Laminar-turbulent transition mechanisms of separated flows using the Harmonic Balance method

Flow separation affects the performance of aerodynamic designs due to the increased drag and unsteadiness arising from the laminar to turbulence transition of the separated shear layer. To date, most numerical techniques to analyse the stability of laminar boundary layers subject to external disturbances are linear and thus fail to describe the nonlinear transitional and turbulent regimes. In this study, we apply a recently proposed computational framework (Rigas et al., JFM 2021) that solves the nonlinear Navier-Stokes equations in truncated frequency/wavenumber space using the Harmonic Balance method. Nonlinear optimisation is employed to calculate the optimal forcing-response mechanisms that maximise the skin friction coefficient of wall-bounded flows with localised separation, so-called laminar separation bubbles. We show that an efficient path to transition is initiated by the Kelvin-Helmholtz (KH) instability which then nonlinearly transfers energy to streamwise streaks and KH super-harmonic waves. The interacting multi-modal instabilities cause spanwise deformation of the mean bubble and earlier reattachment of the shear layer.