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Linear disturbance evolution in the semi-infinite Stokes layer and related flows

Ramage, Alexander 2017. Linear disturbance evolution in the semi-infinite Stokes layer and related flows. PhD Thesis, Cardiff University.
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Abstract

The stability of the semi-infinite Stokes layer is explored. This is the flow generated in a semi-infinite region of otherwise stationary fluid by the sinusoidal oscillation of a bounding plate and is described by an exact solution to the Navier--Stokes equations. A linear stability analysis is carried out, based on Floquet theory, that reduces the disturbance equations to an eigenvalue problem that determines the asymptotic temporal behaviour of disturbances. This method is also applied to the finite Stokes layer (being the flow in a channel bounded by oscillating plates) and modifications incorporating a mean flow. Linear disturbances are simulated numerically and intriguing features of the spatial/temporal evolution are reproduced and expanded on. Consistency between the linear stability analysis and the simulations is demonstrated, as is evidence suggesting some disturbances exhibit temporal growth at every spatial location (absolute instabilities). Through modification of Briggs' method, the conditions for absolute instability in temporally periodic flows are discussed. It is shown that the Stokes layer is indeed subject to absolute instability by appealing to the symmetries of the flow. This approach provides further insight into the spatial/temporal evolution of disturbances. Finally, the Stokes layer is modified by a low-amplitude, high-frequency oscillation to approximate the noise associated with the mechanical generation of plate motion in experiments. It is shown that the introduction of noise can be dramatically destabilising and can have a significant effect on the disturbance evolution. In cases where the flow is subject to a high level of noise, the spatial/temporal evolution of the disturbance holds little resemblance to the evolution of disturbances in the pure Stokes layer.

Item Type: Thesis (PhD)
Date Type: Completion
Status: Unpublished
Schools: Mathematics
Funders: EPSRC
Date of First Compliant Deposit: 14 December 2017
Last Modified: 15 Dec 2017 13:12
URI: http://orca.cf.ac.uk/id/eprint/107589

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