ABC  FLOWS

         .......... because the existence of a dynamo effect is always a delicate question .
 

   A = Arnold, B=Beltrami, C=Childress flow.

   Steady, Periodic,Three-dimensional, incompressible flows with chaotic stream-lines.

    Candidates for fast dynamo action .

    U = (Asinkz + Ccosky,  Bsinkx + Acoskz,  Csinky+Bcoskx).

 
    When A,B and C are varied, windows of dynamo action may or may not be present.
     The size and location of the chaotic regions become quite different.
     For A=B=C=1 dynamo action is present in at least two windows in RM.
    If A or B or C vanishes the flow becomes 2D and non-chaotic. Dynamo action is possible with a 3D magnetic field. 
 

   Existence of stagnation points in the flow.

       a-type : The streamlines are converging in two directions and diverging in the other one.
       b-type : The streamlines are diverging in one direction and convergingin the other two.
 

    Chaotic  regions  ->   stagnation points

     Magnetic regions  ->  Guess!!!!
 

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