Fluid Mechanics and Acoustics Laboratory - UMR 5509

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Home > Teams > Turbulence & Instabilities > Publications T&I > Publications T&I 2019

Article in 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

Kinetic-magnetic energy exchanges in rotating magnetohydrodynamic turbulence

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 $\mathbf{\Omega}∥\mathbf{B}$.
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