Convective, absolute and global azimuthal magnetorotational instabilities. (English) Zbl 1491.76033
Summary: We study the convective and absolute forms of azimuthal magnetorotational instability (AMRI) in a cylindrical Taylor-Couette (TC) flow with an imposed azimuthal magnetic field. We show that the domain of the convective AMRI is wider than that of the absolute AMRI. Actually, it is the absolute instability which is the most relevant and important for magnetic TC flow experiments. The absolute AMRI, unlike the convective one, stays in the device, displaying a sustained growth that can be experimentally detected. We also study the global AMRI in a TC flow of finite height using direct numerical simulation and find that its emerging butterfly-type structure – a spatio-temporal variation in the form of axially upward and downward travelling waves – is in a very good agreement with the linear analysis, which indicates the presence of two dominant absolute AMRI modes in the flow giving rise to this global butterfly pattern.
MSC:
| 76E25 | Stability and instability of magnetohydrodynamic and electrohydrodynamic flows |
| 76E15 | Absolute and convective instability and stability in hydrodynamic stability |
| 76E07 | Rotation in hydrodynamic stability |
| 76W05 | Magnetohydrodynamics and electrohydrodynamics |
| 76U05 | General theory of rotating fluids |
| 76M99 | Basic methods in fluid mechanics |
Keywords:
absolute instability; convective instability; Taylor-Couette flow; rotating cylinder; travelling wave; butterfly pattern; open-source code library OpenFOAMReferences:
| [1] | Balbus, S. & Hawley, J.1998Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys.70, 1-53. |
| [2] | Belson, B.A., Tu, J.H. & Rowley, C.W.2014Algorithm 945: modred—a parallelized model reduction library. ACM Trans. Math. Softw.40, 30. · Zbl 1369.65199 |
| [3] | Chomaz, J.-M.2005Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech.37, 357-392. · Zbl 1117.76027 |
| [4] | Gailitis, A.1996Design of a liquid sodium MHD dynamo experiment. Magnetohydrodynamics32, 58-62. |
| [5] | Gailitis, A. & Freibergs, Y.1980Nature of the instability of a turbulent dynamo. Magnetohydrodynamics16, 116-121. |
| [6] | Gailitis, A., Gerbeth, G., Gundrum, Th., Lielausis, O., Lipsbergs, G., Platacis, E. & Stefani, F.2018Self-excitation in a helical liquid metal flow: the Riga dynamo experiments. J. Plasma. Phys.84, 735840301. |
| [7] | Gammie, C.F.1996Layered accretion in T Tauri disks. Astrophys. J.457, 355-362. |
| [8] | Hollerbach, R., Teeluck, V. & Rüdiger, G.2010Nonaxisymmetric magnetorotational instabilities in cylindrical Taylor-Couette flow. Phys. Rev. Lett.104, 044502. |
| [9] | Huerre, P. & Monkewitz, P.A.1990Local and global instabilities in spatially developing flows. Ann. Rev. Fluid Mech.22, 473-537. · Zbl 0734.76021 |
| [10] | Ji, H., Goodman, J. & Kageyama, A.2001Magnetorotational instability in a rotating liquid metal annulus. Mon. Not. R. Astron. Soc.325, L1-L5. |
| [11] | Kirillov, O.N., Stefani, F. & Fukumoto, Y.2014Local instabilities in magnetized rotational flows: a short-wavelength approach. J. Fluid Mech.760, 591-633. · Zbl 1331.76130 |
| [12] | Lesur, G., Kunz, M. & Fromang, S.2014Thanatology in protoplanetary discs. The combined influence of Ohmic, Hall, and ambipolar diffusion on dead zones. Astron. Astrophys.566, A56. |
| [13] | Liu, W., Goodman, J., Herron, I. & Ji, H.2006Helical magnetorotational instability in magnetized Taylor-Couette flow. Phys. Rev. E74, 056302. |
| [14] | Mamatsashvili, G., Chagelishvili, G., Pessah, M.E., Stefani, F. & Bodo, G.2020Zero net flux MRI turbulence in disks: sustenance scheme and magnetic Prandtl number dependence. Astrophys. J.904, 47. |
| [15] | Monchaux, R., et al.2009The von Kármán sodium experiment: turbulent dynamical dynamos. Phys. Fluids21, 035108. |
| [16] | Müller, U., Stieglitz, R., Busse, F.H. & Tilgner, A.2008The Karlsruhe two-scale dynamo experiment. C. R. Phys.9, 729-740. |
| [17] | Nornberg, M.D., Ji, H., Schartman, E., Roach, A. & Goodman, J.2010Observation of magnetocoriolis waves in a liquid metal Taylor-Couette experiment. Phys. Rev. Lett.104, 074501. |
| [18] | Ponomarenko, Yu.B.1973On the theory of hydromagnetic dynamo. J. Appl. Mech. Tech. Phys.14, 775-779. |
| [19] | Priede, J. & Gerbeth, G.2009Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow. Phys. Rev. E79, 046310. |
| [20] | Rincon, F.2019Dynamo theories. J. Plasma Phys.85, 205850401. |
| [21] | Rüdiger, G., Gellert, M., Hollerbach, R., Schultz, M. & Stefani, F.2018Stability and instability of hydromagnetic Taylor-Couette flows. Phys. Rep.741, 1-89. · Zbl 1392.76015 |
| [22] | Seilmayer, M., Galindo, V., Gerbeth, G., Gundrum, Th., Stefani, F., Gellert, M., Rüdiger, G., Schultz, M. & Hollerbach, R.2014Experimental evidence for nonaxisymmetric magnetorotational instability in a rotating liquid metal exposed to an azimuthal magnetic field. Phys. Rev. Lett.113, 024505. |
| [23] | Seilmayer, M., Ogbonna, J. & Stefani, F.2020Convection-caused symmetry breaking of azimuthal magnetorotational instability in a liquid metal Taylor-Couette flow. Magnetohydrodynamics56, 225. |
| [24] | Sisan, D., Mujica, N., Tillotson, W., Huang, Y., Dorland, W., Hassam, A., Antonsen, T. & Lathrop, D.P.2004Experimental observation and characterization of the magnetorotational instability. Phys. Rev. Lett.93, 114502. |
| [25] | Stefani, F., Gailitis, A. & Gerbeth, G.2008Magnetohydrodynamic experiments on cosmic magnetic fields. Z. Angew. Math. Mech.88, 930-954. · Zbl 1160.76058 |
| [26] | Stefani, F., Gailitis, A., Gerbeth, G., Giesecke, A., Gundrum, Th., Rüdiger, G., Seilmayer, M. & Vogt, T.2019The DRESDYN project: liquid metal experiments on dynamo action and magnetorotational instability. Geophys. Astrophys. Fluid Dyn.113, 51-70. · Zbl 1499.86021 |
| [27] | Stefani, F., Gerbeth, G. & Gailitis, A.1999 Velocity profile optimization for the riga dynamo experiment. In Transfer Phenomena in Magnetohydrodynamics and Electroconducting Flows (ed. A. Alemany, P. Marty & J.P. Thibault), Fluid Mechanics and its Applications, vol. 51, pp. 31-44. Kluwer Academic Publishers. |
| [28] | Stefani, F., Gerbeth, G., Gundrum, Th., Hollerbach, R., Priede, J., Rüdiger, G. & Szklarski, J.2009Helical magnetorotational instability in a Taylor-Couette flow with strongly reduced Ekman pumping. Phys. Rev. E80, 066303. |
| [29] | Stefani, F., Gundrum, Th., Gerbeth, G., Rüdiger, G., Schultz, M., Szklarski, J. & Hollerbach, R.2006Experimental evidence for magnetorotational instability in a Taylor-Couette flow under the influence of a helical magnetic field. Phys. Rev. Lett.97, 184502. |
| [30] | Stefani, F. & Kirillov, O.N.2015Destabilization of rotating flows with positive shear by azimuthal magnetic fields. Phys. Rev. E92, 051001. |
| [31] | Tobias, S.M., Proctor, M.R.E. & Knobloch, E.1997The role of absolute instability in the solar dynamo. Astron. Astrophys.318, L55. |
| [32] | Weber, N., Galindo, V., Stefani, F., Weier, T. & Wondrak, Th.2013Numerical simulation of the Tayler instability in liquid metals. New J. Phys.15, 043034. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
