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Correlation functions in turbulence : numerical simulations and comparison with the functional renormalization group analysis

Abstract : The aim of this thesis is a comparison of the data from direct numerical simulations (DNS) of a three-dimensional homogeneous isotropic turbulent flow with recent analytical predictions obtained by means of the functional renormalization group (FRG) approach. The main results of the thesis concern the spatio-temporal correlation function of velocity, which is expected to decay as a Gaussian function of time at small time lags and as an exponential at large time lags. The numerical results show that the two-point correlation function of the Fourier modes of velocity indeed decays as a Gaussian in time at small time lags. The same behavior is observed for triple velocity correlations, which can be linked to the spectral energy transfer function. However, the behavior at large time delays is indiscernible due to the low-level magnitude of the correlation functions.Another important result of the thesis concerns the spatio-temporal correlations in passive scalar turbulence. The simulations of a scalar in a Navier-Stokes velocity field demonstrate a Gaussian decay as well for the scalar correlation function at small time delays, similar to the velocity correlation. The influence of the velocity temporal correlations on the scalar is studied in simulations with synthetic velocity fields. In the case of a random white-in-time velocity (also known as Kraichnan's model), the scalar correlations demonstrate a purely exponential decay in time. Adding a finite correlation time to the synthetic velocity leads to the emergence of a portion of Gaussian decay at small time lags in the scalar correlation function, while it turns to the exponential at time delays larger than the typical velocity correlation time. These results reveal the crossover between the two temporal correlation regimes, as predicted by the FRG.The last part of the thesis presents a preliminary study of the shell model of random passive scalar advection with the use of the FRG approach. The normal scaling of the second-order scalar structure is obtained, and the possible directions for studying the anomalous scaling are discussed.
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Submitted on : Monday, March 7, 2022 - 11:44:10 AM
Last modification on : Friday, March 25, 2022 - 9:44:25 AM


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Anastasiia Gorbunova. Correlation functions in turbulence : numerical simulations and comparison with the functional renormalization group analysis. Fluid mechanics [physics.class-ph]. Université Grenoble Alpes [2020-..], 2021. English. ⟨NNT : 2021GRALY073⟩. ⟨tel-03599573⟩



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