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Modelling of transport in homogeneous turbulence

Abstract : Modelling is essential to understand and reproduce the dominant physical mechanisms occurring in natural turbulent flows such as atmospheric and oceanic ones. Indeed, the dynamics of geophysical flows results of multiple complex processes interacting with each others, at various scales, intensities, and on different characteristic times. The fine description of such flows is currently out of reach of direct numerical simulations, notably because of Reynolds numbers limitations. Consequently, we address in this thesis the modelling of homogeneous turbulence, using the spectral formalism of the eddy-damped quasi-normal Markovian (EDQNM) approximation. This first allows us to obtain results rapidly in terms of computational resources at very large Reynolds numbers, and thus to investigate separately some of the fundamental mechanisms at stake in natural turbulent flows, namely shear, mean temperature gradient, stratification, helicity, and combinations of these processes. In this framework, a two-step approach is considered: first, EDQNM is used to close the non-linear terms in the second-order moments equations, and anisotropy is then modelled through spherically-averaged tensors. This methodology is applied to the various configurations mentioned above, permits to propose new theoretical results, and to assess them numerically at large Reynolds numbers. Among the most important findings, we focused on (i) the prediction of the decay and growth laws of crucial one-point statistics such as the kinetic energy, the scalar variance, and helicity; (ii) the determination of spectral scalings; and (iii) the scale by scale distribution of anisotropy.
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Antoine Briard. Modelling of transport in homogeneous turbulence. Mechanics of the fluids [physics.class-ph]. Université Pierre et Marie Curie - Paris VI, 2017. English. ⟨NNT : 2017PA066201⟩. ⟨tel-01677226⟩

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