Journal
JOURNAL OF FLUID MECHANICS
Volume 696, Issue -, Pages 94-121Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2012.10
Keywords
absolute/convective instability; bifurcation; jets
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Funding
- Knut and Alice Wallenberg (KAW) Foundation through the Ekman consortium
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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.
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