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Two-dimensional oscillation of convection roll in a finite liquid metal layer under a horizontal magnetic field

Published online by Cambridge University Press:  25 January 2021

Y. Tasaka Open the ORCID record for Y. Tasaka [Opens in a new window] ,
T. Yanagisawa Open the ORCID record for T. Yanagisawa [Opens in a new window] ,
K. Fujita ,
T. Miyagoshi Open the ORCID record for T. Miyagoshi [Opens in a new window]  and
A. Sakuraba
Y. Tasaka*
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo060-8628, Japan
T. Yanagisawa
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo060-8628, Japan Japan Agency for Marine–Earth Science and Technology (JAMSTEC), Yokosuka237-0061, Japan
K. Fujita
Affiliation:
Laboratory for Flow Control, Faculty of Engineering, Hokkaido University, Sapporo060-8628, Japan
T. Miyagoshi
Affiliation:
Japan Agency for Marine–Earth Science and Technology (JAMSTEC), Yokosuka237-0061, Japan
A. Sakuraba
Affiliation:
Department of Earth and Planetary Science, University of Tokyo, Tokyo113-0033, Japan
*
†Email address for correspondence: tasaka@eng.hokudai.ac.jp
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Abstract

We investigate the two-dimensional (2-D) oscillation of quasi-2-D convection rolls in a liquid metal layer confined by a vessel of aspect ratio five with an imposed horizontal magnetic field. Laboratory experiments were performed in the range of Rayleigh $Ra$ and Chandrasekhar $Q$ numbers of $7.9 \times 10^4 \le Ra \le 1.8 \times 10^5$ and $2.5 \times 10^4 \le Q \le 1.9 \times 10^5$ by decreasing $Q$ at set $Ra$-number intervals to elucidate the features and mechanisms of oscillatory convection. Ultrasonic velocity profile measurements and supplemental numerical simulations show that the 2-D oscillations are caused by oscillations of recirculation vortex pairs between the main rolls, which are intensified by periodic vorticity entrainment from the vortex pair by the main rolls. The investigations also suggest that the oscillations occur at sufficiently large Reynolds $Re$ numbers to induce instabilities on the vortex pair. The $Re$ number is smaller for larger $Q/Ra$ in the 2-D oscillation regime and the variations can be approximated by the effective $Ra$ number; namely, the value reduced by the critical value for the onset of convection depending on $Q$. The variations steepen with further large $Q/Ra$ and approach a scaling law of the velocity reduction as $(Ra/Q)^{1/2}$, which is established assuming that viscous dissipation is dominated by Hartmann braking at the walls perpendicular to the magnetic field. The results suggest that these phenomena are organized by the relationship between buoyancy and magnetic damping due to Hartmann braking.

JFM classification

MHD and Electrohydrodynamics: Magneto convection Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 911 , 25 March 2021 , A19
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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