The Chandrasekhar number is a

dimensionless quantity A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...

used in magnetic

convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convec ...

to represent ratio of the

Lorentz force In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...

to the

viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

. It is named after the

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

n astrophysicist

Subrahmanyan Chandrasekhar Subrahmanyan Chandrasekhar (; ) (19 October 1910 – 21 August 1995) was an Indian-American theoretical physicist who spent his professional life in the United States. He shared the 1983 Nobel Prize for Physics with William A. Fowler for "... ...

. The number's main function is as a measure of the

magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...

, 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 Magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is the study of the magnetic properties and behaviour of electrically conducting fluids. Examples of such magnetofluids include plasmas, liquid metals, ...

: ::

\frac\left(\frac\ +\ (\mathbf \cdot \nabla) \mathbf\right)\ =\ - p\ +\ \nabla^2 \mathbf\ +\frac  \ ( \wedge \mathbf) \wedge\mathbf,

where

\ \sigma

is the

Prandtl number The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as: : \mathrm = \frac = \frac ...

, and

\ \zeta

is the magnetic Prandtl number. The Chandrasekhar number is thus defined as:N.E. Hurlburt, P.C. Matthews and A.M. Rucklidge, "Solar Magnetoconvection," ''Solar Physics'', 192, p109-118 (2000) ::

\ =\ \frac

where

\ \mu_0

is the

magnetic permeability In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined by William ...

\ \rho

is the

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

of the fluid,

\ \nu

is the

kinematic viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inter ...

, and

\ \lambda

is the

magnetic diffusivity The magnetic diffusivity is a parameter in plasma physics which appears in the magnetic Reynolds number. It has SI units of m²/s and is defined as:W. Baumjohann and R. A. Treumann, ''Basic Space Plasma Physics'', Imperial College Press, 1997. :\e ...

\ B_0

and

\ d

are a characteristic magnetic field and a length scale of the system respectively. It is related to the

Hartmann number The Hartmann number (Ha) is the ratio of electromagnetic force to the viscous force, first introduced by Julius Hartmann (18811951) of Denmark. It is frequently encountered in fluid flows through magnetic fields. It is defined by: : \mathrm = B L\s ...

\ Ha

, by the relation: ::

Q\ \ Ha^2\

References

{{Dimensionless numbers in fluid mechanics

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 ...

Magnetohydrodynamics Dimensionless numbers of fluid mechanics Fluid dynamics Astrophysics

Definition

See also

References