Dynamo action in a family of flows with chaotic streamlines
Abstract
The kinematic dynamo problem is investigated for the class of flows u = (A sin z + C cos y, B sin x + A cos z, C sin y + B cos x) which in general have chaotic streamlines. The numerical methods used to solve the problem are described in detail, and results are described from the cases where A, B, and C are nonzero and equal or unequal, respectively. The case where one of A, B, or C is zero is discussed. In this case, the flow is integrable and nonchaotic, but interesting dynamo effects exist, albeit presumably slow ones. The implications of the findings for alphaeffect dynamo theory are examined, and some still outstanding problems are mentioned.
 Publication:

Geophysical and Astrophysical Fluid Dynamics
 Pub Date:
 1986
 DOI:
 10.1080/03091928608208797
 Bibcode:
 1986GApFD..36...53G
 Keywords:

 Dynamo Theory;
 Laminar Flow;
 Streamlining;
 Chaos;
 Energy Spectra;
 Magnetohydrodynamics;
 Scale Effect;
 Fluid Mechanics and Heat Transfer