Large scale analysis of three-dimensional turbulent von Kármán swirling flows

In this paper, we are interested by the large-scale structures and dynamics of turbulent von Kármán (vK) swirling flows. In particular, we investigate the symmetry properties of these structures for a wide range of turbulent flow regimes. Results from scheme-consistency preserving large eddy simulations model, performed at different Reynolds numbers (Re), are carefully analyzed with different handy modal decompositions to understand the dynamical ingredients affecting the flow symmetries. Applying proper orthogonal decomposition (POD) on three-dimensional three-components simulated velocity fields, we numerically corroborate for the first time previous experimental studies which showed that the flow can be characterized by a metastable state at Re>104, associated with an axisymmetric one-cell structure that breaks the Rπ− symmetry (rotation of π with respect to any radial axis passing through the center of the container), inducing long term intermittent fluctuations in the angular momentum. Then, applying POD on a two-dimensional three-component Fourier representation of the velocity fields, we show in detail how the different azimuthal Fourier modes contribute to the statistically stationary mean state and to the large fluctuations, relying on energy decomposition, symmetry, and spatial analysis of the flow.