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One-winged butterflies: mode selection for azimuthal magnetorotational instability by thermal convection

Published online by Cambridge University Press:  27 August 2024

Ashish Mishra Open the ORCID record for Ashish Mishra [Opens in a new window] ,
George Mamatsashvili Open the ORCID record for George Mamatsashvili [Opens in a new window] ,
Martin Seilmayer Open the ORCID record for Martin Seilmayer [Opens in a new window]  and
Frank Stefani Open the ORCID record for Frank Stefani [Opens in a new window]
Ashish Mishra
Affiliation:
Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, D-01328 Dresden, Germany Center for Astronomy and Astrophysics, ER 3-2, TU Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
George Mamatsashvili*
Affiliation:
Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, D-01328 Dresden, Germany Abastumani Astrophysical Observatory, Abastumani 0301, Georgia
Martin Seilmayer
Affiliation:
Staatliche Studienakademie Bautzen, Löbauer Str. 1, 02625 Bautzen, Germany
Frank Stefani
Affiliation:
Helmholtz-Zentrum Dresden-Rossendorf, Bautzner Landstr. 400, D-01328 Dresden, Germany
*
†Email address for correspondence: g.mamatsashvili@hzdr.de
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Abstract

The effects of thermal convection on turbulence in accretion discs, and particularly its interplay with the magnetorotational instability (MRI), are of significant astrophysical interest. Despite extensive theoretical and numerical studies, such an interplay has not been explored experimentally. We conduct linear analysis of the azimuthal version of MRI (AMRI) in the presence of thermal convection and compare the results with our experimental data published before. We show that the critical Hartmann number ($Ha$) for the onset of AMRI is reduced by convection. Importantly, convection breaks symmetry between $m = \pm 1$ instability modes ($m$ is the azimuthal wavenumber). This preference for one mode over the other makes the AMRI wave appear as a ‘one-winged butterfly’.

JFM classification

Instability: Absolute/convective instability MHD and Electrohydrodynamics: Magneto convection
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 992 , 10 August 2024 , R1
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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References

Ali, M. & Weidman, P.D. 1990 On the stability of circular Couette flow with radial heating. J. Fluid Mech. 220, 53–84.CrossRefGoogle Scholar
Balbus, S.A. & Hawley, J.F. 1991 A powerful local shear instability in weakly magnetized disks. I. linear analysis. Astrophys. J. 376, 214–222.CrossRefGoogle Scholar
Bodo, G., Cattaneo, F., Mignone, A. & Rossi, P. 2013 Fully convective magnetorotational turbulence in stratified shearing boxes. Astrophys. J. Lett. 771 (2), L23.CrossRefGoogle Scholar
Coleman, M.S.B., Blaes, O., Hirose, S. & Hauschildt, P.H. 2018 Convection enhances magnetic turbulence in AM CVn accretion disks. Astrophys. J. 857 (1), 52.CrossRefGoogle Scholar
Held, L.E. & Latter, H.N. 2018 Hydrodynamic convection in accretion discs. Mon. Not. R. Astron. Soc. 480 (4), 4797–4816.Google Scholar
Held, L.E. & Latter, H.N. 2021 Magnetohydrodynamic convection in accretion discs. Mon. Not. R. Astron. Soc. 504 (2), 2940–2960.CrossRefGoogle Scholar
Held, L.E. & Mamatsashvili, G. 2022 MRI turbulence in accretion discs at large magnetic Prandtl numbers. Mon. Not. R. Astron. Soc. 517 (2), 2309–2330.CrossRefGoogle Scholar
Hollerbach, R. & Rüdiger, G. 2005 New type of magnetorotational instability in cylindrical Taylor–Couette flow. Phys. Rev. Lett. 95, 124501.CrossRefGoogle ScholarPubMed
Hollerbach, R., Teeluck, V. & Rüdiger, G. 2010 Nonaxisymmetric magnetorotational instabilities in cylindrical Taylor–Couette flow. Phys. Rev. Lett. 104, 044502.CrossRefGoogle ScholarPubMed
Klahr, H.H., Henning, T. & Kley, W. 1999 On the azimuthal structure of thermal convection in circumstellar disks. Astrophys. J. 514 (1), 325–343.CrossRefGoogle Scholar
Landau, L.D. & Lifshitz, E.M. 1987 Fluid Mechanics. Pergamon.Google Scholar
Mamatsashvili, G., Chagelishvili, G., Pessah, M.E., Stefani, F. & Bodo, G. 2020 Zero net flux MRI turbulence in disks: sustenance scheme and magnetic Prandtl number dependence. Astrophys. J. 904, 47.CrossRefGoogle Scholar
Mishra, A., Mamatsashvili, G., Galindo, V. & Stefani, F. 2021 Convective, absolute and global azimuthal magnetorotational instabilities. J. Fluid Mech. 922, R4.CrossRefGoogle Scholar
Mishra, A., Mamatsashvili, G. & Stefani, F. 2022 From helical to standard magnetorotational instability: predictions for upcoming liquid sodium experiments. Phys. Rev. Fluids 7 (6), 064802.CrossRefGoogle Scholar
Mishra, A., Mamatsashvili, G. & Stefani, F. 2023 Nonlinear evolution of magnetorotational instability in a magnetized Taylor–Couette flow: scaling properties and relation to upcoming DRESDYN-MRI experiment. Phys. Rev. Fluids 8 (8), 083902.CrossRefGoogle Scholar
Rincon, F. 2019 Dynamo theories. J. Plasma Phys. 85, 205850401.CrossRefGoogle Scholar
Seilmayer, M., Galindo, V., Gerbeth, G., Gundrum, T., Stefani, F., Gellert, M., Rüdiger, G., Schultz, M. & Hollerbach, R. 2014 Experimental evidence for nonaxisymmetric magnetorotational instability in a rotating liquid metal exposed to an azimuthal magnetic field. Phys. Rev. Lett. 113, 024505.CrossRefGoogle Scholar
Seilmayer, M., Ogbonna, J. & Stefani, F. 2020 Convection-caused symmetry breaking of azimuthal magnetorotational instability in a liquid metal Taylor–Couette flow. Magnetohydrodynamics 56, 225–236.Google Scholar
Seilmayer, M., Stefani, F. & Gundrum, T. 2016 Proceedings of the 10th PAMIR International Conference in Fundamental and Applied MHD, vol. 10, pp. 537–541. University of Cagliari.Google Scholar
Stefani, F., Gailitis, A., Gerbeth, G., Giesecke, A., Gundrum, T., Rüdiger, G., Seilmayer, M. & Vogt, T. 2019 The DRESDYN project: liquid metal experiments on dynamo action and magnetorotational instability. Geophys. Astrophys. Fluid Dyn. 113 (1-2), 51–70.CrossRefGoogle Scholar
Stefani, F., Gerbeth, G., Gundrum, T., Hollerbach, R., Priede, J., Rüediger, G. & Szklarski, J. 2009 Helical magnetorotational instability in a Taylor–Couette flow with strongly reduced Ekman pumping. Phys. Rev. E 80, 066303.CrossRefGoogle Scholar
Stefani, F., Gundrum, T., Gerbeth, G., Rüdiger, G., Schultz, M., Szklarski, J. & Hollerbach, R. 2006 Experimental evidence for magnetorotational instability in a Taylor–Couette flow under the influence of a helical magnetic field. Phys. Rev. Lett. 97, 184502.CrossRefGoogle Scholar
Umurhan, O.M., Menou, K. & Regev, O. 2007 Weakly nonlinear analysis of the magnetorotational instability in a model channel flow. Phys. Rev. Lett. 98 (3), 034501.CrossRefGoogle Scholar
Wang, Y., Gilson, E.P., Ebrahimi, F., Goodman, J. & Ji, H. 2022 Observation of axisymmetric standard magnetorotational instability in the laboratory. Phys. Rev. Lett. 129 (11), 115001.CrossRefGoogle ScholarPubMed