Nonlinear input-output analysis of laminar-turbulent transition for wall-bounded flows

In a linear input-output analysis framework, the most amplified instabilities are typically described by considering singular vectors of the resolvent operator of the linearized Navier-Stokes equations. In this study, we extend the methodology to take into account nonlinear triadic interactions by considering a finite number of harmonics in the frequency domain using the Harmonic Balance Method. Optimal nonlinear forcing mechanisms that lead to transition and maximize the skin-friction coefficient are identified using direct-adjoint looping. We demonstrate the framework on a zero-pressure flat-plate boundary layer by considering three-dimensional perturbations triggered by a few optimal forcing modes of finite amplitude. Depending on the frequency, spanwise wavenumber, amplitude and symmetries of the perturbation, we recover all the transition stages associated with K-type and H-type transition mechanisms, oblique waves, streaks, and their breakdown. The proposed frequency-domain framework identifies the worst-case frequency disturbances for wall-bounded laminar-turbulent transition.