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On the global linear stability of the boundary layer on rotating bodies

By S.J. Garrett and N. Peake


This paper was published as Advances in Turbulence XI: Proceedings of the 11th EUROMECH European Turbulence Conference, June 25-28, 2007, Porto, Portugal; Palma, J. M. L. M.; Silva Lopes, A. (Eds.), pp. 550-552. It is available from http://www.springer.com/materials/mechanics/book/978-3-540-72603-6Metadata only entryBy taking the local approach of working at a fixed Reynolds number (equivalently\ud at fixed distance from the axis of rotation) and assuming that the\ud steady flow is spatially uniform, [1] shows that the boundary layer on a rotating\ud disk is locally absolutely unstable at Reynolds numbers in excess of a\ud critical value. The value of the critical Reynolds number agrees exceedingly\ud well with experimentally measured values of the transition Reynolds number,\ud leading to a clear hypothesis that absolute instability plays a role in turbulent\ud transition on the disk.\ud In contrast to this local analysis, [2] solve the linearised Navier–Stokes\ud equations directly for the rotating disk. When they make the same homogenous\ud flow approximation as in [1], they recover those results in full. However,\ud when the spatial inhomogeneity of the boundary layer is included there is no\ud evidence of an unstable global oscillator in the long-term response.\ud In order to address this discrepancy between the local results and the\ud numerical simulations of the full inhomogeneous flow, we consider the linear\ud global modes of the rotating disk/cone boundary layer

Publisher: Springer
Year: 2007
OAI identifier: oai:lra.le.ac.uk:2381/8847
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