# Atwood number

The Atwood number (A) is a dimensionless number in fluid dynamics used in the study of hydrodynamic instabilities in density stratified flows. It is a dimensionless density ratio defined as

$\mathrm{A} = \frac{\rho_1 - \rho_2} {\rho_1 + \rho_2}$

where

$\rho_1$ = density of heavier fluid
$\rho_2$ = density of lighter fluid

## Field of application

Atwood number is an important parameter in the study of Rayleigh–Taylor instability and Richtmyer–Meshkov instability. In Rayleigh–Taylor instability, the penetration distance of heavy fluid bubbles into the light fluid is a function of acceleration time scale, $\mathrm{A} g t^2$ [1] where g is the gravitational acceleration and t is the time.

## References

1. Glimm, J.; Grove, J. W.; Li, X.-L.; Oh, W.; Sharp, D. H. (2001). "A critical analysis of Rayleigh–Taylor growth rates". J. Comput. Phys. 169 (2): 652–677. Bibcode:2001JCoPh.169..652G. doi:10.1006/jcph.2000.6590.