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Global stability behaviour for the BEK family of rotating boundary layers

Davies, Christopher and Thomas, Christian 2017. Global stability behaviour for the BEK family of rotating boundary layers. Theoretical and computational fluid dynamics 31 (5-6) , pp. 519-536. 10.1007/s00162-016-0406-9

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Abstract

Numerical simulations were conducted to investigate the linear global stability behaviour of the Bödewadt, Ekman, von Kármán (BEK) family of flows, for cases where a disc rotates beneath an incompressible fluid that is also rotating. This extends the work reported in recent studies that only considered the rotating-disc boundary layer with a von Kármán configuration, where the fluid that lies above the boundary layer remains stationary. When a homogeneous flow approximation is made, neglecting the radial variation of the basic state, it can be shown that linearised disturbances are susceptible to absolute instability. We shall demonstrate that, despite this prediction of absolute instability, the disturbance development exhibits globally stable behaviour in the BEK boundary layers with a genuine radial inhomogeneity. For configurations where the disc rotation rate is greater than that of the overlying fluid, disturbances propagate radially outwards and there is only a convective form of instability. This replicates the behaviour that had previously been documented when the fluid did not rotate beyond the boundary layer. However, if the fluid rotation rate is taken to exceed that of the disc, then the propagation direction reverses and disturbances grow while convecting radially inwards. Eventually, as they approach regions of smaller radii, where stability is predicted according to the homogeneous flow approximation, the growth rates reduce until decay takes over. Given sufficient time, such disturbances can begin to diminish at every radial location, even those which are positioned outwards from the radius associated with the onset of absolute instability. This leads to the confinement of the disturbance development within a finitely bounded region of the spatial–temporal plane

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Uncontrolled Keywords: Rotating flows Boundary layer stability Global stability Vorticity-based simulation
Publisher: Springer
ISSN: 1432-2250
Funders: EPSRC
Date of First Compliant Deposit: 18 November 2016
Date of Acceptance: 5 August 2016
Last Modified: 18 Sep 2019 11:02
URI: http://orca-mwe.cf.ac.uk/id/eprint/96282

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