Investigations of time-growing instabilities in laminar separation bubbles

The occurrence of temporally growing unstable disturbances is investigated based on eigenvalues with zero group velocity from linear stability theory (LST) and compared with observations of upstream travelling disturbances obtained in a two-dimensional direct numerical simulation (DNS) of an unsteady laminar separation bubble. Numerical solutions of the Orr–Sommerfeld equation using analytically constructed base-flow velocity profiles modelled by a modified hyperbolic tangent function help to identify the role of parameters, such as maximum reverse flow, wall distance and intensity of the shear layer, as well as Reynolds number on the possibility that a true time-growing instability occurs. Then, the viscous or inviscid nature of the solutions found is classified on the basis of their eigenfunctions. For large wall distances two unstable modes are found. Apart from a low-frequency motion of the bubble the DNS exhibit high-frequency oscillations which periodically appear and disappear. Part of these disturbances travel upstream and amplify with respect to time. Their initial occurrence and their frequency are in excellent agreement with the results of the parameter study based on LST and a closer examination of the disturbances yields insight into their spatial structure.