Thanks to physicsphdstu in a comment to the earlier post on mixing and unmixing in fluids, this video explains in further detail, using a variety of experiments, what is going on. The experiments are conducted by G. I. Taylor, a pioneer in this area of research.
The video has been cued to begin at the 3:00 mark where the relevant experiments begin. The top view of the experiment at the 5:00 mark is particularly enlightening. It illustrates what eigenperson said in another comment that what was happening was not mixing in the common sense of the term but relative motion of different layers of the fluid, each layer carrying along with it its portion of the dye. When looked at sideways, the superposition of the different layers gives the impression of smearing or ‘mixing’. But real mixing would require that the layers not stay separate, which is what occurs in normal turbulent flow.
There is something quite quaint about this old-style lecturing from (I believe) the 1960s. What is also interesting is how we can tell almost immediately, without being able to quite put our finger on the reasons, that it is an old video.