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Bifurcations and convective instabilities of steady flows in a constricted channel

  • João A. Isler (a1), Rafael S. Gioria (a2) and Bruno S. Carmo (a1)

Abstract

Stability and nonlinear analyses were employed to study symmetric and asymmetric steady flows through a straight channel with a smooth constriction with 50 % occlusion. Linear stability analysis was carried out to determine the unstable regions and the critical Reynolds numbers for the primary and secondary global instabilities. The primary bifurcation demonstrated an intricate aspect: the three-dimensional modes transfer their energy to the two-dimensional mode, which causes a symmetry breaking of the flow. This behaviour could be observed for Reynolds number lower than the critical, showing that this primary bifurcation is hysteretical. The secondary bifurcation also presented subcritical behaviour, exhibiting a pitchfork diagram with a large hysteretic curve. Given the subcritical character of both bifurcations, the relevance of non-normal growth in these flows were assessed, so that their convective mechanisms were exhaustively investigated. In addition, we could show that, for the secondary instability, optimal initial disturbances with large enough initial energy were able to promote a subcritical nonlinear saturation for a Reynolds number lower than the critical. The physical mechanism behind the transition process occurred by nonlinear interaction between the two- and three-dimensional modes, which established oscillatory behaviour, moreover, this energy exchange between the modes led the flow to the nonlinear saturated state. Therefore, the two-dimensional modes play a key role in the primary and secondary bifurcations of this system.

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Corresponding author

Email address for correspondence: joao.isler@usp.br

References

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Bifurcations and convective instabilities of steady flows in a constricted channel

  • João A. Isler (a1), Rafael S. Gioria (a2) and Bruno S. Carmo (a1)

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