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:

$R e m$ is the magnetic Reynolds number
$R e$ 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

Categories:

Dimensionless numbers
Fluid mechanics

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Magnetic Prandtl number

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