Numerical range

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

${\mathrm{P}\mathrm{r}}_{\mathrm{m}}=\frac{\mathrm{R}{\mathrm{e}}_{\mathrm{m}}}{\mathrm{R}\mathrm{e}}=\frac{\nu }{\eta }=\frac{\text{viscous diffusion rate}}{\text{magnetic diffusion rate}}$

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, and in the interiors of planets and in liquid-metal laboratory dynamos is approximately 10^–5.

References

• Critical Magnetic Prandtl Number for Small Scale Dynamo, Schekochihin, A.A., et al. 2004, Physical Review Letters, 92, 5