WOLFRAM|DEMONSTRATIONS PROJECT

Arnold-Beltrami-Childress (ABC) Flows

​
t
29.5
view
lines
spheres
constants
α
-1.28805
β
0.0314159
γ
-0.502655
initial positions
x
0
-0.188495
z
0
0.251327
z
0
-0.282743
δ
0.0025
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
δ
are shown; as you increase the value, the number of initial conditions decreases.