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Global linear and nonlinear stability of viscous confined plane wakes with co-flow

Published online by Cambridge University Press:  04 April 2011

OUTI TAMMISOLA ,
FREDRIK LUNDELL ,
PHILIPP SCHLATTER ,
ARMIN WEHRFRITZ  and
L. DANIEL SÖDERBERG
OUTI TAMMISOLA*
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
FREDRIK LUNDELL
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Wallenberg Wood Science Center, KTH Mechanics, SE-100 44 Stockholm, Sweden
PHILIPP SCHLATTER
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
ARMIN WEHRFRITZ
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden
L. DANIEL SÖDERBERG
Affiliation:
Wallenberg Wood Science Center, KTH Mechanics, SE-100 44 Stockholm, Sweden Innventia AB, Box 5604, SE-114 86 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

The global stability of confined uniform density wakes is studied numerically, using two-dimensional linear global modes and nonlinear direct numerical simulations. The wake inflow velocity is varied between different amounts of co-flow (base bleed). In accordance with previous studies, we find that the frequencies of both the most unstable linear and the saturated nonlinear global mode increase with confinement. For wake Reynolds number Re = 100 we find the confinement to be stabilising, decreasing the growth rate of the linear and the saturation amplitude of the nonlinear modes. The dampening effect is connected to the streamwise development of the base flow, and decreases for more parallel flows at higher Re. The linear analysis reveals that the critical wake velocities are almost identical for unconfined and confined wakes at Re ≈ 400. Further, the results are compared with literature data for an inviscid parallel wake. The confined wake is found to be more stable than its inviscid counterpart, whereas the unconfined wake is more unstable than the inviscid wake. The main reason for both is the base flow development. A detailed comparison of the linear and nonlinear results reveals that the most unstable linear global mode gives in all cases an excellent prediction of the initial nonlinear behaviour and therefore the stability boundary. However, the nonlinear saturated state is different, mainly for higher Re. For Re = 100, the saturated frequency differs less than 5% from the linear frequency, and trends regarding confinement observed in the linear analysis are confirmed.

JFM classification

Instability: Absolute/convective instability Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 675 , 25 May 2011 , pp. 397 - 434
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

‡

Present address: Aalto University, Faculty of Engineering and Architecture, Department of Energy Technology, PO Box 14300, FI-00076 Aalto, Finland

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