Abstract
The region of instability of the Hill-Shafranov viscous MHD vortex with respect to azimuthal axisymmetric perturbations of the velocity field is determined numerically as a function of the Reynolds number and magnetization in a linear formulation. An approximate formulation of the linear stability problem for MHD flows with circular streamlines is considered. The further evolution of the perturbations in the supercritical region is studied using a nonlinear analog model (a simplified initial system of equations that takes into account some important properties of the basic equations). For this model, the secondary flows resulting from the instability are determined.
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M. A. Gol’dshtik, E. M. Zhdanova, and V. N. Shtern, “Spontaneous swirling of a submerged jet,” Dokl. Akad. Nauk SSSR, 277, No. 4, 815–818 (1984).
M. A. Gol’dshtik, V. N. Shtern, and N. I. Yavorskii, Viscous Flows with Paradoxical Properties [in Russian], Nauka, Novosibirsk (1989).
M. A. Lavrent’ev and B. V. Shabat, Problems of Hydrodynamics and Their Mathematical Models [in Russian], Nauka, Moscow (1973).
A. M. Sagalakov and A. Yu. Yudintsev, “Three-dimensional self-oscillating magnetohydrodynamic flows of a fluid of finite conductivity in an annular channel in the presence of a longitudinal magnetic field,” Magn. Gidrodin., No. 1, 41–48 (1993).
B. A. Lugovtsov, “Is spontaneous swirling of axisymmetric flow possible?” J. Appl. Mech. Tech. Phys., 35, No. 2, 207–210 (1994).
Yu. G. Gubarev and B. A. Lugovtsov, “Spontaneous swirling in axisymmetric flows,” J. Appl. Mech. Tech. Phys., 36, No. 4, 52–59 (1995).
B. A. Lugovtsov, “Spontaneous swirling in axisymmetric flows of a conducting fluid in a magnetic field,” J. Appl. Mech. Tech. Phys., 37, No. 6, 802–809 (1996).
B. A. Lugovtsov, “Axisymmetric spontaneous swirling in an ideally conducting fluid in a magnetic field,” J. Appl. Mech. Tech. Phys., 38, No. 6, 839–841 (1997).
B. A. Lugovtsov, “Rotationally symmetrical spontaneous swirling in MHD flows,” J. Appl. Mech. Tech. Phys., 41, No. 5, 870–878 (2000).
J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press (1970)
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 40–50, May–June, 2007.
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Kotel’nikova, M.S., Lugovtsov, B.A. Spontaneous swirling in axisymmetric MHD flows of an ideally conducting fluid with closed streamlines. J Appl Mech Tech Phys 48, 331–339 (2007). https://doi.org/10.1007/s10808-007-0042-7
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DOI: https://doi.org/10.1007/s10808-007-0042-7