Chandrasekhar number


Chandrasekhar number

The Chandrasekhar number is a dimensionless quantity used in magnetic convection to represent ratio of the Lorentz force to the viscosity. It is named after the Indian astrophysicist Subrahmanyan Chandrasekhar.

The number's main function is as a measure of the magnetic field, being proportional to the square of a characteristic magnetic field in a system.

Definition

The Chandrasekhar number is usually denoted by the letter \ Q, and is motivated by a dimensionless form of the Navier-Stokes equation in the presence of a magnetic force in the equations of magnetohydrodynamics:

\frac{1}{\sigma}\left(\frac{\partial^{}\mathbf{u}}{\partial t^{}}\ +\ (\mathbf{u} \cdot \nabla) \mathbf{u}\right)\ =\ - {\mathbf \nabla }p\ +\ \nabla^2 \mathbf{u}\ +\frac {\sigma}{\zeta} {Q}\ ({\mathbf \nabla} \wedge \mathbf{B}) \wedge\mathbf{B},

where \ \sigma is the Prandtl number, and \ \zeta is the magnetic Prandtl number.

The Chandrasekhar number is thus defined as [1]:

 {Q}\ =\ \frac{{B_0}^2 d^2}{\mu_0 \rho \nu \lambda}

where \ \mu_0 is the magnetic permeability, \ \rho is the density of the fluid, \ \nu is the kinematic viscosity, and \ \lambda is the magnetic diffusivity. \ B_0 and \ d are a characteristic magnetic field and a length scale of the system respectively.

It is related to the Hartmann number, \ H, by the relation:

 Q\ {=}\ H^2\

References

  1. ^ N.E. Hurlburt, P.C. Matthews and A.M. Rucklidge, "Solar Magnetoconvection," Solar Physics, 192, p109-118 (2000)

See also


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