Linear and Nonlinear Analysis of Wavy-Surface-Induced Laminar Separation Bubbles

Linear global stability analysis is performed on a laminar separation bubble formed dueto surface waviness. The eigenspectrum shows a globally unstable mode, responsiblefor the three-dimensionalisation of the bubble, and a family of low-frequency globallystable modes. An adjoint sensitivity analysis shows high sensitivity of the stable modesupstream of the bubble’s reattachment point. Direct numerical simulation (DNS)alongside with a linear impulse response analysis are performed. DNS shows that, whentransition occurs due to self-excited mechanisms, low-frequency upstream propagatingwaves form inside the bubble; this is not the case in linear impulse analysis. It isconjectured that these upstream propagating waves correspond to the low-frequencystable modes in the spectrum which become active through nonlinearity when transitionoccurs.