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IMA Journal of Applied Mathematics Advance Access originally published online on September 29, 2007
IMA Journal of Applied Mathematics 2007 72(6):761-784; doi:10.1093/imamat/hxm038
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

The stability of the boundary layer on a compliant rotating disc

Jo-Anne L. John and Sharon O. Stephen{dagger}

School of Mathematics, University of Birmingham,Birmingham B15 2TT, UK

{dagger} Email: s.o.stephen{at}bham.ac.uk

Received on February 27, 2007; Accepted on August 24, 2007

The boundary layer over a infinite rotating disc is 3D and of finite depth. The breakdown and eventual transition of flow over the surface is preceded by the emergence of crossflow vortices that are stationary with respect to the disc. These result from an inviscid instability mechanism associated with an inflexion point within the boundary layer's velocity profile or a mechanism induced by the balance between viscous and Coriolis forces. It has been seen in past studies that compliance can substantially postpone the onset of transition, therefore the aim of this research is to investigate whether compliance can be used as a useful tool to do so here. We use numerical and asymptotic methods to predict possible behaviour by calculating growth rates and producing neutral solutions for the wave number and orientation of both inviscid and viscous modes. The results obtained suggest that the inviscid mode of instability will be stabilized by compliance but the viscous mode will be greatly destabilized.

Keywords: hydrodynamic stability; compliant surfaces; rotating disc.


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