The absolute instability of the boundary layer on a rotating cone

Abstract

This paper is concerned with the existence of local absolute instability in the boundary-layer flow over the outer surface of a rotating cone, thereby extending earlier work by Lingwood who considered the rotating disk. Both still outer fluids and non-zero axial flow are considered, viscous and streamline-curvature effects are included, and the analysis is conducted for a wide range of cone half-angles, ψ. In still outer fluid our predicted local Reynolds numbers at the onset of absolute instability is relatively insensitive to the value of ψ, and is in reasonable agreement with experimental data for the onset of turbulence when ψ > 50 ° . For ψ < 50 ° the discrepancy increases, suggesting that some other mechanism may be responsible for transition on more slender cones. The introduction of axial flow is found to significantly increase the Reynolds number for local absolute instability for each half-angle.