Exponential vs Algebraic Growth and Transition Prediction in Boundary Layer Flow

For applications regarding transition prediction, wing design andcontrol of boundary layers, the fundamental understanding of disturbancegrowth in the flat-plate boundary layer is an important issue. In thepresent work we investigate the energy growth of eigenmodes andnon-modal optimal disturbances. We present a set of linear governingequations for the parabolic evolution of wavelike disturbances validboth for the exponential and algebraic growth scenario. The base flow istaken as the Falkner–Skan similarity solution with favorable, adverseand zero pressure gradients. The optimization is carried out over theinitial streamwise position as well as the spanwise wave number andfrequency. The exponential growth is maximized in the sense that theenvelope of the most amplified eigenmode is calculated. In the case ofalgebraic growth, an adjoint-based optimization technique is used. Wefind that the optimal algebraic disturbance introduced at a certaindownstream position gives rise to a larger growth than for the optimaldisturbance introduced at the leading edge. The exponential andalgebraic growth is compared and a unified transition-predictionmethod based on available experimental data is suggested.