Magnetohydrodynamic waves in a rectangular vessel

Politis, Gerasimos; Pedcenko, Alex; Molokov, S.

doi:10.22364/mhd.53.1.3

Cited by 2 publications

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“…It should be noted that the nonlinear sloshing waves in the two directions have been previously observed in a hydrodynamic SW problem driven by a simple, rotating, harmonic force imitating the Lorentz force. 28 Nearly plane sloshing has been observed here in many stable nonlinear cases.…”

Section: Stability Diagram For Centered Circlesmentioning

confidence: 58%

The onset of instabilities and finite amplitude waves in a model of aluminum reduction cells with nonuniform cathode current

et al. 2021

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In aluminum reduction cells, the electric current density at the cathode is seldom uniform. This may be due to a variety of reasons. One of the reasons is that a mass of undissolved alumina may get enrobed by the cryolitic bath, and this mix freezes due to the decrease in temperature below the liquidus point. Thus, an electrically resistive solid layer ("mud") is formed at a part of the cathode. This leads to horizontal electric currents in the liquid aluminum layer, and their magnetohydrodynamic (MHD) interaction with the vertical magnetic field induces a rotating flow of aluminum. This may cause undesirable MHD instabilities. A quasi-two-dimensional model for the laboratory facility has been presented. The results show that the dominating feature of the flow is a depression of the free surface of the liquid metal above the mud spot. This is due to strong rotation of the liquid metal around the mud spot, which causes the centrifugal force. Other effects may include superimposed conventional MHD instability, which manifests itself in a rotating interface, modulated waves, reflection of the waves from the corners of the domain, sloshing, etc. It has been shown that small mud spots do not affect the cell stability, while the large ones may cause such deep depressions that the centrifugal force completely removes the liquid metal above the spot.

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Section: Stability Diagram For Centered Circlesmentioning

confidence: 58%

The onset of instabilities and finite amplitude waves in a model of aluminum reduction cells with nonuniform cathode current

et al. 2021

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Transport Properties of the Azimuthal Magnetorotational Instability

Guseva

Willis

Hollerbach

et al. 2017

ApJ

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The magnetorotational instability (MRI) is thought to be a powerful source of turbulence in Keplerian accretion disks. Motivated by recent laboratory experiments, we study the MRI driven by an azimuthal magnetic field in an electrically conducting fluid sheared between two concentric rotating cylinders. By adjusting the rotation rates of the cylinders, we approximate angular velocity profiles w µ r q . We perform direct numerical simulations of a steep profile close to the Rayleigh line  -q 2 and a quasi-Keplerian profile » -q 3 2 and cover wide ranges of Reynolds ( Ŕe 4 10 4 ) and magnetic Prandtl numbers (   0 Pm 1). In the quasi-Keplerian case, the onset of instability depends on the magnetic Reynolds number, with » Rm 50 c , and angular momentum transport scales as Pm Re 2 in the turbulent regime. The ratio of Maxwell to Reynolds stresses is set by Rm. At the onset of instability both stresses have similar magnitude, whereas the Reynolds stress vanishes or becomes even negative as Rm increases. For the profile close to the Rayleigh line, the instability shares these properties as long as 

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Magnetohydrodynamic waves in a rectangular vessel

Cited by 2 publications

References 0 publications

The onset of instabilities and finite amplitude waves in a model of aluminum reduction cells with nonuniform cathode current

The onset of instabilities and finite amplitude waves in a model of aluminum reduction cells with nonuniform cathode current

Transport Properties of the Azimuthal Magnetorotational Instability

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