Numerical simulations for frequency prediction via mean flows

Abstract : Fluid flows play an important role in many natural phenomena as well as in many industrial applications. In this thesis, we are interested in oscillating flows origins from a Hopf bifurcation. The open shear-driven square cavity has two limit cycles separated by an unsteady quasi-periodic state. We have described this scenario in detail by using direct numerical simulations, linear stability analysis, and Floquet analysis. The Hopf bifurcation in Taylor-Couette flow gives rise to two solutions, spirals (traveling waves) and ribbons (standing waves in the axial direction). We discovered that the ribbons branch is followed by two consecutive heteroclinic cycles connecting two pairs of axisymmetric vortices. We studied in detail these two heteroclinic cycles. The linear stability analysis about the stationary solution is used to compute the threshold of the bifurcations. Another approach is the linearization about the mean field. This approach gives frequencies very close to that of the nonlinear system and shows in most cases a nearly zero growth rate. We have shown that spirals, ribbons, the lid-driven cavity and the flow around a prismatic object verify this property. In the thermosolutal convection, the frequencies obtained by the linearization about the mean field of the standing waves do not match the nonlinear frequencies and the growth rate is far from zero, on the other hand for the traveling waves this property is fully satisfied. We studied the validity of a self-consistent model in the case of the traveling waves. The self-consistent model consists of the mean field governing equation coupled with the linearized Navier-Stokes equation through the most unstable mode and the Reynolds stress term. This model calculates the mean field, the nonlinear frequency, and the amplitude without time integration. The self-consistent model is assumed to be valid for flows that satisfy the property of the mean field. We have shown that in this case, this model predicts the nonlinear frequency only very close to the threshold. We have improved significantly the predictions by considering higher orders in the Reynolds stress term.
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Contributor : Yacine Bengana <>
Submitted on : Monday, July 1, 2019 - 10:42:07 PM
Last modification on : Saturday, July 6, 2019 - 1:03:13 AM


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Yacine Bengana. Numerical simulations for frequency prediction via mean flows. Fluids mechanics [physics.class-ph]. Université de recherche Paris Sciences et Lettres - PSL Research University, 2018. English. ⟨tel-02170483⟩



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