# 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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Article dans Phys. Rev. Fluids (2021)

## Quasiperiodic fluctuations of von Kármán turbulence driven by viscous stirring

Ryo Araki & Susumu Goto

We numerically simulate the von Kármán swirling flow driven by viscous stirring with a pair of inversely rotating smooth disks at moderate Reynolds numbers well beyond the first Hopf bifurcation. Despite the time-independent driving mechanism, quantities such as the kinetic energy and its dissipation rate fluctuate quasiperiodically with a period longer than the disk rotation period. We employ the toroidal-poloidal and boundary-bulk decompositions to explain the quasiperiodic fluctuations, which are always observed in the examined Reynolds-number range, and a nontrivial relation between the energy input and dissipation rates. The toroidal-poloidal decomposition of the energy reveals that the quasiperiodic fluctuations originate from the exchange of the two energy components ; the growth of the toroidal energy $E^\mathrm{tor}$ leads to the growth of the poloidal energy $E^\mathrm{pol}$ due to the centrifugal instability, whereas the growth of $E^\mathrm{pol}$ leads to the decay of $E^\mathrm{tor}$ due to the angular momentum transfer. The boundary-bulk decomposition distinguishes the qualitatively different dynamics coexisting in the system, which explains the nontrivial energy cycle.