Kinetic-magnetic energy exchanges in rotating magnetohydrodynamic turbulence

ABSTRACT

We use direct numerical simulations to study the dynamics of incompressible homogeneous turbulence subjected to a uniform magnetic field $\mathit{B}$ in a rotating frame with rotation vector $\mathbf{\Omega }$. We consider two cases: $\mathbf{\Omega }\parallel \mathit{B}$ and $\mathbf{\Omega }\perp \mathit{B}$. The initial state is homogeneous isotropic hydrodynamic turbulence with Reynolds number $\mathrm{R}\mathrm{e}=u_{l}l/\nu \simeq 170.$ The magnetic Prandtl number $\mathrm{P}\mathrm{m}=\nu /\eta =1$ and the Elsasser number $\mathrm{\Lambda }=B^2/\left(2\mathrm{\Omega }\eta \right)=0.5$, 0.9 or 2. For both the cases $\mathbf{\Omega }\parallel \mathit{B}$ and $\mathbf{\Omega }\perp \mathit{B},$ the total energy decays as $\sim t^{-5/7}$ for $\mathrm{\Lambda }=0.5$ and 0.9, and as $\sim t^{-6/7}$ for $\mathrm{\Lambda }=2$. 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 $k_{\parallel }^{\mathrm{\Omega }}=|\mathbf{\Omega }\mathbf{\cdot }\mathit{k}|/\mathrm{\Omega }\approx 0$. At $k_{\parallel }^{\mathrm{\Omega }}=0,$ the inertial and Alfvén waves frequencies vanish when $\mathbf{\Omega }\parallel \mathit{B}$, but only the inertial waves frequency vanishes when $\mathbf{\Omega }\perp \mathit{B}$. When $\mathbf{\Omega }\parallel \mathit{B}$, 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 $\mathbf{\Omega }\perp \mathit{B}$, and weakened for $\mathbf{\Omega }\parallel \mathit{B}$.

KEYWORDS:

• Direct numerical simulations
• homogeneous rotating magnetohydrodynamic turbulence
• kinetic-magnetic energy exchanges
• inertial waves
• Alfvén waves

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

F. S. Baklouti http://orcid.org/0000-0002-5863-196X