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The laminar-turbulent transition in boundary-layer flows is often affected by wall imperfections, because the latter may interact with either the freestream perturbations or the oncoming boundary-layer instability modes, leading to a modification of the accumulation of the normal modes. The present paper particularly focuses on the latter mechanism in a transonic boundary layer, namely, the effect of a two-dimensional (2D) roughness element on the oncoming Tollmien-Schlichting (T-S) modes when they propagate through the region of the rapid mean-flow distortion induced by the roughness. The wave scattering is analyzed by adapting the local scattering theory developed for subsonic boundary layers (WU, X. S. and DONG, M. A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 794, 68–108 (2006)) to the transonic regime, and a transmission coefficient is introduced to characterize the effect of the roughness. In the sub-transonic regime, in which the Mach number is close to, but less than, 1, the scattering system reduces to an eigenvalue problem with the transmission coefficient being the eigenvalue; while in the super-transonic regime, in which the Mach number is slightly greater than 1, the scattering system becomes a high-dimensional group of linear equations with the transmission coefficient being solved afterward. In the large-Reynolds-number asymptotic theory, the Kármán-Guderley parameter is introduced to quantify the effect of the Mach number. A systematical parametric study is carried out, and the dependence of the transmission coefficient on the roughness shape, the frequency of the oncoming mode, and the Kármán-Guderley parameter is provided. [ABSTRACT FROM AUTHOR]

Forward-/backward-facing steps in boundary-layer flows are often seen in engineering applications, and they have potential impacts on laminar-turbulent transition through scattering of the oncoming instability modes (e.g., Tollmien-Schlichting (T-S) waves). This issue is studied in the present paper by applying a local scattering framework, which is a rather generic mathematical framework on describing the mode scattering process. In this framework, a high-Reynolds-number triple-deck formalism is employed, and a transmission coefficient, defined as the ratio of the asymptotic amplitude of the instability mode downstream of the step to that upstream, is introduced. Through the systematical study, it has been found that both the forward- and backward-facing steps have a destabilizing effect on the oncoming T-S waves in subsonic boundary layers, this effect increases with the height of the step and/or the frequency of the T-S wave, and a backward-facing step (BFS) always has a greater impact than a forward-facing step (FFS). These facts agree with most of the previous investigations. However, one numerical study (WORNER, A., RIST, U., andWAGNER, S. Humps/steps influence on stability characteristics of two-dimensional laminar boundary layer. AIAA Journal, 41, 192-197 (2003)), which was based on an ad-hoc configuration, showed an opposite impact of an FFS. Through the investigation on the specific configuration, it is revealed that the wrong conclusion was drawn by misinterpreting the numerical results. [ABSTRACT FROM AUTHOR]

The phenomena associated with the entrainment of free-stream turbulence (FST) into boundary-layer flows are relevant for a number of subjects. It has been believed that the continuous spectra of the Orr-Sommerfeld (O-S)/Squire equations describe the entrainment process, and thus they are used to specify the inlet condition in simulation of bypass transition. However, Dong and Wu (Dong, M. and Wu, X. On continuous spectra of the Orr-Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances. Journal of Fluid Mechanics, 732, 616-659 (2013)) pointed out that continuous spectra exhibit several non-physical features due to neglecting the non-parallelism. They further proposed a large-Reynolds-number asymptotic approach, and showed that the non-parallelism is a leading-order effect even for the short-wavelength disturbance, for which the response concentrates in the edge layer. In this paper, the asymptotic solution is verified numerically by studying its evolution in incompressible boundary layers. It is found that the numerical results can be accurately predicted by the asymptotic solution, implying that the latter is adequate for moderate Reynolds numbers. By introducing a series of such solutions as the inflow perturbations, the bypass transition is investigated via the direct numerical simulation (DNS). The transition processes, including the evolution of streaks, the amplification of secondary-instability modes, and the emergence of turbulent spots, agree with the experimental observations. [ABSTRACT FROM AUTHOR]