PMID: 12786492Jun 6, 2003Paper

Linear magnetohydrodynamic Taylor-Couette instability for liquid sodium

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
G RüdigerDima Shalybkov

Abstract

The linear stability of MHD Taylor-Couette flow of infinite vertical extension is considered for liquid sodium with its small magnetic Prandtl number Pm of order 10(-5). The calculations are performed for a container with R(out)=2R(in), with an axial uniform magnetic field and with boundary conditions for both vacuum and perfect conductions. For resting outer cylinder subcritical excitation in comparison to the hydrodynamical case occurs for large Pm but it disappears for small Pm. For rotating outer cylinder the Rayleigh line plays an exceptional role. The hydromagnetic instability exists with Reynolds numbers exactly scaling with Pm(-1/2) so that the moderate values of order 10(4) (for Pm=10(-5)) result. For the smallest step beyond the Rayleigh line, however, the Reynolds numbers scale as 1/Pm leading to much higher values of order 10(6). Then it is the magnetic Reynolds number Rm that directs the excitation of the instability. It results as lower for insulating than for conducting walls. The magnetic Reynolds number has to exceed here values of order 10 leading to frequencies of about 20 Hz for the rotation of the inner cylinder if containers with (say) 10 cm radius are considered. With vacuum boundary conditions the excita...Continue Reading

References

Sep 21, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Günther Rüdiger, Dima Shalybkov

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Citations

Mar 5, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Günther Rüdiger, Dima Shalybkov
Feb 21, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Dima Shalybkov
May 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jānis PriedeGunter Gerbeth
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Stanislav BoldyrevVladimir Pariev
Feb 1, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Jacek Szklarski, Günther Rüdiger
Oct 4, 2005·Physical Review Letters·Rainer Hollerbach, Günther Rüdiger

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