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Numerical simulation of the spatiotemporal development of linear disturbances in Stokes layers: Absolute instability and the effects of high-frequency harmonics

Ramage, Alexander, Davies, Christopher, Thomas, Christian and Togneri, Michael 2020. Numerical simulation of the spatiotemporal development of linear disturbances in Stokes layers: Absolute instability and the effects of high-frequency harmonics. Physical Review Fluids 5 (10) , 103901. 10.1103/PhysRevFluids.5.103901

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Abstract

For a family of oscillatory Stokes layers, the spatiotemporal evolution of impulsively excited disturbances is investigated, using direct numerical simulations of the linearized Navier-Stokes equations. The semi-infinite planar Stokes layer is modified to incorporate a low-amplitude, high-frequency harmonic, which provides a simplified model of the external noise found in physical experiments. For the unmodified Stokes layer, impulsively excited disturbances are known to form family-tree-like structures, composed of multiple wave packets. The long-term behavior that is encompassed within these structures is studied, together with the effects upon them of the alterations to the base flow. In the absence of any base-flow modification, the disturbances are discovered to exhibit a subharmonic pattern of temporal growth, with a periodicity that is twice that of the basic state. It is also shown that when linear instability first arises, it takes an absolute rather than a convective form. Inclusion of a high-frequency harmonic into the basic state is found to have a strong and destabilizing impact upon the impulse response. The development of the family-tree-like disturbance structure can be disrupted, changing the character of the absolute instability and promoting its appearance at much reduced Reynolds numbers.

Item Type: Article
Date Type: Published Online
Status: Published
Schools: Mathematics
Publisher: American Physical Society
ISSN: 2469-990X
Date of First Compliant Deposit: 22 October 2020
Date of Acceptance: 15 September 2020
Last Modified: 23 Oct 2020 11:30
URI: http://orca-mwe.cf.ac.uk/id/eprint/135864

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