Arnold–Beltrami–Childress flow

The Arnold–Beltrami–Childress (ABC) flow is a three-dimensional incompressible velocity field which is an exact solution of Euler's equation. Its representation in Cartesian coordinates is the following:

where ( x ˙ , y ˙ , z ˙ ) is the material derivative of the Lagrangian motion of a fluid parcel located at ( x ( t ) , y ( t ) , z ( t ) ) .

It is notable as a simple example of a fluid flow that can have chaotic trajectories.

It is named after Vladimir Arnold, Eugenio Beltrami, and Steven Childress.