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Etude de la dynamique non-linéaire des écoulements chauffés et soumis à des champs magnétiques

Abstract : The growth of thermal convection out of different perturbations of the conductive base state is investigated using a spectral element time-stepping code. The fluid is subject to a vertical heat transfer in a cylindrical cavity with an upper free surface corresponding to the so-called Rayleigh-Bénard-Marangoni situation and the heat exchange through the free surface is evaluated via the Biot number. The results of the stability diagrams show that the evolution of the primary thresholds are largely influenced by the Biot number, the Marangoni number, and the aspect ratio of the cavity. Flow transitions are elucidated in quantitative detail as a function of the Rayleigh number for different Biot numbers in the tension free limit Ma = 0. The results shown are obtained by solving the full nonlinear field equations numerically among a continuation method. When an axisymmetric m = 0 Fourier mode is obtained at onset, the non-linear evolution shows the coexistence of different convective structures, the axisymmetric structures with up-ow or down-ow at the center and mixed-mode structures which appear on secondary subcritical branches. The action of a constant magnetic field is then considered for melts in the same type of configuration with an upper free surface. We show the global stabilizing effect of the magnetic field on the primary bifurcation thresholds and the selective effect on the different instability modes. We also analyze the evolution of the convective structures above the thresholds and show how the magnetic field modifies the transitions between these structures. When applying a magnetic body forcing in the azimuthal direction (RMF), one can damp the unavoidable thermal fluctuations inside the melt and delay the transition to the Rayleigh-Bénard instability (for rigid-rigid circular plates at top and bottom). The rotation effect also changes the transitions from steady to oscillatory, except for the m = 0 Fourier mode where the transitionis first steady until a critical Taylor number and then becomes oscillatory. The dynamics of the transitions to the axisymmetric flow, below and above this value of critical magnetic Taylor number, is particularly interesting and will be described.
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  • HAL Id : tel-00569060, version 1

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Anas El Gallaf. Etude de la dynamique non-linéaire des écoulements chauffés et soumis à des champs magnétiques. Sciences de l'ingénieur [physics]. Ecole Centrale de Lyon, 2009. Français. ⟨NNT : 2009ECDL0024⟩. ⟨tel-00569060⟩

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