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
regions -> Guess!!!!