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Subcritical transition to turbulence in wall-bounded shear flows : spots, pattern formation and low-order modelling

Abstract : The thesis focuses on the transition from laminar to turbulent flow in canonical wall-bounded shear flows presenting a linearly stable laminar flow. The subcritical transition in these shear flows is characterised by spatiotemporal intermittency in the transitional regime. This manifests as spatial localization of turbulence which self-organizes into large-scale coherent structures such as spots and bands. In this regard, these structures are investigated in different wall-bounded shear flows with high fidelity numerical simulations. The primary control parameter for the simulations is the Reynolds number Re. In the first part of the thesis, turbulent spots are investigated in four different shear flow cases: plane Couette, plane Poiseuille, Couette-Poiseuille and Waleffe flow. These flow scenarios present different symmetries and boundary conditions. Performing the simulations in large domains, the in-plane turbulent fluctuations are shown to decay algebraically away from the spot. The emergence of two distinct large-scale flow topologies dictates the spatial decay exponent. The large-scale flow structure and consequently the decay exponent are found to depend only on the symmetry of the flow and is independent of the Re. Arguments from 2D kinematics and flow symmetry are used to justify theoretically these observations. In the second part, the transition from turbulent to laminar in plane Poiseuille flow is investigated. The transitional regime is found to portray two distinct behaviours: (a) pattern formation with alternate regions of laminar and turbulent (b) spatially localised independent turbulent bands. Adopting the methodology of an impulse response with ensemble averaging, evidence for a linear instability of the turbulent flow leading to pattern formation is presented. The evolution of the pattern with Re is documented with its geometric properties as well as global observables such as the friction factor. High-order statistics of turbulent fluctuations reveal a continuous link between featureless turbulence and the transitional regime. In order to gather more insight into the formation and evolution of the pattern with Re, a low-order model of the shear flow is motivated. The third part explores a low-order model presented in the literature. The 1D PDE model presented by Manneville, featuring a Turing instability as an extension of the Waleffe model, is revisited. This was adapted with suitable parameters and extended with the introduction of nonlinear advection and stochastic noise. The model accurately captures the phenomenology of the transitional regime of plane Poiseuille flow. It features pattern formation with multistability, wavelength selection by noise and excitability at low Re. These results are extrapolated from the model and validated against the observations in the DNS simulations.
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Submitted on : Thursday, February 24, 2022 - 10:55:12 AM
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Pavan Kashyap. Subcritical transition to turbulence in wall-bounded shear flows : spots, pattern formation and low-order modelling. Fluid mechanics [physics.class-ph]. Université Paris-Saclay, 2021. English. ⟨NNT : 2021UPAST139⟩. ⟨tel-03586857⟩



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