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Abstract
AbstractExisting 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.
Highlights
This paper describes recent advances in the study of boundary-layer transition over rotating cones
We are concerned with the distinct convective instability mechanisms that dominate within the boundary layers over slender and broad rotating cones
In this paper we have highlighted the motivation for the hypothesis of a centrifugalinstability mode within the general class of rotating-cone boundary-layer flows
Summary
This paper describes recent advances in the study of boundary-layer transition over rotating cones. We are concerned with the distinct convective instability mechanisms that dominate within the boundary layers over slender and broad rotating cones. Previous studies including Garrett et al (2010), Hussain (2010), Hussain et al (2011) have shown that there is a close link between the rotating disk and cone problems in still fluid and axial flow. The current still fluid study forms an important stepping stone to analysing the more complex problem where axial flow is introduced. This work should be considered as a further step towards fully classifying the instability mechanics within the global class of boundary layer flows over rotating bodies.
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