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Waves and non-propagating modes in stratified MHD turbulence subject to a weak mean magnetic field

Published online by Cambridge University Press:  11 December 2024

A. Salhi Open the ORCID record for A. Salhi [Opens in a new window] ,
A. Khlifi Open the ORCID record for A. Khlifi [Opens in a new window] ,
R. Marino Open the ORCID record for R. Marino [Opens in a new window] ,
F. Feraco Open the ORCID record for F. Feraco [Opens in a new window] ,
R. Foldes Open the ORCID record for R. Foldes [Opens in a new window]  and
C. Cambon Open the ORCID record for C. Cambon [Opens in a new window]
A. Salhi*
Affiliation:
Faculty of Sciences of Tunis, Tunis El Manar University, 2092 El Manar, Tunisia
A. Khlifi
Affiliation:
LR99ES17, Materials, Organisation and Properties, Faculty of Sciences of Tunis, 2092 El Manar, Tunisia Preparatory Institute for Engineering Studies of Bizerte, University of Carthage, 7021 Bizerte, Tunisia
R. Marino
Affiliation:
CNRS, École Centrale de Lyon, INSA de Lyon, Université Claude Bernard Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, F-69134 Écully, France
F. Feraco
Affiliation:
CNRS, École Centrale de Lyon, INSA de Lyon, Université Claude Bernard Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, F-69134 Écully, France Dipartimento di Fisica, Università della Calabria, Rende I-87036, Italy
R. Foldes
Affiliation:
CNRS, École Centrale de Lyon, INSA de Lyon, Université Claude Bernard Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, F-69134 Écully, France
C. Cambon
Affiliation:
CNRS, École Centrale de Lyon, INSA de Lyon, Université Claude Bernard Lyon 1, Laboratoire de Mécanique des Fluides et d'Acoustique, F-69134 Écully, France
*
†Email address for correspondence: [email protected]
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Abstract

In this study we consider a freely decaying, stably stratified homogeneous magnetohydrodynamic turbulent plasma with a weak vertical background magnetic field ($\boldsymbol {B}_0=B_0\hat {\boldsymbol {z}}),$ aligned with the density gradient of strength $N$ (i.e. Brunt–Väisälä frequency). Both linear theory and direct numerical simulations (DNS) are used to analyse the flow dynamics for a Boussinesq fluid with unitary magnetic and thermal Prandtl numbers. We implemented a normal mode decomposition emphasizing different types of motions depending on whether both the Froude $F_r$ and Alfvén–Mach $M$ numbers are small or only $F_r$ is small but $M$ is finite. In the former case, there is a non-propagating (NP) mode and fast modes: Alfvén waves with frequency $\omega _a$ and magnetogravity waves with frequency $\omega _{ag}$. In the latter case, there are fast gravity waves with frequency $\omega _g$ and slow modes: NP mode and slow Alfvén waves. The numerical simulations carried out are started from initial isotropic conditions with zero initial magnetic and density fluctuations, so that the initial energy of the NP mode is strictly zero, for $0< B_0/(L_iN)\leqslant 0.12$ and a weak mean magnetic field ($B_0=0.2$ or $B_0=0.4),$ where $L_i$ denotes the isotropic integral length scale. The DNS results indicate a weak turbulence regime for which $F_r$ is small and $M$ is finite. It is found that the vertical magnetic energy as well as the energy of the NP mode are drastically reduced as $N$ increases, while there is instead a forward cascade even for the magnetic field. The contribution coming from the energy of fast (gravity) waves does not exceed $50\,\%,$ while that coming from the energy of the NP mode does not exceed $10\,\%.$ Vertical motions are more affected by the effect of stratification than by the effect of the mean magnetic field, while it is the opposite for horizontal motions. We show that the spectrum of slow (Alfvén) waves and fast (gravity) waves tends to follow the power law $k_\perp ^{-3}$ for a wide range of time, $3< t<20$. At high vertical (or horizontal) wavenumbers, the main contribution to total energy comes from the energy of slow Alfvén waves. At large and intermediate horizontal (or vertical) scales, the spectra of the energy of NP mode exhibit a flat shape.

JFM classification

MHD and Electrohydrodynamics: MHD turbulence Turbulent Flows: Stratified turbulence Turbulent Flows: Wave-turbulence interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1001 , 25 December 2024 , A28
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© The Author(s), 2024. Published by Cambridge University Press

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