Magnetic Prandtl number

The Magnetic Prandtl number (Pr_m) is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) and magnetic diffusivity. ^[1] It is defined as:

$${\displaystyle \mathrm {{Pr}_{m}} ={\frac {\mathrm {{Re}_{m}} }{\mathrm {Re} }}={\frac {\nu }{\eta }}={\frac {\text{viscous diffusion rate}}{\text{magnetic diffusion rate}}}}$$

where:

• Re_m 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

• Prandtl number

References

1. 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. arXiv: astro-ph/0308336 . Bibcode:2004PhRvL..92e4502S. doi:10.1103/physrevlett.92.054502. ISSN   0031-9007. PMID   14995310. S2CID   119389465.
2. Schumacher, Jörg; Sreenivasan, Katepalli R. (7 October 2020). "Colloquium: Unusual dynamics of convection in the Sun" . Reviews of Modern Physics. 92 (4) 041001. Bibcode:2020RvMP...92d1001S. doi:10.1103/RevModPhys.92.041001. S2CID   225111979 . Retrieved 17 April 2021.