Magnetic Prandtl number
The Magnetic Prandtl number (Prm) is a dimensionless quantity occurring in magnetohydrodynamics which approximates the ratio of momentum diffusivity (viscosity) and magnetic diffusivity. It is defined as:
- Rem is the magnetic Reynolds number
- Re is the Reynolds number
- ν is the momentum diffusivity (kinematic viscosity)
- η is the magnetic diffusivity
As another example, a magnetic Prandtl number of order unity is a widely accepted value for the thin accretion discs. Nevertheless this complicates the problem of launching jets: strong concentrations of magnetic field are required at the inner regions of the disc in order to launch jets, but a magnetic Prandtl number of order unity causes the field to diffuse away faster than it accretes inward.
- Critical Magnetic Prandtl Number for Small Scale Dynamo, Schekochihin, A.A., et al. 2004, Physical Review Letters, 92, 5