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Instabilités et transition à la turbulence dans les écoulements périodiques

Abstract : This work focuses on the computation and stability analysis of both steady-state and time-periodic solutions with an emphasis on very high-dimensional systems such as the discrete Navier-Stokes equations.Our results are obtained with texttt{nekStab}, a user-friendly open-source toolbox for global stability analysis based on Krylov methods and a time-stepper formulation.Our package texttt{nekStab} inherits the flexibility and all the capabilities of the highly parallel spectral element-based open-source solver texttt{Nek5000}, enabling the characterization of the stability of complex flow configurations and several post-processing options.The performances and accuracy of our toolbox are first illustrated using standard benchmarks from the literature before turning our attention to the persistent sequence of bifurcations in the wake of bluff bodies.Using a Newton-Krylov algorithm, unstable periodic orbits are computed and fully three-dimensional Floquet modes obtained, highlighting a sequence of bifurcations leading to the onset of quasi-periodic dynamics as well as the existence of subharmonic cascade before the onset of temporal chaos.The stability of a jet in crossflow is also investigated for a range of jet to crossflow velocity ratios.After the first bifurcation, we note a surprising change in the nature of the perturbations before the onset of quasi-periodic dynamics and chaos.Finally, we present a parametric study of the influence of the aspect ratio on the first bifurcation taking place in lid-driven cavity flows.We find that very large spanwise aspect ratios need to be considered in order to tend toward the results obtained for cavities homogeneous in the spanwise direction.
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Submitted on : Friday, July 29, 2022 - 2:52:16 PM
Last modification on : Friday, August 5, 2022 - 2:54:00 PM

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  • HAL Id : tel-03740480, version 1

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Ricardo Schuh Frantz. Instabilités et transition à la turbulence dans les écoulements périodiques. Mécanique [physics.med-ph]. HESAM Université, 2022. Français. ⟨NNT : 2022HESAE032⟩. ⟨tel-03740480⟩

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