Dynamo action in a family of flows with chaotic streamlines

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 alpha-effect dynamo theory are examined, and some still outstanding problems are mentioned.