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Numerical simulations of disturbance development in rotating boundary-layers

Thomas, Christian 2007. Numerical simulations of disturbance development in rotating boundary-layers. PhD Thesis, Cardiff University.

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Recent theoretical studies by Lingwood (1995,1997a,b) on the rotating-disk boundary-layer, have shown, using an analysis that deploys the usual 'parallel-flow' approximation, that there exists a region of absolute instability. However, by taking into account the radial variation of the mean flow, Davies h Carpenter (2003) have shown, using numerical simulations, that the absolute instability does not give rise to an unstable linear global mode. In fact convective behaviour is found to dominate the global response. The aim of the current study is to further the studies of Davies h Carpenter (2003) to other rotating boundary-layers. Uniform suction and a uniform axial magnetic field are known to be stabilizing. However, by considering non-parallel effects, globally unstable behaviour is observed, albeit without the promotion of a fixed global frequency. An investigation is also carried out on the so called BEK family of rotating boundary-layers, which includes the Bodewadt, Ekman and von Karman flows. All of these flows are absolutely unstable, when the parallel flow approximation is applied. However, by considering the genuine non-parallel flow, the numerical simulation results indicate that the kind of behaviour found for the von Karman flow is carried over to other flows in the BEK family. The numerical simulation results of the rotating-disk boundary-layer can be modeled using the linearized complex Ginzburg-Landau equation. By deriving expressions for the stability, convection velocity and diffusion/dispersion effects, in terms of the numerical simulation results, the Green's solutions to the Ginzburg-Landau equation can be successfully matched to the parallel and non-parallel rotating-disk boundary-layer. The results suggest that the long-term behaviour depends on the precise balance of the varying frequency, varying growth rate, and diffusion/dispersion effects. It is then possible for an absolutely unstable disturbance to remain globally stable.

Item Type: Thesis (PhD)
Status: Unpublished
Schools: Engineering
Subjects: T Technology > TA Engineering (General). Civil engineering (General)
ISBN: 9781303210129
Date of First Compliant Deposit: 30 March 2016
Last Modified: 03 Nov 2014 09:15

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