Bifurcation and stability analysis of a jet in cross-flow: onset of global instability at a low velocity ratio
2012 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 696, 94-121 p.Article in journal (Refereed) Published
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.
absolute/convective instability, bifurcation, jets
Engineering and Technology
IdentifiersURN: urn:nbn:se:kth:diva-93910DOI: 10.1017/jfm.2012.10ISI: 000302325400005ScopusID: 2-s2.0-84859193620OAI: oai:DiVA.org:kth-93910DiVA: diva2:525170
FunderKnut and Alice Wallenberg FoundationSwedish e‐Science Research Center
QC 201205072012-05-072012-05-032013-04-08Bibliographically approved