I just remembered another video that I had seen some time ago.  Many of you have probably seen it but here it is for those who have not. (The original page where I found it is http://www.maniacworld.com/Laminar-Reverse-Flow.html.)

Prof. Pat McMurtry's explanation is:

This is a feature of very low Reynolds number flow. At very low Reynolds number, the inertial terms (nonlinear terms) become insignificant and the equation of motion is completely linear (pressure and viscous forces balance with inertial terms negligible), meaning that time can be reversed and you will get right back were you started. I would love to have this setup. I have done a similar thing with dye in glycerin but can't control the flow as well. Someone asked me if this was really real or if they just reversed the video. It is definitely real.

It is a Reynolds number effect, so the limiting velocity can not be determined without
considering the viscosity and length scales. There is not an abrupt transition from
linear to nonlinear behavior as in a typical hydrodynamics stability problem. It is more
a matter of the flow gradually gradually tending towards linarity while in a laminar
regime. The flow may be laminar at Reynolds numbers on the order of 100's or 100's
(depending on the flow), but the behavior starts to look linear around Reynolds numbers
of order 1 or below.