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. Numerical results are reported for magnetic Reynolds numbers Rm up to 450 and various choices of A, B and C. For A=B=C=1 dynamo action is present in at least two windows in Rm , the first extending from ≈9 to ≈17.5 and the second beyond ≈27. certain symmetries implied by the flow are preserved in the lower window but are broken in the upper. The fastest growing mode shows concentrated cigar-like structures centered on stagnation points in the flow. When A, B and C are varied, windows of dynamo action may or may not be present. When one of the coefficients vanishes, the flow becomes two-dimensional and non-chaotic, but with three-dimensional magnetic fields, dynamo action is still possible and has been investigated for Rm up to 1500. In the two-dimensional example studied the growth rate achieved a maximum near Rm =300 and then behaved in a way appropriate for a slow dynamo (one whose growth rate tends to zero as Rm ∞). It is not clear yet whether or not in the three-dimensional case the opposite can happen (fast dynamo). The α-effect that is produced by these helical flows acting on very large-scale magnetic fields is calculated. Surprisingly, it can remain finite even when dynamo action is present at the scale of the flow, as long as certain symmetries are not broken.