Magnetic Prandtl number
The Magnetic Prandtl number is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) and magnetic diffusivity. It is defined as:
\[\mathit{Pr_m} = \frac{\mathit{Re_m}}{\mathit{Re}} = \frac{\nu}{\eta} = \frac{\mbox{viscous diffusion rate}}{\mbox{magnetic diffusion rate}}\]
where:
- \(\mathit{Re_m}\) is the magnetic Reynolds number
- \(\mathit{Re}\) is the Reynolds number
- \(\nu\) is the momentum diffusivity (kinematic viscosity)
- \(\eta\) is the magnetic diffusivity
At the base of the Sun's convection zone the Magnetic Prandtl number is approximately \(10^{-2}\), and in the interiors of planets and in liquid-metal laboratory dynamos is approximately \(10^{-5}\).
See also
References
- Critical Magnetic Prandtl Number for Small Scale Dynamo, Schekochihin, A.A., et al. 2004, Physical Review Letters, 92, 5pt:Número de Prandtl magnético
