Linear stability analysis of a three-dimensional laminar separation bubble on a finite wing

Disturbance amplification in a laminar separation bubble forming on the suction surface of a cantilevered NACA0018 wing at an angle of attack of 6 degrees and Reynolds number of 1.25 x 105 is studied using a combination of particle image velocimetry measurements and local and non-local linear stability analyses. The experimental measurements reveal the formation of largely two-dimensional velocity fluctuations leading to the formation of initially two-dimensional roll-up vortices in the separated shear layer at a nearly constant wavenumber and frequency, despite the substantial reduction in the effective angle of attack near the wing tip. The most amplified wavenumber and its growth rate are accurately predicted by linear stability theory outside of the regions of the separation bubble dominated by three-dimensional end effects, with negligible differences between local and non-local stability analyses. Near the wing root and tip, an increase in the magnitudes of spanwise velocities is observed within the laminar separation bubble, and linear stability calculations predict a relative increase in the amplification of spanwise wavenumbers with the same sign as the spanwise flow. However, the calculations show that the most amplified disturbance remains essentially two-dimensional across the entire wingspan.