The University of Southampton
University of Southampton Institutional Repository

The stability of laminar symmetric separated wakes

The stability of laminar symmetric separated wakes
The stability of laminar symmetric separated wakes
Time-dependent computations of the two-dimensional incompressible uniform-velocity laminar flow past a normal flat plate (of unit half-width) in a channel are presented. Attention is restricted to cases in which the well-known anti-symmetric (von Kármán-type) vortex shedding is suppressed by the imposition of a symmetry plane on the downstream plate centreline. With a further symmetry plane at the channel's upper boundary, the only two governing parameters in the problem are the channel half-width, H, and the Reynolds number, Re (based on the body half-width and the upstream velocity, U). The former is restricted to the range 3?H?30 and the interest lies in determining the nature of the initial instability which occurs in the separated wake as Re is gradually increased. It is found that for sufficiently large H and at a critical Re, a long-time-scale global (supercritical) instability is initiated, which in its saturated (limit) state takes the form of ‘lumps’ of vorticity being periodically shed from the tail end of the separated bubble. Stability calculations of corresponding mean flow profiles (typical of those found in the separated wake) are undertaken by examining the impulse response of particular profiles via appropriate solution of the Orr–Sommerfeld equation. The results of this analysis extend those available from related published work and are consistent with the behaviour found from the numerical computations. Taken together, all the results suggest that this type of global instability may be generic to many kinds of separated wakes and, indeed, may provide the fundamental explanation for the very low-frequency oscillations often noticed in fully turbulent wake bubbles.
0022-1120
389-411
Castro, Ian P.
66e6330d-d93a-439a-a69b-e061e660de61
Castro, Ian P.
66e6330d-d93a-439a-a69b-e061e660de61

Castro, Ian P. (2005) The stability of laminar symmetric separated wakes. Journal of Fluid Mechanics, 532 (1), 389-411. (doi:10.1017/S0022112005004301).

Record type: Article

Abstract

Time-dependent computations of the two-dimensional incompressible uniform-velocity laminar flow past a normal flat plate (of unit half-width) in a channel are presented. Attention is restricted to cases in which the well-known anti-symmetric (von Kármán-type) vortex shedding is suppressed by the imposition of a symmetry plane on the downstream plate centreline. With a further symmetry plane at the channel's upper boundary, the only two governing parameters in the problem are the channel half-width, H, and the Reynolds number, Re (based on the body half-width and the upstream velocity, U). The former is restricted to the range 3?H?30 and the interest lies in determining the nature of the initial instability which occurs in the separated wake as Re is gradually increased. It is found that for sufficiently large H and at a critical Re, a long-time-scale global (supercritical) instability is initiated, which in its saturated (limit) state takes the form of ‘lumps’ of vorticity being periodically shed from the tail end of the separated bubble. Stability calculations of corresponding mean flow profiles (typical of those found in the separated wake) are undertaken by examining the impulse response of particular profiles via appropriate solution of the Orr–Sommerfeld equation. The results of this analysis extend those available from related published work and are consistent with the behaviour found from the numerical computations. Taken together, all the results suggest that this type of global instability may be generic to many kinds of separated wakes and, indeed, may provide the fundamental explanation for the very low-frequency oscillations often noticed in fully turbulent wake bubbles.

Text
the_stability_of_laminar_symmetric_separated_wakes.pdf - Version of Record
Download (549kB)

More information

Published date: 2005

Identifiers

Local EPrints ID: 23204
URI: http://eprints.soton.ac.uk/id/eprint/23204
ISSN: 0022-1120
PURE UUID: 6d4d294a-db85-411d-a6e5-1f33402c133a

Catalogue record

Date deposited: 14 Mar 2006
Last modified: 15 Mar 2024 06:44

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×