise locations that promote the overall flow dynamics to develop increasing degrees of chaos and, ultimately, broadband turbulence. Our findings suggest that the modes responsible for symmetry breaking are identifiable as hydrodynamic instability mechanisms around the limit cycle of the fundamental harmonic coherent structure.