The presence of large surface irregularities such as humps, where the height is similar to the local boundary-layer (BL) displacement thickness, introduces regions of localized strong streamwise gradients in the base flow quantities. These large gradients can significantly modify the spatial development of incoming disturbances that lead to laminar–turbulent transition in wall-bounded flows [e.g., Tollmien–Schlichting (TS) waves]. Techniques such as Parabolized Stability Equations (PSE) are not suited for BL instability analysis in such regions: their formulation assumes that streamwise variations of base flow and disturbance quantities are small, allowing a marching procedure for their resolution. On the other hand, the Adaptive Harmonic Linearized Navier–Stokes (AHLNS) equations can handle these large streamwise gradients by using a fully elliptic system of equations, similar to Linearized Navier–Stokes (LNS), Harmonic LNS (HLNS), or Direct Numerical Simulation (DNS). Moreover, in AHLNS (as in PSE), a wave-like character of the instabilities is assumed, leading to a significant reduction in the number of streamwise grid points required compared with LNS, HLNS, or DNS computations. In the present study, an efficient combination of PSE and AHLNS is used to investigate the effect of height, length, and shape of a single hump placed on a flat plate in a two-dimensional flow field at Ma∞ = 0.5 without pressure gradient. The effect of this hump on the spatial evolution of TS waves, in terms of N-factors, is presented. An expected laminar–turbulent transition onset, via the eN methodology, is also described. It is shown that the shape of the surface irregularity, together with the height and length, plays an important role for the location of laminar–turbulent transition onset in convectively unstable flows.

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The Parabolized Stability Equations (PSE), Adaptive Harmonic Linearized Navier-Stokes (AHLNS) and Harmonic Navier-Stokes (HNS) solvers are used to analyze the linear and nonlinear stability of swept-wing boundary layers under the influence of smooth wall deformations of varying size and geometry. Special attention is given to the validity of the slowly varying flow assumption of PSE via a comparison with AHLNS and HNS results. The surface deformations analyzed in this work are found to affect the development of the primary stationary crossflow instability mode as well as higher harmonics. Analysis of the locally most amplified mode reveals successive modulation of the growth rate in the vicinity of the surface deformation. This process was found to be largely governed by linear terms and driven by the base flow modification due to the deformed wall. Similarly, the base flow modification causes higher harmonics to experience a significant destabilization. This is followed by stabilization as nonlinear interactions become dominant. The PSE methodology proved capable of predicting the stability response for small wall deformations with only minor amplitude discrepancies compared to HNS results. The main difference was found to occur in the wall-normal velocity profiles of the mean flow distortion mode. The deviations of the PSE results compared to harmonic stability methods increased as the protuberance was made steeper. Moreover, the PSE framework was not able to converge for all cases nonlinearly.