Competing instabilities of the 3D boundary-layer flow over spinning bodies

This talk will provide a mathematical description of the onset of counter-rotating spiral vortices observed for boundary-layer flow over a family of slender rotating cones in quiescent fluid. Existing experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary layer. The mode manifests as Gortler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to model the centrifugal mode as the half-angle is reduced. Instead, an alternative formulation is developed  posing new scalings and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode. Our results confirm our earlier predictions pertaining to the existence of the new Gortler mode and capture the effects of the governing centrifugal instability mechanism. Meanwhile, favourable comparisons are drawn between the numerical and asymptotic neutral stability curve predictions