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Title: The effect of anisotropic and isotropic roughness on the convective stability of the rotating disk boundary layer
Authors: Cooper, A. J.
Harris, J. H.
Garrett, Stephen John
Oezkan, M.
Thomas, P. J.
First Published: 21-Jan-2015
Publisher: American Institute of Physics (AIP)
Citation: Physics of Fluids, 2015, 27 (1), 014107
Abstract: A theoretical study investigating the effects of both anisotropic and isotropic surface roughness on the convective stability of the boundary-layer flow over a rotating disk is described. Surface roughness is modelled using a partial-slip approach, which yields steady-flow profiles for the relevant velocity components of the boundary-layer flow which are a departure from the classic von Kármán solution for a smooth disk. These are then subjected to a linear stability analysis to reveal how roughness affects the stability characteristics of the inviscid Type I (or cross-flow) instability and the viscous Type II instability that arise in the rotating disk boundary layer. Stationary modes are studied and both anisotropic (concentric grooves and radial grooves) and isotropic (general) roughness are shown to have a stabilizing effect on the Type I instability. For the viscous Type II instability, it was found that a disk with concentric grooves has a strongly destabilizing effect, whereas a disk with radial grooves or general isotropic roughness has a stabilizing effect on this mode. In order to extract possible underlying physical mechanisms behind the effects of roughness, and in order to reconfirm the results of the linear stability analysis, an integral energy equation for three-dimensional disturbances to the undisturbed three-dimensional boundary-layer flow is used. For anisotropic roughness, the stabilizing effect on the Type I mode is brought about by reductions in energy production in the boundary layer, whilst the destabilizing effect of concentric grooves on the Type II mode results from a reduction in energy dissipation. For isotropic roughness, both modes are stabilized by combinations of reduced energy production and increased dissipation.
DOI Link: 10.1063/1.4906091
ISSN: 1070-6631
eISSN: 1089-7666
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2015 AIP Publishing LLC. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Physics of Fluids, 2015, 27 (1), 014107 and may be found at Deposited with reference to the publisher’s archiving policy available on the SHERPA/RoMEO website.
Appears in Collections:Published Articles, Dept. of Mathematics

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