Physics:Magnetic Prandtl number
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The Magnetic Prandtl number (Prm) is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) and magnetic diffusivity.[1] It is defined as:
- [math]\displaystyle{ \mathrm{Pr}_\mathrm{m} = \frac{\mathrm{Re_m}}{\mathrm{Re}} = \frac{\nu}{\eta} = \frac{\mbox{viscous diffusion rate}}{\mbox{magnetic diffusion rate}} }[/math]
where:
- Rem is the magnetic Reynolds number
- Re is the Reynolds number
- ν is the momentum diffusivity (kinematic viscosity)
- η is the magnetic diffusivity
At the base of the Sun's convection zone the Magnetic Prandtl number is approximately 10−2,[2] and in the interiors of planets and in liquid-metal laboratory dynamos is approximately 10−5.
See also
References
- ↑ Schekochihin, Alexander A.; Cowley, Steven C.; Maron, Jason L.; McWilliams, James C. (2004-02-03). "Critical Magnetic Prandtl Number for Small-Scale Dynamo". Physical Review Letters 92 (5): 054502. doi:10.1103/physrevlett.92.054502. ISSN 0031-9007. PMID 14995310. Bibcode: 2004PhRvL..92e4502S.
- ↑ Schumacher, Jörg; Sreenivasan, Katepalli R. (7 October 2020). "Colloquium: Unusual dynamics of convection in the Sun". Reviews of Modern Physics 92 (4): 041001. doi:10.1103/RevModPhys.92.041001. Bibcode: 2020RvMP...92d1001S. https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.92.041001. Retrieved 17 April 2021.
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