Local scattering theory for transition prediction in boundary-layer flows

With the development of aerospace technology, higher and higher accuracy for transition prediction is required in engineering. Because the traditional transition prediction approaches based on smooth boundary layers do not satisfy the accuracy requirement when surface imperfections, e.g. roughness, steps and gaps, are present, it is of practical importance to develop a new model to predict transition with the impacts of surface imperfections being taken into account. For natural-route transition triggered by the accumulation of the boundary-layer normal modes, the transition onset may be affected through the local receptivity and linear-mode local scattering regimes, therefore, a new transition-prediction model can be developed by adding the quantitative impacts of the two regimes to the traditional e^N transition-prediction approach. In order to quantify these impacts, the author and his collaborators developed a generic theoretical framework, the local scattering theory. Through combination of large-Reynolds-number asymptotic and finite-Reynolds-number theories, this framework describes the two system characteristic parameters, i.e. the local receptivity and transmission coefficients, which are used to predict the variation of the transition onset influenced by the surface imperfections. The present paper reviews the progress of the local scattering theory in the recent years, and highlights the applications of the theory in the viscous and inviscid instability regimes in two-dimensional laminar boundary layers.