Astronomy: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 India n 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:

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

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

The Chandrasekhar number is thus defined as:

$Q=\frac{{B_0}^2{d}^2}{{\mu }_0\rho \nu \lambda }$

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, $Ha$, by the relation:

$Q=H{a}^2$

See also

• Rayleigh number
• Taylor number