Nonlinear solutions for wall-bounded transition in the frequency domain

In a linear 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. Two approaches will be compared: a global approach considering the full Jacobian of the problem and an efficient spatial marching technique based on the One-Way Navier-Stokes (OWNS) equations, which substantially reduces the computational cost. We demonstrate the framework on a Blasius boundary layer by considering three-dimensional spanwise-periodic perturbations triggered by a few optimal forcing modes of finite amplitude.