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Evolution of the rotating Rayleigh–Taylor instability under the influence of magnetic fields

Published online by Cambridge University Press:  23 April 2025

Narinder Singh Open the ORCID record for Narinder Singh [Opens in a new window]  and
Anikesh Pal Open the ORCID record for Anikesh Pal [Opens in a new window]
Narinder Singh
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, U.P., India Department of Mechanical Engineering and Program in Integrated Applied Mathematics, University of New Hampshire, Durham, NH 03824, USA
Anikesh Pal*
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, U.P., India
*
Corresponding author: Anikesh Pal, [email protected]
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Abstract

The combined effects of the imposed vertical mean magnetic field ($B_0$, scaled as the Alfvèn velocity) and rotation on the heat transfer phenomenon driven by the Rayleigh–Taylor (RT) instability are investigated using direct numerical simulations. In the hydrodynamic (HD) case, as the strength of the Coriolis frequency ($f$) increases, the Coriolis force enhances the mixing of fluids that dampens the growth of the mixing layer height ($h$) and reversible exchanges between the fluids, leading to a reduction in the heat transport, characterised by the Nusselt number ($Nu$). In non-rotating magnetohydrodynamic (MHD) cases, we find a significant delay in the onset of RT instability with increasing $B_0$, consistent with the linear theory in the literature. The imposed $B_0$ forms vertically elongated thermal plumes that exhibit a larger reversible buoyancy flux due to limited mixing, enabling them to transport heat efficiently between the bottom hot fluid and the upper cold fluid. This leads to enhanced heat transfer in the initial regime of unbroken elongated plumes in non-rotating MHD cases compared to the corresponding HD case. In the turbulent regime of broken small-scale structures, the imposed $B_0$ collimates the flow along the vertical magnetic field lines, reducing vertical velocity fluctuations ($u_3^{\prime }$) and increasing the growth of $h$. The increased $h$ primarily drives the heat transfer enhancement in the turbulent regime of non-rotating MHD over the corresponding HD case. When rotation is added along with the imposed $B_0$, the growth and breakdown of vertically elongated plumes are inhibited by the instability-damping effect of the Coriolis force. Consequently, heat transfer is also reduced in the rotating MHD cases compared to the corresponding non-rotating MHD cases. Interestingly, heat transport in rotating MHD cases is enhanced compared to the corresponding rotating HD cases because $B_0$ reduces mixing and mitigates the instability-damping effect of the Coriolis force. The presence of the ultimate state regime $Nu\simeq Ra^{1/2}Pr^{1/2}$, where $Ra$ is the Rayleigh number and $Pr$ is the Prandtl number, is observed in the non-rotating HD and MHD cases. However, the rotating HD and MHD cases depart from this ultimate state scaling. Furthermore, the dynamic balance between different forces is analysed to understand the behaviour of the thermal plumes. The turbulent kinetic energy budget reveals the conversion of the turbulent kinetic energy, generated by the buoyancy flux, into turbulent magnetic energy.

JFM classification

MHD and Electrohydrodynamics: MHD turbulence Geophysical and Geological Flows: Rotating flows Convection: Buoyancy-driven instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1009 , 25 April 2025 , A46
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© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Singh and Pal supplementary material movie 1

The evolution of the temperature field in the vertical x2 - x3 center plane (x1 = 0) for the non-rotating HD case B00f0.
Download Singh and Pal supplementary material movie 1(File)
File 5.6 MB
Supplementary material: File

Singh and Pal supplementary material movie 2

The evolution of the temperature field in the vertical x2 - x3 center plane (x1 = 0) for the rotating HD case B00f8.
Download Singh and Pal supplementary material movie 2(File)
File 2.3 MB
Supplementary material: File

Singh and Pal supplementary material movie 3

The evolution of the temperature field in the vertical x2 - x3 center plane (x1 = 0) for the non-rotating MHD case B00.15f0.
Download Singh and Pal supplementary material movie 3(File)
File 3.8 MB
Supplementary material: File

Singh and Pal supplementary material movie 4

The evolution of the temperature field in the vertical x2 - x3 center plane (x1 = 0) for the rotating MHD case B00.15f8.
Download Singh and Pal supplementary material movie 4(File)
File 2.9 MB
Supplementary material: File

Singh and Pal supplementary material movie 5

The evolution of the temperature field in the vertical x2 - x3 center plane (x1 = 0) for the non-rotating MHD case B00.3f0.
Download Singh and Pal supplementary material movie 5(File)
File 2 MB