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Bifurcation and stability analysis of a jet in cross-flow: onset of global instability at a low velocity ratio

Published online by Cambridge University Press:  06 March 2012

Miloš Ilak ,
Philipp Schlatter ,
Shervin Bagheri  and
Dan S. Henningson
Miloš Ilak*
Affiliation:
Linné FLOW Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
Philipp Schlatter
Affiliation:
Linné FLOW Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
Shervin Bagheri
Affiliation:
Linné FLOW Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
Dan S. Henningson
Affiliation:
Linné FLOW Centre, Department of Mechanics, Royal Institute of Technology (KTH), SE-10044 Stockholm, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

We study direct numerical simulations (DNS) of a jet in cross-flow at low values of the jet-to-cross-flow velocity ratio . We observe that, as the ratio 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 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 and that good qualitative predictions about the dynamics can still be made at slightly higher values of 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.

JFM classification

Instability: Absolute/convective instability Nonlinear Dynamical Systems: Bifurcation Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 696 , 10 April 2012 , pp. 94 - 121
Copyright
Copyright © Cambridge University Press 2012

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Footnotes

‡

Present address: United Technologies Research Center, 411 Silver Lane, MS 129-85, East Hartford, CT 06108, USA.

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