Arnold–Beltrami–Childress flow
The Arnold–Beltrami–Childress flow or Gromeka–Arnold–Beltrami–Childress 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 is the material derivative of the Lagrangian motion of a fluid parcel located at
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 Stephen Childress. Ippolit S. Gromeka's name has been historically neglected, though much of the discussion has been done by him first.
