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

Ilak M, Schlatter P, Bagheri S, Henningson DS (2012)

Publication Type: Journal article

Publication year: 2012

Journal

Journal of Fluid Mechanics Cambridge University Press (CUP)

Book Volume: 696

Pages Range: 94-121

DOI: 10.1017/jfm.2012.10

Abstract

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. © 2012 Cambridge University Press.

Authors with CRIS profile

Philipp Schlatter

Involved external institutions

Royal Institute of Technology / Kungliga Tekniska Högskolan (KTH) SE Sweden (SE)

How to cite

APA:

Ilak, M., Schlatter, P., Bagheri, S., & Henningson, D.S. (2012). Bifurcation and stability analysis of a jet in cross-flow: Onset of global instability at a low velocity ratio. Journal of Fluid Mechanics, 696, 94-121. https://doi.org/10.1017/jfm.2012.10

MLA:

Ilak, Milos, et al. "Bifurcation and stability analysis of a jet in cross-flow: Onset of global instability at a low velocity ratio." Journal of Fluid Mechanics 696 (2012): 94-121.

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