Direct numerical simulation of 2-D and 3-D instability waves in a laminar separation bubble

Abstract

are presented, where the bubble is generated by prescribing a locally decelerated free-stream velocity along a at-plate. Controlled disturbances are introduced into the ow eldupstream of the bubble by suction and blowing through the wall in order to study the linear and nonlinear stability characteristics of the ow. A number of generic cases with di erent two-dimensional (2-D) and three-dimensional (3-D) initial disturbance amplitudes are investigated, (i) a linear case, (ii) a case subject to secondary instability (strong ampli cation of 3-D disturbances by resonance with a large amplitude 2-D wave), (iii) a 3-D nonlinear case (interaction of two oblique waves), and (iv) a nonlinear case combining the interaction of two oblique waves with a 2-D wave. Good quantitative agreement of the numerical results with (local) linear stability theory is observed throughout case (i) and for the initial disturbance development of the priming waves in the other cases despite the nonparallel base ow. For the nonlinear disturbance development, however, unexpected results are obtained: Secondary instability is hard to distinguish from primary instability and apparently breaks down as soon as the priming 2-D disturbances saturate. However, the nonlinear mechanism identi ed in cases (iii) and (iv), is obviously much more likely to produce large amplitude 3-D disturbances necessary for the generation of a transitional laminar separation bubble. The mechanism leads to a nonlinearly saturated regime with reasonably turbulent mean- ow characteristics as well as longitudinal vortices in the reattachment zone. 2.