Atwood number

The Atwood number 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

:$A\; =\; frac\{\; ho\_1\; -\; ho\_2\}\; \{\; ho\_1\; +\; ho\_2\}$

where

: $ho\_1$ = density of heavier fluid: $ho\_2$ = 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, $A\; g\; t^2$ [Glimm, J., Grove, J. W., Li, X.-L., Oh, W., and Sharp, D. H., A critical analysis ofRayleigh–Taylor growth rates, J. Comput. Phys., 169, 652-677 (2001).] where "g" is the gravitational acceleration and "t" is the time.

References