Transient growth in developing plane and Hagen Poiseuille flow

Duck, Peter W. (2005) Transient growth in developing plane and Hagen Poiseuille flow. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461 (2057). pp. 1311-1333. ISSN 1471-2946

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Abstract

The stability of developing entry flow in both two-dimensional channels and circular pipes is investigated for large Reynolds numbers. The basic flow is generated by uniform flow entering a channel/pipe, which then provokes the growth of boundary layers on the walls, until (far downstream) fully developed flow is attained; the length for this development is well known to be O(Reynolds number)×the channel/pipe width/diameter. This enables the use of high-Reynolds-number theory, leading to boundary-layer-type equations which govern the flow; as such, there is no need to impose heuristic parallel-flow approximations. The resulting base flow is shown to be susceptible to significant, three-dimensional, transient (initially algebraic) growth in the streamwise direction, and, consequently, large amplifications to flow disturbances are possible (followed by ultimate decay far downstream). It is suggested that this initial amplification of disturbances is a possible and alternative mechanism for flow transition.

Item Type:	Article
Uncontrolled Keywords:	non-modal stability, by-pass transition, developing flows, Reynolds' experiment
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 70 Mechanics of particles and systems
Depositing User:	Ms Lucy van Russelt
Date Deposited:	09 Aug 2006
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/455

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