Arnold-Beltrami-Childress (ABC) Flows

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The ABC flow, a three-parameter velocity field that provides a simple stationary solution of Euler's equations in three dimensions for incompressible, inviscid fluid flows, can be considered to be a prototype for the study of turbulence. It is named after V. Arnold, E. Beltrami, and S. Childress.


Trajectories for a set of initial conditions differing by factors of are shown; as you increase the value, the number of initial conditions decreases.


Contributed by: Enrique Zeleny (August 2012)
Open content licensed under CC BY-NC-SA



The ABC flow is explicitly given by:

, , .


[1] R. Ricca, An Introduction to the Geometry and Topology of Fluid Flows, Dordrecht; Boston: Kluwer Academic Publishers, 2001.

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