Arnold–Beltrami–Childress flow
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The Arnold–Beltrami–Childress (ABC) flow or Gromeka–Arnold–Beltrami–Childress (GABC) 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:[1][2]
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 (1881)[3] name has been historically neglected, though much of the discussion has been done by him first.[4]