Influence of an axial magnetic field on the stability of spherical Couette flows with different gap widths

Travnikov, V. V.; Eckert, Kerstin; Odenbach, Stefan

doi:10.1007/s00707-011-0452-8

Cited by 28 publications

(55 citation statements)

References 19 publications

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“…This super-rotation was recently observed experimentally in the DTS experiment, using a spherical shell filled with liquid Sodium in presence of a dipolar magnetic field imposed by a permanent magnet inside the inner sphere [11], [12]. More recently, it was shown that several non-axisymmetric instabilities are generated from these magnetized spherical Couette flows, including destabilization of the meridional return flow [13], [14], or from the free shear layers and jets produced by the magnetic field [15], [16].…”

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confidence: 99%

Instabilities in magnetized spherical Couette flow

Gissinger

Goodman

2011

Phys. Rev. E

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We report 3D numerical simulations of the flow of an electrically conducting fluid in a spherical shell when an magnetic field is applied. Different spherical Couette configurations are investigated, by varying the rotation ratio between the inner and the outer sphere, the geometry of the imposed field, and the magnetic boundary conditions on the inner sphere. Either a Stewartson layer or a Shercliff layer, accompanied by a radial jet, can be generated depending on the rotation speeds and the magnetic field strength, and various non-axisymmetric destabilizations of the flow are observed. We show that instabilities arising from the presence of boundaries present striking similarities with the magnetorotational instability (MRI). To this end, we compare our numerical results to experimental observations of the Maryland experiment [Sisan et al, Phys. Rev. Lett. 93, 114502 (2004)], who claimed to observe MRI in a similar setup.

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confidence: 99%

Instabilities in magnetized spherical Couette flow

Gissinger

Goodman

2011

Phys. Rev. E

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“…After a primary Hopf bifurcation, several branches of periodic rotating waves (RW) appear, which in turn give rise to quasiperiodic modulated rotating waves (MRW) at a secondary Hopf bifurcations. In case of the MSC problem the existence of RW has been confirmed by experimental studies 41 14,17,29 by describing the type of flows in terms of bifurcation theory.…”

Section: Introductionmentioning

confidence: 83%

“…This configuration has been previously addressed in the numerical studies of Refs. 14,17,29,32. Beyond a critical value Re c the basic flow becomes unstable to non-axisymmetric perturbations whose topology depends strongly on the applied magnetic field strength (measured by the Hartman number Ha).…”

Section: Introductionmentioning

confidence: 99%

Chaotic wave dynamics in weakly magnetized spherical Couette flows

García

Seilmayer

Giesecke

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Direct numerical simulations of a liquid metal filling the gap between two concentric spheres are presented. The flow is governed by the interplay between the rotation of the inner sphere (measured by the Reynolds number Re) and a weak externally applied axial magnetic field (measured by the Hartmann number Ha). By varying the latter a rich variety of flow features, both in terms of spatial symmetry and temporal dependence, is obtained. Flows with two or three independent frequencies describing their time evolution are found as a result of Hopf bifurcations. They are stable on a sufficiently large interval of Hartmann numbers where regions of multistability of two, three and even four types of these different flows are detected. The temporal character of the solutions is analysed by means of an accurate frequency analysis and Poincaré sections. An unstable branch of flows undergoing a period doubling cascade and frequency locking of three-frequency solutions is described as well. a)

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“…Later, many researchers have extensively studied this problem for a variety of imposed magnetic fields (axial and/or dipolar) and different boundary conditions, i.e., insulating or conducting walls. Among these are Hollerbach [9], Hollerbach and Skinner [10], Schmitt et al [11], Nataf et al [12], Travnikov et al [13], Gissinger et al [14], Kaplan [15], Lalaoua and Bouabdallah [16]. Numerical studies of Dormy et al [17] and Hollerbach et al [18] highlight the nature and structure of the flow that appear when the magnetic field lines are not parallel to the rotation axis.…”

Section: Introductionmentioning

confidence: 99%

Stabilty of a Conducting Fluid Contained Between Two Rotating Spheres Subjected to a Dipolar Magnetic Field

Lalaoua¹,

Bouda²,

Merah³

2017

Topical Problems of Fluid Mechanics 2017

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The motion of fluid enclosed between two concentric rotating spheres, so-called the spherical Couette flow, presents a wealth of phenomena encountered during laminar turbulent transition, depending on the gap width and the Reynolds number. In the case, where the fluid is taken as an electrically conducting, and a magnetic field is imposed, knows as magnetic spherical Couette flow, the flow behaviour and pattern formation can be drastically changed. This flow problem offers the possibility of exploring a wide variety of instabilities and plays an important role to understand the geophysics and astrophysics phenomena as well as to study the dynamics of the Earth's outer core. In this paper, the flow of an electrically conducting fluid, liquid sodium, in an annulus between two concentric rotating spheres subjected to a dipolar magnetic field is investigated numerically using a three-dimensional computational fluid dynamics. The outer sphere is stationary while the inner one rotates freely about a vertical axis passing through its center. The spherical shell is completely filled with liquid sodium. The numerical studies are performed for the medium gap width β=0.18, and carried out for a wide range of Hartmann number, Ha, from 0 up to 5000. Both inner and outer spheres are considered insulating walls. Computations for the onset of Taylor vortices in spherical Couette flow without an imposed magnetic field show a good agreement with the previous works. It is established that the imposed magnetic field radically alters the flow structures leading to significant topological changes on the flow patterns. In particular, we found that depending on the magnetic field imposed, the basic state consists of either a shear layer or a counter-rotating jet and both becoming thinner and thinner for increasingly strong imposed fields, but with the jet also becoming stronger.

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Influence of an axial magnetic field on the stability of spherical Couette flows with different gap widths

Cited by 28 publications

References 19 publications

Instabilities in magnetized spherical Couette flow

Instabilities in magnetized spherical Couette flow

Chaotic wave dynamics in weakly magnetized spherical Couette flows

Stabilty of a Conducting Fluid Contained Between Two Rotating Spheres Subjected to a Dipolar Magnetic Field

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