Onset of transition in boundary layers

Abstract

AbstractLaminar‐turbulent transition in boundary layers involves a cascade of weak and strong instabilities. In the model considered here the first instability occurs with respect to two‐dimensional TS waves and causes streamwise, nearly periodic concentrations of vorticity. Linear stability analysis of this periodic flow leads to Floquet systems of equations. These systems support different classes of three‐dimensional disturbances which may initiate different routes to transition. Numerical solutions by use of accurate spectral methods reveal the spectrum of eigenmodes, growth rates and disturbance velocities. The characteristics of this secondary instability are in good agreement with results of experiments and computer simulations of transition. Non‐linear self‐interaction of the rapidly growing three‐dimensional disturbances can sustain or enhance the vital periodic accumulations of spanwise vorticity once their amplitude exceeds some threshold. This feedback loop is considered to be the key to the transition process. Owing to the broad‐band nature of secondary instability, however, the prediction of transition in practice requires additional insight into the ‘natural’ disturbance background. The sensitivity of the transition process to initial data in a broad band of frequencies and spanwise wave numbers poses new challenges for non‐linear theories and numerical simulations.