The centrifugal instability of the boundary-layer flow over slender rotating cones

Hussain, Z, Garrett, SJ and Stephen, SO (2014) The centrifugal instability of the boundary-layer flow over slender rotating cones. Journal of Fluid Mechanics, 755. ISSN 0022-1120

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Abstract

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 flow over slender rotating cones. The mode manifests as Görtler-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 identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode.