Abstract
In this study, a new centrifugal instability mode, which dominates within the boundarylayer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and shortwavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundarylayer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtlertype counterrotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.
Original language  English 

Pages (fromto)  7094 
Number of pages  25 
Journal  Journal of Fluid Mechanics 
Volume  788 
Early online date  22 Dec 2015 
DOIs  
Publication status  Published  10 Feb 2016 
Externally published  Yes 
Keywords
 boundary layer stability
 rotating flows
 transition to turbulence
ASJC Scopus subject areas
 Condensed Matter Physics
 Mechanics of Materials
 Mechanical Engineering
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Paul Griffiths
 Research Centre for Fluid and Complex Systems  Associate
 School of Computing, Electronics and Maths  Associate Head of School  Research
Person: Teaching and Research