Nonparallel stability analysis of axisymmetric stagnation-point flow

Abstract

The method of multiple scales has been used to extend linear-stability theory to nonparallel axisymmetric boundary-layer flow in the neighborhood of the stagnation point on a blunt body of revolution. The extended theory includes nonparallel planar effects as well as the effects of such possibly destabilizing three-dimensional mechanisms as the stretching of vortex filaments in the rapidly diverging boundary-layer flow. These mechanisms have not been previously incorporated into stability theory. Stability predictions based on the extended theory are found to be in close agreement with predictions of parallel-flow stability theory based on the Orr–Sommerfeld equation; axisymmetric and planar nonparallel effects are concluded to be of negligible importance in the axisymmetric stagnation-point boundary layer.

Instability

“…Grabowski (1980) applied linear stability theory to the boundary layer near a stagnation point on a body of revolution. The decrease is least for favorable pressure gradients, about 10% for zero pressure gradients, and grows rapidly as the pressure gradient becomes more adverse.…”