Effects of phase difference between instability modes on boundary-layer transition

Phase effect on the modal interaction of flow instabilities is investigated for laminar-to-turbulent transition in a flat-plate boundary-layer flow. Primary and secondary three-dimensional (3-D) oblique waves at various initial phase differences between these two instability modes. Three numerical methods are used systematic approach entire process, i.e. before onset well into fully turbulent Floquet analysis predicts subharmonic resonance where mode locally resonates given basic composed steady laminar fundamental mode. Because limited to resonating mode, nonlinear parabolised stability equation (PSE) conducted with shifts respect The application PSE offers insights affected by difference up weakly stage transition. Large-eddy simulation (LES) complete boundary layer because becomes prohibitively expensive late modulation leads significant delay location $\Delta Re_{x, tr} \simeq 4\times 10^5$ as predicted current LES. Effects spatial evolution shape further investigated. mechanism discussed, based results relevant literature data.