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Poles are artefacts of our observation techniques. For example a tornado has 2 poles essentially. Which leads on to your second point. Complex tornadic systems do indeed have the complex laminar flows ken is uncovering.
Complex tornadic systems do indeed have the complex laminar flows ken is uncovering... Your analogy of laminar flow is misleading you . You should perhaps consider rotational flow ? As you know rotationl flow in fluid dynamics is very intriguing!
Although not common useage Tornadic systems do have a polar structure for which the term pole is appropriate. The point here is semantic , but that in itself is the very point!
I have found great difficulty in conceiving of the existence of vortices in a medium, side by side, revolving in the same direction about parallel axes. The contiguous portions of consecutive vortices must be moving in opposite directions; and it is difficult to understand how the motion of one part of the medium can coexist with, and even produce, an opposite motion of a part in contact with it. In (a mechanical) mechanism, when two wheels are intended to revolve in the same direction, a wheel is placed between them so as to be in gear with both, and this wheel is called an 'idle wheel'. The hypothesis about the vortices which I have to suggest is that a layer of particles, acting as idle wheels, is interposed between each vortex and the next, so that each vortex has a tendency to make the neighboring vortices revolve in the same direction. On Physical Lines of Force, 1861 by James Clerk Maxwell