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

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

## Nos partenaires

Article dans Journal of Turbulence (2019)

## Kinetic-magnetic energy exchanges in rotating magnetohydrodynamic turbulence

Fatma Salma Baklouti, Amor Khlifi, Abdelaziz Salhi, Fabien Godeferd, Claude Cambon, Thierry Lehner

We use direct numerical simulations to study the dynamics of incompressible homogeneous turbulence subjected to a uniform magnetic field B in a rotating frame with rotation vector $\mathbf{\Omega}$. We consider two cases : $\mathbf{\Omega}∥\mathbf{B}$ and $\mathbf{\Omega}\perp\mathbf{B}$. The initial state is homogeneous isotropic hydrodynamic turbulence with Reynolds number $Re=u_\ell\mathrm{\ell}/\nu≃170$. The magnetic Prandtl number $Pm=\nu/\eta=1$ and the Elsasser number $\Lambda=B^2/(2\Omega\eta)=0.5$, $0.9$ or $2$. For both the cases $\mathbf{\Omega}∥\mathbf{B}$ and $\mathbf{\Omega}\perp\mathbf{B}$, the total energy decays as $\sim t^{−5/7}$ for $\Lambda=0.5$ and $0.9$, and as $\sim t^{−6/7}$ for $\Lambda=2$. In the spectral range $2 < k < 20$, the kinetic energy spectrum scales as $\sim k^{−p}$ where $p$ increases with time $(2\le p\le 4.2)$. This scaling is similar to that observed in quasi-static MHD. The two rotating MHD flow cases differ mainly in how kinetic and magnetic fluctuations exchange energy, with a mechanism mostly driven by the dynamics of the spectral buffer layer around $k^\Omega_{∥}=|\mathbf{\Omega}\cdot \mathbf{k}|/\Omega\approx0$. At $k^\Omega_{∥}=0$, the inertial and Alfvén waves frequencies vanish when $\mathbf{\Omega}∥\mathbf{B}$, but only the inertial waves frequency vanishes when $\mathbf{\Omega}\perp \mathbf{B}$. When $\mathbf{\Omega}∥\mathbf{B}$, rotation results in an increased reduction of magnetic fluctuations generation. In terms of anisotropy, we show that the elongated structures occurring in rapidly non-magnetised rotating flows are distorted or inhibited for $\mathbf{\Omega}\perp \mathbf{B}$, and weakened for $\mathbf{\Omega}∥\mathbf{B}$.