The phenomenon is something called 'Taylor columns' and illustrates the impact of the Coriolis force on fluid dynamics.  The details are too hard to derive easily in class (especially without some background on fluid dynamics).  Use two round dishes filled with water.  Set up the one on the turntable at the beginning of class and let it run so that the water builds up coherent rotation.  In the stationary one, dip your hand in through the water to set up some currents.  Then add food coloring in a few spots - the food coloring follows the currents and slowly diffuses outward from where it was placed.  On the turntable, pass your hand through the water to set up currents and again add food coloring in a few spots.  Rather than diffuse in 3D, the food coloring follows the currents, which are almost 2D vertical sheets known as Taylor columns.

Different colored spots stay pretty well separated.