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Bifurcation and stability analysis of a jet in cross-flow: onset of global instability at a low velocity ratio
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9627-5903
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-8209-1449
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7864-3071
2012 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 696, 94-121 p.Article in journal (Refereed) Published
Abstract [en]

We study direct numerical simulations (DNS) of a jet in cross-flow at low values of the jet-to-cross-flow velocity ratio R. We observe that, as the ratio R increases, the flow evolves from simple periodic vortex shedding (a limit cycle) to more complicated quasi-periodic behaviour, before finally becoming turbulent, as seen in the simulation of Bagheri et al. (J. Fluid. Mech., vol. 624, 2009b, pp. 33-44). The value of R at which the first bifurcation occurs for our numerical set-up is found, and shedding of hairpin vortices characteristic of a shear layer instability is observed. We focus on this first bifurcation, and find that a global linear stability analysis predicts well the frequency and initial growth rate of the nonlinear DNS at the critical value of R and that good qualitative predictions about the dynamics can still be made at slightly higher values of R where multiple unstable eigenmodes are present. In addition, we compute the adjoint global eigenmodes, and find that the overlap of the direct and the adjoint eigenmode, also known as a 'wavemaker', provides evidence that the source of the first instability lies in the shear layer just downstream of the jet.

Place, publisher, year, edition, pages
2012. Vol. 696, 94-121 p.
Keyword [en]
absolute/convective instability, bifurcation, jets
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-93910DOI: 10.1017/jfm.2012.10ISI: 000302325400005Scopus ID: 2-s2.0-84859193620OAI: oai:DiVA.org:kth-93910DiVA: diva2:525170
Funder
Knut and Alice Wallenberg FoundationSwedish e‐Science Research Center
Note

QC 20120507

Available from: 2012-05-07 Created: 2012-05-03 Last updated: 2017-12-07Bibliographically approved

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Schlatter, PhilippBagheri, ShervinHenningson, Dan S.

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Ilak, MilosSchlatter, PhilippBagheri, ShervinHenningson, Dan S.
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