Laminar flow separation over tapered wings, Part 3: A theoretical study

The final part of this three-way study focuses on linear global stability analysis of flows over tapered wings. Swept and tapered NACA 0015 wings with an aspect ratio of 4 are considered for 200 ≤ Re ≤ 400. Adjoint global modes are computed for these geometries for the first time. Regions of maximum flow receptivity and sensitivity (the wavemaker) are identified for informing flow control. The wavemaker of the leading unstable mode is in the wake inside the laminar separation bubble (LSB). As Re is increased, its spanwise extent shrinks and at Re = 400 the structure changes to two regions associated with top and bottom shear layers of the LSB. As sweep and taper are introduced to the wing, the wavemaker moves in the spanwise direction following the displacement of peak recirculation of the LSB. The regions of flow receptivity are associated with the leading and trailing edges of the wing. Projecting these regions onto the wing surface shows that the peak receptivity to momentum forcing is located near the separation line at the spanwise location of peak recirculation. Present results provide theoretical insights into the instability mechanisms of finite tapered wings and establish a basis for future studies at higher Reynolds numbers.