Magnetic Prandtl number explained

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:

Pr _{m} = (Re _{m})/(Re) = (\nu)/(η) = (viscousdiffusionrate)/(magneticdiffusionrate)

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

Notes and References

1. Schekochihin . Alexander A. . Cowley . Steven C. . Maron . Jason L. . McWilliams . James C. . Critical Magnetic Prandtl Number for Small-Scale Dynamo . Physical Review Letters . 92 . 5 . 2004-02-03 . 0031-9007 . 10.1103/physrevlett.92.054502 . 054502. 14995310 . astro-ph/0308336 . 2004PhRvL..92e4502S . 119389465 .
2. Schumacher . Jörg . Sreenivasan . Katepalli R. . Colloquium: Unusual dynamics of convection in the Sun . Reviews of Modern Physics . 7 October 2020 . 92 . 4 . 041001 . 10.1103/RevModPhys.92.041001 . 2020RvMP...92d1001S . 225111979 . 17 April 2021.