Growth of boundary-layer streaks due to free-stream turbulence

Abstract

The growth of laminar boundary-layer streaks caused by free-stream turbulence encountering a flat plate in zero-pressure-gradient conditions is investigated experimentally in a wind tunnel and numerically by solving the unsteady boundary-region equations. A comparative discussion amongst the most relevant theoretical frameworks, such as the Goldstein theory, the Taylor–Stewartson theory, the optimal-growth theory and the Orr-Sommerfeld theory, is first presented and parallels and complimentary aspects of the theories are pointed out to justify the use of the Goldstein theory in our study. The statistical properties of the positive and negative fluctuations of the laminar streaks are discussed, showing how the total time average of the boundary-layer fluctuations masks the true character of the disturbance flow and revealing that the maximum values and the root-mean-square of positive and negative fluctuations grow downstream at the same rate. The downstream growth rate of the low-frequency disturbances and the decay rate of the high-frequency disturbances are also computed for the first time. The numerical solutions of the unsteady boundary-region equations are compared successfully with the streak profiles measured in the wind tunnel and with direct numerical simulation results available in the literature.