Nonlinear stages of transition and breakdown to turbulence

This chapter provides an overview of the nonlinear stages of laminar-turbulent transition in high-speed boundary-layers, with a particular focus on direct numerical simulations (DNS) that capture all stages of the transition process. A brief outline of the technical motivation and challenges is provided, followed by a description of a well-tested simulation strategy used to investigate both linear and nonlinear transition stages. Controlled and natural transition scenarios are discussed in detail, including various techniques used to introduce disturbance waves into the computational domain. Emphasis is placed on nonlinear mechanisms relevant to transition. The chapter discusses both traveling-wave and crossflow-dominated transition scenarios, illustrating various nonlinear mechanisms through numerical investigations for canonical geometries and flow conditions. The discussion includes considerations of computational domain design, grid resolution, and comparisons between controlled and natural transition simulations. Where available, numerical results are compared to experimental measurements.