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On the roughness instability of growing boundary layers

Published online by Cambridge University Press:  13 July 2021

Philip Hall Open the ORCID record for Philip Hall [Opens in a new window]
Philip Hall*
Affiliation:
School of Mathematics, Monash University, Clayton, Victoria, Australia
*
†Email address for correspondence: phil.hall@monash.edu
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Abstract

The streamwise vortex instability of boundary layers caused by wall roughness in the form of surface undulations is investigated. The instability is characterised by a roughness parameter $\varGamma$ depending on the geometry and fluid properties. At $O(1)$ values of $\varGamma$ disturbances develop on the same length scale as the basic boundary layer flow. The instability is driven by a boundary condition relating the disturbance wall shears in the streamwise and normal directions. The undulations have a wavelength comparable with the boundary layer depth and the amplitude is asymptotically small compared with the depth. If the roughness parameter is large then, apart from a narrow window of vortex wavenumbers, the instability responds in a quasi-parallel manner. Falkner–Skan boundary layers are considered in detail and the dependence on the angle of the wedge associated with the flows investigated. A particular susceptibility to roughness instabilities of flows past $90^{\circ }$ wedges is uncovered. The limits of small and large wavenumbers are considered and universal results given for the critical roughness height $h$ and wavelength $b$ needed for instability.

JFM classification

Instability: Shear-flow instability Boundary Layers: Boundary layer stability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 922 , 10 September 2021 , A28
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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