# Laboratoire de Mécanique des Fluides et d’Acoustique - UMR 5509

LMFA - UMR 5509
Laboratoire de Mécanique des Fluides et d’Acoustique
Lyon
France

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## Donato VALLEFUOCO

Jeudi 16 novembre à 13h45, amphi 201 - ECL

### Numerical study of unconfined and confined anisotropic turbulence

Jury :
Pierre-Philippe Cortet (Examinateur)
Sébastien Galtier (Examinateur)
Fabien Godeferd (Directeur)
Aurore Naso (Examinatrice, co-encadrante)
Yannick Ponty (Rapporteur)
Pierre Sagaut (Rapporteur)
Julian Scott (Examinateur)
Résumé :

In turbulent flows of practical interest, turbulence interacts with confinement and external forces, leading to statistical inhomogeneity and anisotropy. Isolating their contributions to some targeted statistics is indispensible for understanding the underlying physical phenomena. The aim of this thesis has therefore been to gain further insight into direction- and scale-dependent anisotropy in a set of idealized and realistic contexts.

Both spectral space and separation space statistical characterizations have been employed. The spectral characterization concerns the anisotropic statistics of turbulence under the form of directional energy, polarization and helicity spectra. The separation space characterization is built on two-point second- and third-order velocity increment moments, and two-point velocity correlations.

First, we studied the effect of large-scale spectral forcing. The considered forcing methods are the non-helical and the helical Euler scheme, and the ABC-scheme. We showed that both forcings have a drawback in that, if the number of sufficiently excited modes is too low, anisotropy is bound to arise even at small scales. In the case of Euler forcing, this depends on both the range of forcing wavenumbers and its helicity contents. The ABC forcing, for which the amount of injected helicity cannot be controlled, excites only six modes and therefore always generates anisotropy at all resolved scales.

Our second step was to analyze the scale- and direction-dependent anisotropy of homogeneous rotating turbulence. Surpringly, anisotropy arises at all scales even at low rotation rate. In particular, we identified two anisotropic ranges with different features. In the large scales, directional anisotropy is larger and decreases with wavenumber. At smaller scales, it is much weaker although still significant and slowly increases with wavenumber all the way to the dissipative scales. Another interesting and original conclusion of this part of the work concerns the role of the Zeman scale and its link with the flow scale-dependent anisotropy. The Zeman scale was previously argued to be the characteristic lengthscale separating rotation-affected scales from isotropic ones. Upon closer investigation using several simulations at different parameters, we found that the separating scale between large and weak anisotropy is rather the characteristic lengthscale at which rotation and dissipation effects balance. This result, however, does not contradict Zeman’s argument about isotropy recovery in the asymptotic limit of vanishing viscosity, since the separating scale vanishes at infinite Reynolds number, and therefore only the decreasing anisotropy range should persist and scales much smaller than the Zeman one may recover isotropy.

Finally, we considered the von Karman flow between two counter-rotating bladed disks in a cylindrical cavity. We repeated the separation space analysis in different small sub-regions, in order to question the possible analogies in the flow dynamics with that of homogeneous rotating turbulence. The motivation of this is to investigate possible similar mechanisms that could persist in a variety of flow configurations, independently of the specifics of the energy injection mechanism. We found that, in the regions of the domain where the mean flow has a larger average rotation rate, the distributions of the statistics in separation space display some of the features typical of rotating turbulence.