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Cascade bidimensionnelle d'un traceur : diagnostic dans l'espace physique et modélisation

Abstract : We present numerical and theoretical results concerning the two-dimensional turbulent cascades, and especially the cascade of a tracer, from a standpoint in physical space. Such an approach allows to demonstrate the non-intermittent character of the inverse energy cascade, even in situations dominated by coherent structures. The main part of the thesis is devoted to the analysis and modeling of the cascade of a tracer. We propose a method to diagnose the cascade of a tracer : considering the evolution of a tracer increment, we define in physcal space a scale-to-scale flux of tracer variance. We then get interested into the problem of turbulent mixing parameterization. We motivate the use of an anisotropic model, which we call strain diffusivity (SD). We connect its diffusive properties to the geometrical properties of the advecting flow. Vorticity in two dimensions is an active tracer, and its subgrid-scale parameterization affects velocity. The inverse energy cascade constrains admissible parameterizations to conserve energy. We show that SD conserves energy and that it is the only one among a certain class of simple models. We study numerically the properties of the tools we introduced. We show that, at contrast with an isotropic diffusivity/hyperdiffusivity, SD induces a diffusion that is well correlated to the local flux of tracer variance. We check that it does impose the effective gaussian filter it is obtained from. However the reduction of the error committed when using it in conjunction with a spectral method is not obvious. Nevertheless, it produces a much better representation of the large scales of the flow when used on vorticity in small-scale forced situation. We finally compare the cascade properties of vorticity and a passive tracer. The criterions we use are based on conditional averages of the lagrangian derivatives of the squared tracer gradient. We demonstrate in random fields an kinematic difference between vorticity and a passive tracer, which partly remains in turbulent fields.
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https://tel.archives-ouvertes.fr/tel-00007421
Contributor : Dubos Thomas <>
Submitted on : Tuesday, November 16, 2004 - 4:15:03 PM
Last modification on : Thursday, December 10, 2020 - 12:37:26 PM
Long-term archiving on: : Friday, April 2, 2010 - 8:43:19 PM

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  • HAL Id : tel-00007421, version 1

Citation

Thomas Dubos. Cascade bidimensionnelle d'un traceur : diagnostic dans l'espace physique et modélisation. Dynamique des Fluides [physics.flu-dyn]. Université Pierre et Marie Curie - Paris VI, 2001. Français. ⟨tel-00007421⟩

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