Simulation numérique directe de la turbulence hélicitaire maximale et modèles LES de la turbulence magnétohydrodynamique

TL;DRAbstract

Homogeneous and isotropic turbulence was first formalized by Kolmogorov (1941), through dimensional analysis. He managed to show that the spectral density of kinetic energy, E(k), was following a k{-5/3} law. This behaviour is known as Kolmogorov's cascade. For many geophysical and astrophysical flow, kinetic helicity plays an important role. For instance, Parker (1955) showed that for conductive fluids such as Sun, kinetic helicity could contribute to amplify the magnetic field. Brissaud {it et al} (1973) tried to show that kinetic helicity could have an influence on the spectral density of kinetic energy. Through dimensional analysis they suggested the existence of a cascade for which the kinetic energy spectra would follow a k^{-7/3} law. In the first part of this thesis we will confirm thanks to Direct Numerical Simulations (DNS) the existence of such an asymptotic limit in k^{-7/3}. We will also use helical decomposition to perform a deep analysis of the physics encountered within

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