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 ${\displaystyle ({\dot {x}},{\dot {y}},{\dot {z}})}$ is the material derivative of the Lagrangian motion of a fluid parcel located at ${\displaystyle (x(t),y(t),z(t)).}$

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