The role of large surface roughness in transition of 3D boundary layers

Surface roughness can influence significantly transition of 3D boundary layers through alteration of the base flow whereby modifying crossflow stability or even inducing new instabilities. We study the impact of a wavy-wall roughness with a large height on the 3D boundary layer represented by the Falkner-Skan-Cooke flow. The flow structure is characterized by a wall layer, the main layer, and a critical layer. First, the immediate response to the roughness is in a viscous wall layer, where the disturbance is nonlinear. This layer converts the surface displacement into a 'blowing velocity' into the main layer. The nonlinear streaming effect in the wall layer leads to a mean flow distortion. In the main layer, which occupies the bulk of the boundary layer, the flow field is decomposed into the base flow, the steady streaming and the forced perturbations. The former is described by an initial-value problem, while the latter is governed by the Rayleigh equation, the solution to which becomes singular at a position denoted as the critical level. The singularity is resolved by introducing viscous effects in the critical layer. As the regularized solution acquires much greater amplitude, the critical layer is strongly nonlinear. There are velocity jumps coupling the dynamics in the critical layer and the main layer. Numerical solutions show that nonlinearity enhances the response. The secondary instability analysis indicates that the nonlinearly saturated critical layer can support strong inviscid instability.